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17:12:56",{"text":11,"minutes":126,"time":127,"words":128},2.1,126000,420,{"stem":130,"path":131,"title":132,"date":133,"collapsed":9,"readingTime":134},"posts\u002FUGCourses\u002F2.sophomore-autumn\u002FProbability-Theory","\u002F2025\u002F01\u002F21\u002FProbability-Theory","概率论与数理统计","2025-01-21 12:52:11",{"text":11,"minutes":135,"time":136,"words":137},2.205,132300,441,{"stem":139,"path":140,"title":141,"date":142,"collapsed":9,"readingTime":143},"posts\u002FUGCourses\u002F2.sophomore-autumn\u002Fengineering-training","\u002F2024\u002F09\u002F17\u002Fengineering-training","工程训练","2024-09-17 21:40:26",{"text":11,"minutes":144,"time":145,"words":146},2.385,143100,477,{"stem":148,"path":149,"title":150,"date":78,"collapsed":9,"readingTime":151},"posts\u002FUGCourses\u002F2.sophomore-autumn\u002Findex","\u002Fugcourses\u002Fsophomore-autumn","大二秋冬",{"text":80,"minutes":81,"time":81,"words":81},{"stem":153,"path":154,"title":155,"date":156,"collapsed":9,"readingTime":157},"posts\u002FUGCourses\u002F2.sophomore-autumn\u002Fsolid-state-physics","\u002F2024\u002F09\u002F11\u002Fsolid-state-physics","固体物理基础","2024-09-11 19:15:26",{"text":158,"minutes":159,"time":160,"words":161},"4 min read",3.21,192600,642,{"stem":163,"path":164,"title":165,"date":166,"collapsed":9,"readingTime":167},"posts\u002FUGCourses\u002F3.sophomore-spring\u002FAIFrontier","\u002Fugcourses\u002Fsophomore-spring\u002Faifrontier","人工智能前沿","2025-06-12 14:58:16",{"text":168,"minutes":169,"time":170,"words":171},"25 min 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19:39:00",{"text":60,"minutes":200,"time":201,"words":202},0.535,32100,107,{"stem":204,"path":205,"title":206,"date":207,"collapsed":9,"readingTime":208},"posts\u002FUGCourses\u002F4.junior-autumn\u002F1.microelectronic-devices\u002FLecture10","\u002Fugcourses\u002Fjunior-autumn\u002Fmicroelectronic-devices\u002Flecture10","Lecture 10：从 MOS 电容到 MOSFET","2026-09-10 00:10:00",{"text":209,"minutes":210,"time":211,"words":212},"18 min read",17.615,1056900,3523,{"stem":214,"path":215,"title":216,"date":217,"collapsed":9,"readingTime":218},"posts\u002FUGCourses\u002F4.junior-autumn\u002F1.microelectronic-devices\u002FLecture11","\u002Fugcourses\u002Fjunior-autumn\u002Fmicroelectronic-devices\u002Flecture11","Lecture 11：亚阈值效应与 MOSFET 尺寸缩放","2026-09-10 00:20:00",{"text":219,"minutes":220,"time":221,"words":222},"23 min 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00:50:00",{"text":21,"minutes":51,"time":52,"words":53},{"stem":340,"path":341,"title":342,"date":198,"collapsed":343,"readingTime":344},"posts\u002FUGCourses\u002F4.junior-autumn\u002F1.microelectronic-devices\u002Findex","\u002Fugcourses\u002Fjunior-autumn\u002Fmicroelectronic-devices","微电子器件",true,{"text":158,"minutes":345,"time":346,"words":347},3.055,183300,611,{"stem":349,"path":350,"title":351,"date":352,"collapsed":9,"readingTime":353},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F1.HistoryMetaCharacters","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fhistorymetacharacters","History & Meta Characters","2026-09-10 20:25:44",{"text":269,"minutes":354,"time":355,"words":356},9.36,561600,1872,{"stem":358,"path":359,"title":360,"date":361,"collapsed":9,"readingTime":362},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F10.PastExams\u002F1.ExamAutumn2223","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fpastexams\u002Fexamautumn2223","22-23 秋冬历年卷","2026-09-10 20:26:49",{"text":319,"minutes":363,"time":364,"words":365},20.295,1217700,4059,{"stem":367,"path":368,"title":369,"date":370,"collapsed":9,"readingTime":371},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F10.PastExams\u002F2.Exam2021","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fpastexams\u002Fexam2021","20-21 历年卷","2026-09-10 20:26:50",{"text":289,"minutes":290,"time":291,"words":292},{"stem":373,"path":374,"title":375,"date":376,"collapsed":9,"readingTime":377},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F10.PastExams\u002F3.ExamRecall1","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fpastexams\u002Fexamrecall1","不知名回忆卷 1","2026-09-10 20:26:51",{"text":116,"minutes":378,"time":379,"words":380},4.215,252900,843,{"stem":382,"path":383,"title":384,"date":385,"collapsed":9,"readingTime":386},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F10.PastExams\u002F4.ExamRecall23","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fpastexams\u002Fexamrecall23","不知名回忆卷 2\u002F3","2026-09-10 20:26:52",{"text":387,"minutes":388,"time":389,"words":390},"12 min read",11.235,674100,2247,{"stem":392,"path":393,"title":394,"date":395,"collapsed":9,"readingTime":396},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F11.Detailed\u002F1.Chapter1-Introduction","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fdetailed\u002Fchapter1-introduction","Chapter 1：Introduction","2026-09-10 20:27:26",{"text":397,"minutes":398,"time":399,"words":400},"19 min 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20:27:54",{"text":209,"minutes":454,"time":455,"words":456},17.85,1071000,3570,{"stem":458,"path":459,"title":460,"date":461,"collapsed":9,"readingTime":462},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F11.Detailed\u002F8.Chapter8-CProgrammingInUnix","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fdetailed\u002Fchapter8-cprogramminginunix","Chapter 8：C Programming in Unix","2026-09-10 20:27:57",{"text":463,"minutes":464,"time":465,"words":466},"17 min read",16.855,1011300,3371,{"stem":468,"path":469,"title":470,"date":471,"collapsed":9,"readingTime":472},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F2.LinuxUnix","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Flinuxunix","Linux & Unix","2026-09-10 20:25:46",{"text":41,"minutes":473,"time":474,"words":475},29.33,1759800,5866,{"stem":477,"path":478,"title":479,"date":480,"collapsed":9,"readingTime":481},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F3.Vi","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fvi","Vi","2026-09-10 20:25:47",{"text":329,"minutes":482,"time":483,"words":484},7.95,477000,1590,{"stem":486,"path":487,"title":488,"date":489,"collapsed":9,"readingTime":490},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F4.ViCopy","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fvicopy","Vi（详细版）","2026-09-10 20:25:49",{"text":279,"minutes":491,"time":492,"words":493},13.785,827100,2757,{"stem":495,"path":496,"title":497,"date":498,"collapsed":9,"readingTime":499},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F5.Shells","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fshells","Shells","2026-09-10 20:25:51",{"text":500,"minutes":501,"time":502,"words":503},"22 min read",21.21,1272600,4242,{"stem":505,"path":506,"title":507,"date":508,"collapsed":9,"readingTime":509},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F6.Network","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fnetwork","Network","2026-09-10 20:25:54",{"text":319,"minutes":510,"time":511,"words":512},20.595,1235700,4119,{"stem":514,"path":515,"title":516,"date":517,"collapsed":9,"readingTime":518},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F7.SystemAdministration","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fsystemadministration","System Administration","2026-09-10 20:26:44",{"text":329,"minutes":519,"time":520,"words":521},7.12,427200,1424,{"stem":523,"path":524,"title":525,"date":526,"collapsed":9,"readingTime":527},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F8.XWindow","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fxwindow","XWindow","2026-09-10 20:26:45",{"text":97,"minutes":528,"time":529,"words":530},5.105,306300,1021,{"stem":532,"path":533,"title":534,"date":535,"collapsed":9,"readingTime":536},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002F9.SystemDevelopmentTools","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad\u002Fsystemdevelopmenttools","System Development Tools","2026-09-10 20:26:47",{"text":387,"minutes":537,"time":538,"words":539},11.35,681000,2270,{"stem":541,"path":542,"title":543,"date":544,"collapsed":343,"readingTime":545},"posts\u002FUGCourses\u002F4.junior-autumn\u002F2.ICCAD\u002Findex","\u002Fugcourses\u002Fjunior-autumn\u002Ficcad","面向 ICCAD 的软件基础技术","2026-09-10 12:37:00",{"text":60,"minutes":546,"time":547,"words":548},0.185,11100,37,{"stem":550,"path":551,"title":552,"date":553,"collapsed":9,"readingTime":554},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002FFeiQilai1","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl\u002Ffeiqilai1","飞起来1.0","2026-09-10 12:51:49",{"text":555,"minutes":556,"time":557,"words":558},"105 min read",104.655,6279300,20931,{"stem":560,"path":561,"title":562,"date":563,"collapsed":9,"readingTime":564},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002FFeiQilai2","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl\u002Ffeiqilai2","飞起来2.0","2026-09-10 12:52:06",{"text":565,"minutes":566,"time":567,"words":568},"29 min read",28.755,1725300,5751,{"stem":570,"path":571,"title":572,"date":573,"collapsed":9,"readingTime":574},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002FFeiQilai3","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl\u002Ffeiqilai3","飞起来3.0","2026-09-10 12:52:12",{"text":116,"minutes":575,"time":576,"words":577},4.49,269400,898,{"stem":579,"path":580,"title":581,"date":582,"collapsed":9,"readingTime":583},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002FLecture13","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl\u002Flecture13","Lecture 13：浮点数标准","2026-09-10 12:51:27",{"text":11,"minutes":584,"time":585,"words":586},2.575,154500,515,{"stem":588,"path":589,"title":590,"date":591,"collapsed":9,"readingTime":592},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002FLecture6","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl\u002Flecture6","Lecture 6：Behavioral Modeling，非阻塞赋值","2026-09-10 12:51:12",{"text":97,"minutes":593,"time":594,"words":595},5.34,320400,1068,{"stem":597,"path":598,"title":599,"date":600,"collapsed":9,"readingTime":601},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002FPPTCorrespondence","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl\u002Fpptcorrespondence","与PPT的对应","2026-09-10 12:52:18",{"text":269,"minutes":602,"time":603,"words":604},9.275,556500,1855,{"stem":606,"path":607,"title":608,"date":544,"collapsed":343,"readingTime":609},"posts\u002FUGCourses\u002F4.junior-autumn\u002F3.HDL\u002Findex","\u002Fugcourses\u002Fjunior-autumn\u002Fhdl","硬件描述语言原理与应用",{"text":60,"minutes":61,"time":62,"words":63},{"stem":611,"path":612,"title":613,"date":614,"collapsed":9,"readingTime":615},"posts\u002FUGCourses\u002F4.junior-autumn\u002F4.analogICDesign\u002F1.BeforeMidterm","\u002Fugcourses\u002Fjunior-autumn\u002Fanalogicdesign\u002Fbeforemidterm","期中前","2026-09-10 20:28:52",{"text":616,"minutes":617,"time":618,"words":619},"11 min read",10.835,650100,2167,{"stem":621,"path":622,"title":623,"date":624,"collapsed":9,"readingTime":625},"posts\u002FUGCourses\u002F4.junior-autumn\u002F4.analogICDesign\u002F2.MidtermExam2425","\u002Fugcourses\u002Fjunior-autumn\u002Fanalogicdesign\u002Fmidtermexam2425","24-25 期中","2026-09-10 20:29:00",{"text":21,"minutes":626,"time":627,"words":628},1.22,73200,244,{"stem":630,"path":631,"title":632,"date":633,"collapsed":9,"readingTime":634},"posts\u002FUGCourses\u002F4.junior-autumn\u002F4.analogICDesign\u002F3.FinalExamReview","\u002Fugcourses\u002Fjunior-autumn\u002Fanalogicdesign\u002Ffinalexamreview","期末考试整理","2026-09-10 20:29:09",{"text":387,"minutes":635,"time":636,"words":637},11.36,681600,2272,{"stem":639,"path":640,"title":641,"date":642,"collapsed":343,"readingTime":643},"posts\u002FUGCourses\u002F4.junior-autumn\u002F4.analogICDesign\u002Findex","\u002Fugcourses\u002Fjunior-autumn\u002Fanalogicdesign","模拟集成电路设计","2026-09-10 20:00:00",{"text":80,"minutes":81,"time":81,"words":81},{"stem":645,"path":646,"title":647,"date":78,"collapsed":9,"readingTime":648},"posts\u002FUGCourses\u002F4.junior-autumn\u002Findex","\u002Fugcourses\u002Fjunior-autumn","大三秋冬",{"text":80,"minutes":81,"time":81,"words":81},{"stem":650,"path":651,"title":652,"date":653,"collapsed":9,"readingTime":654},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F1.Chapter3-Device","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter3-device","Chapter 3：器件 Device","2026-09-10 21:14:41",{"text":249,"minutes":655,"time":656,"words":657},6.055,363300,1211,{"stem":659,"path":660,"title":661,"date":653,"collapsed":9,"readingTime":662},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F10.Chapter12-Arithmetic","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter12-arithmetic","Chapter 12：算术运算电路 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期中试题",{"text":80,"minutes":81,"time":81,"words":81},{"stem":693,"path":694,"title":695,"date":653,"collapsed":9,"readingTime":696},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F13.PastExams\u002F3.FinalPolished","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fpastexams\u002Ffinalpolished","期末历年卷（AI 润色版）",{"text":21,"minutes":697,"time":698,"words":699},1.575,94500,315,{"stem":701,"path":702,"title":703,"date":653,"collapsed":9,"readingTime":704},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F14.ExamRecall2026","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fexamrecall2026","数字集成电路回忆 2026",{"text":60,"minutes":705,"time":706,"words":707},0.49,29400,98,{"stem":709,"path":710,"title":711,"date":653,"collapsed":9,"readingTime":712},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F2.Chapter4-Wire","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter4-wire","Chapter 4：导线 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Gate",{"text":31,"minutes":729,"time":730,"words":731},8.635,518100,1727,{"stem":733,"path":734,"title":735,"date":653,"collapsed":9,"readingTime":736},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F5.Chapter7-SequentialLogic","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter7-sequentiallogic","Chapter 7：时序逻辑 Sequential Logic",{"text":463,"minutes":737,"time":738,"words":739},16.645,998700,3329,{"stem":741,"path":742,"title":743,"date":653,"collapsed":9,"readingTime":744},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F6.Chapter8-Speed","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter8-speed","Chapter 8：延迟与速度 Speed",{"text":745,"minutes":746,"time":747,"words":748},"33 min read",32.885,1973100,6577,{"stem":750,"path":751,"title":752,"date":653,"collapsed":9,"readingTime":753},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F7.Chapter9-Power","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter9-power","Chapter 9：功耗 Power",{"text":754,"minutes":755,"time":756,"words":757},"31 min read",31.005,1860300,6201,{"stem":759,"path":760,"title":761,"date":653,"collapsed":9,"readingTime":762},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F8.Chapter10-Interconnect","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter10-interconnect","Chapter 10：互连 Interconnect",{"text":463,"minutes":763,"time":764,"words":765},16.32,979200,3264,{"stem":767,"path":768,"title":769,"date":653,"collapsed":9,"readingTime":770},"posts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F9.Chapter11-Timing","\u002Fugcourses\u002Fjunior-spring\u002Fdigitalicdesign\u002Fchapter11-timing","Chapter 11：时序 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read",43.985,2639100,8797,{"stem":824,"path":825,"title":826,"date":653,"collapsed":9,"readingTime":827},"posts\u002FUGCourses\u002F5.junior-spring\u002F2.computerOrganization\u002F14.L15","\u002Fugcourses\u002Fjunior-spring\u002Fcomputerorganization\u002Fl15","L15：期末复习问答",{"text":269,"minutes":828,"time":829,"words":830},9.105,546300,1821,{"stem":832,"path":833,"title":834,"date":653,"collapsed":9,"readingTime":835},"posts\u002FUGCourses\u002F5.junior-spring\u002F2.computerOrganization\u002F2.L2-Binary","\u002Fugcourses\u002Fjunior-spring\u002Fcomputerorganization\u002Fl2-binary","L2：二进制数制",{"text":80,"minutes":81,"time":81,"words":81},{"stem":837,"path":838,"title":839,"date":653,"collapsed":9,"readingTime":840},"posts\u002FUGCourses\u002F5.junior-spring\u002F2.computerOrganization\u002F3.L3-CMemory","\u002Fugcourses\u002Fjunior-spring\u002Fcomputerorganization\u002Fl3-cmemory","L3：C 语言与内存模型",{"text":841,"minutes":842,"time":843,"words":844},"98 min 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系统配置","2025-08-26 19:38:06",{"text":158,"minutes":911,"time":912,"words":913},3.815,228900,763,{"stem":915,"path":916,"title":917,"date":918,"collapsed":9,"readingTime":919},"posts\u002Fubuntu\u002F2.cadence\u002F1.mmsim","\u002Fubuntu\u002Fcadence\u002Fmmsim","在 Ubuntu 24.04 上安装 Cadence MMSIM 15.1 的兼容性问题","2026-09-09 14:06:40",{"text":158,"minutes":920,"time":921,"words":922},3.5,210000,700,{"stem":924,"path":925,"title":926,"date":918,"collapsed":9,"readingTime":927},"posts\u002Fubuntu\u002F2.cadence\u002F2.innovus","\u002Fubuntu\u002Fcadence\u002Finnovus","Innovus安装",{"text":11,"minutes":928,"time":929,"words":930},2.08,124800,416,{"stem":932,"path":933,"title":934,"date":918,"collapsed":9,"readingTime":935},"posts\u002Fubuntu\u002F2.cadence\u002Findex","\u002Fubuntu\u002Fcadence","Ubuntu24.04安装Cadence 系列软件",{"text":269,"minutes":936,"time":937,"words":938},9.98,598800,1996,{"stem":940,"path":941,"title":942,"date":918,"collapsed":9,"readingTime":943},"posts\u002Fubuntu\u002F3.synopsys","\u002Fubuntu\u002Fsynopsys","Ubuntu 24.04 安装 Synopsys",{"text":269,"minutes":944,"time":945,"words":946},9.555,573300,1911,{"stem":948,"path":949,"title":950,"date":918,"collapsed":9,"readingTime":951},"posts\u002Fubuntu\u002F4.vivado","\u002Fubuntu\u002Fvivado","Ubuntu 24.04 安装 Vivado 2020.1",{"text":60,"minutes":952,"time":953,"words":954},0.62,37200,124,{"stem":956,"path":957,"title":958,"date":918,"collapsed":9,"readingTime":959},"posts\u002Fubuntu\u002F5.migrate","\u002Fubuntu\u002Fmigrate","硬盘迁移系统",{"text":60,"minutes":960,"time":961,"words":962},0.64,38400,128,{"stem":964,"path":965,"title":966,"date":967,"collapsed":9,"readingTime":968},"posts\u002Fubuntu\u002Findex","\u002Fubuntu","Ubuntu装进移动硬盘","2025-08-25 19:38:06",{"text":269,"minutes":969,"time":970,"words":971},9.26,555600,1852,{"id":973,"title":661,"body":974,"categories":25213,"collapsed":9,"date":653,"description":25214,"draft":9,"extension":25215,"hideInArchive":343,"hideInList":343,"image":25216,"meta":25217,"navigation":343,"path":660,"permalink":25216,"published":25216,"readingTime":25219,"recommend":25216,"references":25216,"seo":25220,"sitemap":25221,"stem":659,"tags":25283,"type":25285,"updated":653,"__hash__":25286},"content\u002Fposts\u002FUGCourses\u002F5.junior-spring\u002F1.digitalICDesign\u002F10.Chapter12-Arithmetic.md",{"type":975,"value":976,"toc":25133},"minimark",[977,982,986,1024,1031,1034,1105,1108,1141,1145,1288,1291,1345,1349,1352,1357,1361,1365,1370,1375,1379,1384,1387,1392,1737,1740,1744,1773,2498,2505,2519,2523,2528,2728,2731,2734,2853,3145,3148,3234,3242,3246,3249,3254,3258,3263,3266,3270,3274,3281,3286,3512,3515,3832,4022,4026,4031,4034,4391,4841,4852,4857,4864,4869,4872,4917,4921,4926,4929,5629,5960,5965,5968,6527,6530,7005,7134,7316,7515,7783,7790,7801,7805,7810,7895,7900,7905,7908,8597,8600,9186,10937,10941,10946,11112,11172,11176,11182,11204,11208,11313,11498,11501,11989,11992,12640,12646,12649,12654,12658,12663,12666,13177,13180,13327,13330,13751,13884,14362,14365,14368,14371,14376,14380,14386,14785,14790,14795,14798,14809,14813,14816,14821,14832,14836,14841,14844,14848,14853,14857,14981,15045,15050,15053,15059,15064,15067,15084,15090,15096,15187,15191,15195,16576,16579,16953,17079,17084,17793,18336,18344,18619,18622,18627,18632,18636,18641,18646,18649,18652,18656,18661,18668,19135,19137,19596,20805,20809,20934,20937,20959,20962,20966],[978,979,981],"h2",{"id":980},"基本的计算机组成-major-components-of-a-computer","基本的计算机组成 ｜ Major Components of a Computer",[983,984,985],"h3",{"id":985},"本节概述",[987,988,989,997,1003],"ol",{},[990,991,992,993],"li",{},"处理器的核心结构可以概括为：\n",[994,995,996],"strong",{},"Processor = Control + Datapath + Memory + Interconnect",[990,998,999,1000],{},"后续 Arithmetic 章节主要关注：\n",[994,1001,1002],{},"Datapath 中的执行单元",[990,1004,1005,1006],{},"重点对象包括：",[1007,1008,1009,1012,1015,1018,1021],"ul",{},[990,1010,1011],{},"加法器",[990,1013,1014],{},"乘法器",[990,1016,1017],{},"除法器",[990,1019,1020],{},"移位器",[990,1022,1023],{},"ALU",[1025,1026,1027],"p",{},[1028,1029],"img",{"alt":1028,"src":1030},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-01.png",[983,1032,1033],{"id":1033},"计算机与数字处理器基本结构",[987,1035,1036],{},[990,1037,1038,1041,1044],{},[994,1039,1040],{},"计算机系统组成",[994,1042,1043],{},"Computer = Processor + Memory + Devices",[1007,1045,1046,1073,1086],{},[990,1047,1048,1051],{},[994,1049,1050],{},"Processor 处理器",[1007,1052,1053,1056],{},[990,1054,1055],{},"负责执行程序，是计算机系统的核心。",[990,1057,1058,1059],{},"主要包括：\n",[1007,1060,1061,1067],{},[990,1062,1063,1066],{},[994,1064,1065],{},"Control 控制单元","：产生控制信号，决定指令如何执行、数据如何流动。",[990,1068,1069,1072],{},[994,1070,1071],{},"Datapath 数据通路","：负责数据运算、暂存和传输，是算术逻辑单元所在位置。",[990,1074,1075,1078],{},[994,1076,1077],{},"Memory 存储器",[1007,1079,1080,1083],{},[990,1081,1082],{},"保存程序和数据。",[990,1084,1085],{},"供处理器读取指令、读取数据、写回结果。",[990,1087,1088,1091],{},[994,1089,1090],{},"Devices 输入输出设备",[1007,1092,1093,1099],{},[990,1094,1095,1098],{},[994,1096,1097],{},"Input 输入设备","：键盘、传感器、摄像头等。",[990,1100,1101,1104],{},[994,1102,1103],{},"Output 输出设备","：显示器、通信接口等。",[983,1106,1107],{"id":1107},"通用数字处理器抽象",[987,1109,1110],{},[990,1111,1112,1115],{},[994,1113,1114],{},"基本数据流 Input \u002F Output ↔ Datapath ↔ Memory",[1007,1116,1117,1123,1129,1135],{},[990,1118,1119,1122],{},[994,1120,1121],{},"Input \u002F Output","：负责与外部设备交换数据。",[990,1124,1125,1128],{},[994,1126,1127],{},"Datapath","：执行运算、暂存数据、传输数据。",[990,1130,1131,1134],{},[994,1132,1133],{},"Memory","：存放指令和数据。",[990,1136,1137,1140],{},[994,1138,1139],{},"Control","：根据指令控制 Datapath 和 Memory 的工作。",[983,1142,1144],{"id":1143},"basic-building-blocks","Basic Building Blocks",[987,1146,1147,1215,1241,1265],{},[990,1148,1149,1151],{},[994,1150,1071],{},[1007,1152,1153,1175,1185,1195,1205],{},[990,1154,1155,1158],{},[994,1156,1157],{},"Execution units 执行单元",[1007,1159,1160,1163,1166,1169,1172],{},[990,1161,1162],{},"Adder 加法器",[990,1164,1165],{},"Multiplier 乘法器",[990,1167,1168],{},"Divider 除法器",[990,1170,1171],{},"Shifter 移位器",[990,1173,1174],{},"ALU 算术逻辑单元",[990,1176,1177,1180],{},[994,1178,1179],{},"Register file 寄存器堆",[1007,1181,1182],{},[990,1183,1184],{},"存放处理器内部临时数据。",[990,1186,1187,1190],{},[994,1188,1189],{},"Pipeline registers 流水线寄存器",[1007,1191,1192],{},[990,1193,1194],{},"在流水线各阶段之间暂存数据。",[990,1196,1197,1200],{},[994,1198,1199],{},"Multiplexers 多路选择器",[1007,1201,1202],{},[990,1203,1204],{},"在多个输入数据中选择一个输出。",[990,1206,1207,1210],{},[994,1208,1209],{},"Decoders 译码器",[1007,1211,1212],{},[990,1213,1214],{},"将编码信息转换为控制信号或选择信号。",[990,1216,1217,1219],{},[994,1218,1065],{},[1007,1220,1221,1224],{},[990,1222,1223],{},"负责产生控制信号。",[990,1225,1226,1227],{},"常见实现方式：\n",[1007,1228,1229,1232,1235,1238],{},[990,1230,1231],{},"FSM 有限状态机",[990,1233,1234],{},"PLA 可编程逻辑阵列",[990,1236,1237],{},"ROM",[990,1239,1240],{},"Random logic 随机逻辑",[990,1242,1243,1246],{},[994,1244,1245],{},"Interconnect 互连结构",[1007,1247,1248,1251],{},[990,1249,1250],{},"负责模块之间的数据连接与传输。",[990,1252,1253,1254],{},"包括：\n",[1007,1255,1256,1259,1262],{},[990,1257,1258],{},"Switches 开关",[990,1260,1261],{},"Arbiters 仲裁器",[990,1263,1264],{},"Buses 总线",[990,1266,1267,1270],{},[994,1268,1269],{},"Memory 存储结构",[1007,1271,1272],{},[990,1273,1253,1274],{},[1007,1275,1276,1279,1282,1285],{},[990,1277,1278],{},"Cache 高速缓存",[990,1280,1281],{},"TLB 地址转换缓存",[990,1283,1284],{},"DRAM 主存",[990,1286,1287],{},"Buffers 缓冲器",[983,1289,1290],{"id":1290},"现代处理器结构风格",[987,1292,1293,1306,1319,1332],{},[990,1294,1295,1298],{},[994,1296,1297],{},"Pipelined, single issue",[1007,1299,1300,1303],{},[990,1301,1302],{},"流水线单发射。",[990,1304,1305],{},"每个周期通常发射一条指令。",[990,1307,1308,1311],{},[994,1309,1310],{},"Superscalar",[1007,1312,1313,1316],{},[990,1314,1315],{},"超标量结构。",[990,1317,1318],{},"由硬件控制多发射，每周期可发射多条指令。",[990,1320,1321,1324],{},[994,1322,1323],{},"VLIW",[1007,1325,1326,1329],{},[990,1327,1328],{},"Very Long Instruction Word，超长指令字。",[990,1330,1331],{},"由软件 \u002F 编译器安排多发射。",[990,1333,1334,1337],{},[994,1335,1336],{},"Multithreaded",[1007,1338,1339,1342],{},[990,1340,1341],{},"多线程结构。",[990,1343,1344],{},"从多个线程中取指令执行，提高硬件利用率。",[983,1346,1348],{"id":1347},"datapath-bit-sliced-organization","Datapath Bit-Sliced Organization",[1025,1350,1351],{},"多位数据通路 = 重复的一位处理单元 + 统一控制信号。",[1025,1353,1354],{},[1028,1355],{"alt":1028,"src":1356},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-02.png",[978,1358,1360],{"id":1359},"adder-加法器设计","Adder ｜ 加法器设计",[983,1362,1364],{"id":1363},"single-bit-addition","Single-Bit Addition",[1366,1367,1369],"h4",{"id":1368},"half-adder-full-adder","Half adder & Full Adder",[1025,1371,1372],{},[1028,1373],{"alt":1028,"src":1374},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-03.png",[1366,1376,1378],{"id":1377},"brute-force-implementation-from-eqns-直接按照公式硬搭majority-gate电路","Brute force implementation from eqns  ｜ 直接按照公式硬搭majority gate电路",[1025,1380,1381],{},[1028,1382],{"alt":1028,"src":1383},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-04.png",[1366,1385,1386],{"id":1386},"经过优化关键路径后的加法器",[1025,1388,1389],{},[1028,1390],{"alt":1028,"src":1391},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-05.png",[1007,1393,1394,1734],{},[990,1395,1396,1397,1733],{},"先计算进位,然后再利用公式",[1398,1399,1402,1478],"span",{"className":1400},[1401],"katex",[1398,1403,1406],{"className":1404},[1405],"katex-mathml",[1407,1408,1410],"math",{"xmlns":1409},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1411,1412,1413,1473],"semantics",{},[1414,1415,1416,1420,1424,1427,1430,1433,1436,1440,1442,1444,1446,1448,1456,1459],"mrow",{},[1417,1418,1419],"mi",{},"S",[1421,1422,1423],"mo",{},"=",[1417,1425,1426],{},"A",[1417,1428,1429],{},"B",[1417,1431,1432],{},"C",[1421,1434,1435],{},"+",[1421,1437,1439],{"stretchy":1438},"false","(",[1417,1441,1426],{},[1421,1443,1435],{},[1417,1445,1429],{},[1421,1447,1435],{},[1449,1450,1451,1453],"msub",{},[1417,1452,1432],{},[1417,1454,1455],{},"i",[1421,1457,1458],{"stretchy":1438},")",[1460,1461,1463,1470],"mover",{"accent":1462},"true",[1449,1464,1465,1467],{},[1417,1466,1432],{},[1417,1468,1469],{},"o",[1421,1471,1472],{"stretchy":1462},"‾",[1474,1475,1477],"annotation",{"encoding":1476},"application\u002Fx-tex","S = ABC + (A+B+C_i)\\overline{C_o}",[1398,1479,1482,1509,1538,1561,1579],{"className":1480,"ariaHidden":1462},[1481],"katex-html",[1398,1483,1486,1491,1497,1502,1506],{"className":1484},[1485],"base",[1398,1487],{"className":1488,"style":1490},[1489],"strut","height:0.6833em;",[1398,1492,1419],{"className":1493,"style":1496},[1494,1495],"mord","mathnormal","margin-right:0.0576em;",[1398,1498],{"className":1499,"style":1501},[1500],"mspace","margin-right:0.2778em;",[1398,1503,1423],{"className":1504},[1505],"mrel",[1398,1507],{"className":1508,"style":1501},[1500],[1398,1510,1512,1516,1519,1523,1527,1531,1535],{"className":1511},[1485],[1398,1513],{"className":1514,"style":1515},[1489],"height:0.7667em;vertical-align:-0.0833em;",[1398,1517,1426],{"className":1518},[1494,1495],[1398,1520,1429],{"className":1521,"style":1522},[1494,1495],"margin-right:0.0502em;",[1398,1524,1432],{"className":1525,"style":1526},[1494,1495],"margin-right:0.0715em;",[1398,1528],{"className":1529,"style":1530},[1500],"margin-right:0.2222em;",[1398,1532,1435],{"className":1533},[1534],"mbin",[1398,1536],{"className":1537,"style":1530},[1500],[1398,1539,1541,1545,1549,1552,1555,1558],{"className":1540},[1485],[1398,1542],{"className":1543,"style":1544},[1489],"height:1em;vertical-align:-0.25em;",[1398,1546,1439],{"className":1547},[1548],"mopen",[1398,1550,1426],{"className":1551},[1494,1495],[1398,1553],{"className":1554,"style":1530},[1500],[1398,1556,1435],{"className":1557},[1534],[1398,1559],{"className":1560,"style":1530},[1500],[1398,1562,1564,1567,1570,1573,1576],{"className":1563},[1485],[1398,1565],{"className":1566,"style":1515},[1489],[1398,1568,1429],{"className":1569,"style":1522},[1494,1495],[1398,1571],{"className":1572,"style":1530},[1500],[1398,1574,1435],{"className":1575},[1534],[1398,1577],{"className":1578,"style":1530},[1500],[1398,1580,1582,1586,1642,1646],{"className":1581},[1485],[1398,1583],{"className":1584,"style":1585},[1489],"height:1.1333em;vertical-align:-0.25em;",[1398,1587,1589,1592],{"className":1588},[1494],[1398,1590,1432],{"className":1591,"style":1526},[1494,1495],[1398,1593,1596],{"className":1594},[1595],"msupsub",[1398,1597,1601,1633],{"className":1598},[1599,1600],"vlist-t","vlist-t2",[1398,1602,1605,1628],{"className":1603},[1604],"vlist-r",[1398,1606,1610],{"className":1607,"style":1609},[1608],"vlist","height:0.3117em;",[1398,1611,1613,1618],{"style":1612},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1398,1614],{"className":1615,"style":1617},[1616],"pstrut","height:2.7em;",[1398,1619,1625],{"className":1620},[1621,1622,1623,1624],"sizing","reset-size6","size3","mtight",[1398,1626,1455],{"className":1627},[1494,1495,1624],[1398,1629,1632],{"className":1630},[1631],"vlist-s","​",[1398,1634,1636],{"className":1635},[1604],[1398,1637,1640],{"className":1638,"style":1639},[1608],"height:0.15em;",[1398,1641],{},[1398,1643,1458],{"className":1644},[1645],"mclose",[1398,1647,1650],{"className":1648},[1494,1649],"overline",[1398,1651,1653,1725],{"className":1652},[1599,1600],[1398,1654,1656,1722],{"className":1655},[1604],[1398,1657,1660,1711],{"className":1658,"style":1659},[1608],"height:0.8833em;",[1398,1661,1663,1667],{"style":1662},"top:-3em;",[1398,1664],{"className":1665,"style":1666},[1616],"height:3em;",[1398,1668,1670],{"className":1669},[1494],[1398,1671,1673,1676],{"className":1672},[1494],[1398,1674,1432],{"className":1675,"style":1526},[1494,1495],[1398,1677,1679],{"className":1678},[1595],[1398,1680,1682,1703],{"className":1681},[1599,1600],[1398,1683,1685,1700],{"className":1684},[1604],[1398,1686,1689],{"className":1687,"style":1688},[1608],"height:0.1514em;",[1398,1690,1691,1694],{"style":1612},[1398,1692],{"className":1693,"style":1617},[1616],[1398,1695,1697],{"className":1696},[1621,1622,1623,1624],[1398,1698,1469],{"className":1699},[1494,1495,1624],[1398,1701,1632],{"className":1702},[1631],[1398,1704,1706],{"className":1705},[1604],[1398,1707,1709],{"className":1708,"style":1639},[1608],[1398,1710],{},[1398,1712,1714,1717],{"style":1713},"top:-3.8033em;",[1398,1715],{"className":1716,"style":1666},[1616],[1398,1718],{"className":1719,"style":1721},[1720],"overline-line","border-bottom-width:0.04em;",[1398,1723,1632],{"className":1724},[1631],[1398,1726,1728],{"className":1727},[1604],[1398,1729,1731],{"className":1730,"style":1639},[1608],[1398,1732],{},"计算出求和",[990,1735,1736],{},"此种方法会比串行进位加法器速度快，因为串行操作需要三次异或操作",[1366,1738,1739],{"id":1739},"进位加法器设计",[1741,1742,1743],"h5",{"id":1743},"进位行为分析",[1745,1746,1748],"table",{"style":1747},"width: 100%; border: 0; border-collapse: collapse; border-spacing: 0;",[1749,1750,1751],"tbody",{},[1752,1753,1755,1756,1755,1765],"tr",{"style":1754},"border: none;","\n  ",[1757,1758,1760,1755],"td",{"style":1759},"width: 50.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,1761,1762],{},[1028,1763],{"alt":1028,"src":1764},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-06.png",[1757,1766,1768,1755],{"style":1767},"width: 49.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,1769,1770],{},[1028,1771],{"alt":1028,"src":1772},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-07.png",[1007,1774,1775,2329],{},[990,1776,1777,1780,1781,1827,1828,1899,1900],{},[994,1778,1779],{},"Carry status—— 进位状态","\n只看当前位的 ",[1398,1782,1784,1803],{"className":1783},[1401],[1398,1785,1787],{"className":1786},[1405],[1407,1788,1789],{"xmlns":1409},[1411,1790,1791,1800],{},[1414,1792,1793,1795,1798],{},[1417,1794,1426],{},[1421,1796,1797],{"separator":1462},",",[1417,1799,1429],{},[1474,1801,1802],{"encoding":1476},"A,B",[1398,1804,1806],{"className":1805,"ariaHidden":1462},[1481],[1398,1807,1809,1813,1816,1820,1824],{"className":1808},[1485],[1398,1810],{"className":1811,"style":1812},[1489],"height:0.8778em;vertical-align:-0.1944em;",[1398,1814,1426],{"className":1815},[1494,1495],[1398,1817,1797],{"className":1818},[1819],"mpunct",[1398,1821],{"className":1822,"style":1823},[1500],"margin-right:0.1667em;",[1398,1825,1429],{"className":1826,"style":1522},[1494,1495],"，判断它对输入进位 ",[1398,1829,1831,1849],{"className":1830},[1401],[1398,1832,1834],{"className":1833},[1405],[1407,1835,1836],{"xmlns":1409},[1411,1837,1838,1846],{},[1414,1839,1840],{},[1449,1841,1842,1844],{},[1417,1843,1432],{},[1417,1845,1455],{},[1474,1847,1848],{"encoding":1476},"C_i",[1398,1850,1852],{"className":1851,"ariaHidden":1462},[1481],[1398,1853,1855,1859],{"className":1854},[1485],[1398,1856],{"className":1857,"style":1858},[1489],"height:0.8333em;vertical-align:-0.15em;",[1398,1860,1862,1865],{"className":1861},[1494],[1398,1863,1432],{"className":1864,"style":1526},[1494,1495],[1398,1866,1868],{"className":1867},[1595],[1398,1869,1871,1891],{"className":1870},[1599,1600],[1398,1872,1874,1888],{"className":1873},[1604],[1398,1875,1877],{"className":1876,"style":1609},[1608],[1398,1878,1879,1882],{"style":1612},[1398,1880],{"className":1881,"style":1617},[1616],[1398,1883,1885],{"className":1884},[1621,1622,1623,1624],[1398,1886,1455],{"className":1887},[1494,1495,1624],[1398,1889,1632],{"className":1890},[1631],[1398,1892,1894],{"className":1893},[1604],[1398,1895,1897],{"className":1896,"style":1639},[1608],[1398,1898],{}," 做什么：",[987,1901,1902,1992,2176],{},[990,1903,1904,1907],{},[994,1905,1906],{},"Generate 产生进位",[1007,1908,1909,1912,1915],{},[990,1910,1911],{},"(A=1,B=1)",[990,1913,1914],{},"不管 (C_i) 是多少，(C_o=1)",[990,1916,1917],{},[1398,1918,1920,1944],{"className":1919},[1401],[1398,1921,1923],{"className":1922},[1405],[1407,1924,1925],{"xmlns":1409},[1411,1926,1927,1941],{},[1414,1928,1929,1932,1934,1936,1939],{},[1417,1930,1931],{},"G",[1421,1933,1423],{},[1417,1935,1426],{},[1421,1937,1938],{},"⋅",[1417,1940,1429],{},[1474,1942,1943],{"encoding":1476},"G=A\\cdot B",[1398,1945,1947,1965,1983],{"className":1946,"ariaHidden":1462},[1481],[1398,1948,1950,1953,1956,1959,1962],{"className":1949},[1485],[1398,1951],{"className":1952,"style":1490},[1489],[1398,1954,1931],{"className":1955},[1494,1495],[1398,1957],{"className":1958,"style":1501},[1500],[1398,1960,1423],{"className":1961},[1505],[1398,1963],{"className":1964,"style":1501},[1500],[1398,1966,1968,1971,1974,1977,1980],{"className":1967},[1485],[1398,1969],{"className":1970,"style":1490},[1489],[1398,1972,1426],{"className":1973},[1494,1495],[1398,1975],{"className":1976,"style":1530},[1500],[1398,1978,1938],{"className":1979},[1534],[1398,1981],{"className":1982,"style":1530},[1500],[1398,1984,1986,1989],{"className":1985},[1485],[1398,1987],{"className":1988,"style":1490},[1489],[1398,1990,1429],{"className":1991,"style":1522},[1494,1495],[990,1993,1994,1997],{},[994,1995,1996],{},"Propagate 传播进位",[1007,1998,1999,2095,2098],{},[990,2000,1439,2001,1458],{},[1398,2002,2004,2024],{"className":2003},[1401],[1398,2005,2007],{"className":2006},[1405],[1407,2008,2009],{"xmlns":1409},[1411,2010,2011,2021],{},[1414,2012,2013,2015,2019],{},[1417,2014,1426],{},[1421,2016,2018],{"mathvariant":2017},"normal","≠",[1417,2020,1429],{},[1474,2022,2023],{"encoding":1476},"A\\neq B",[1398,2025,2027,2086],{"className":2026,"ariaHidden":1462},[1481],[1398,2028,2030,2034,2037,2040,2083],{"className":2029},[1485],[1398,2031],{"className":2032,"style":2033},[1489],"height:0.8889em;vertical-align:-0.1944em;",[1398,2035,1426],{"className":2036},[1494,1495],[1398,2038],{"className":2039,"style":1501},[1500],[1398,2041,2043,2076,2080],{"className":2042},[1505],[1398,2044,2046],{"className":2045},[1505],[1398,2047,2050],{"className":2048},[1494,2049],"vbox",[1398,2051,2054],{"className":2052},[2053],"thinbox",[1398,2055,2058,2061,2072],{"className":2056},[2057],"rlap",[1398,2059],{"className":2060,"style":2033},[1489],[1398,2062,2065],{"className":2063},[2064],"inner",[1398,2066,2068],{"className":2067},[1494],[1398,2069,2071],{"className":2070},[1505],"",[1398,2073],{"className":2074},[2075],"fix",[1398,2077],{"className":2078},[1500,2079],"nobreak",[1398,2081,1423],{"className":2082},[1505],[1398,2084],{"className":2085,"style":1501},[1500],[1398,2087,2089,2092],{"className":2088},[1485],[1398,2090],{"className":2091,"style":1490},[1489],[1398,2093,1429],{"className":2094,"style":1522},[1494,1495],[990,2096,2097],{},"输出进位等于输入进位",[990,2099,2100],{},[1398,2101,2103,2127],{"className":2102},[1401],[1398,2104,2106],{"className":2105},[1405],[1407,2107,2108],{"xmlns":1409},[1411,2109,2110,2124],{},[1414,2111,2112,2115,2117,2119,2122],{},[1417,2113,2114],{},"P",[1421,2116,1423],{},[1417,2118,1426],{},[1421,2120,2121],{},"⊕",[1417,2123,1429],{},[1474,2125,2126],{"encoding":1476},"P=A\\oplus B",[1398,2128,2130,2149,2167],{"className":2129,"ariaHidden":1462},[1481],[1398,2131,2133,2136,2140,2143,2146],{"className":2132},[1485],[1398,2134],{"className":2135,"style":1490},[1489],[1398,2137,2114],{"className":2138,"style":2139},[1494,1495],"margin-right:0.1389em;",[1398,2141],{"className":2142,"style":1501},[1500],[1398,2144,1423],{"className":2145},[1505],[1398,2147],{"className":2148,"style":1501},[1500],[1398,2150,2152,2155,2158,2161,2164],{"className":2151},[1485],[1398,2153],{"className":2154,"style":1515},[1489],[1398,2156,1426],{"className":2157},[1494,1495],[1398,2159],{"className":2160,"style":1530},[1500],[1398,2162,2121],{"className":2163},[1534],[1398,2165],{"className":2166,"style":1530},[1500],[1398,2168,2170,2173],{"className":2169},[1485],[1398,2171],{"className":2172,"style":1490},[1489],[1398,2174,1429],{"className":2175,"style":1522},[1494,1495],[990,2177,2178,2181],{},[994,2179,2180],{},"Kill \u002F Delete 删除进位",[1007,2182,2183,2186,2189],{},[990,2184,2185],{},"(A=0,B=0)",[990,2187,2188],{},"不管 (C_i) 是多少，(C_o=0)",[990,2190,2191],{},[1398,2192,2194,2225],{"className":2193},[1401],[1398,2195,2197],{"className":2196},[1405],[1407,2198,2199],{"xmlns":1409},[1411,2200,2201,2222],{},[1414,2202,2203,2206,2208,2214,2216],{},[1417,2204,2205],{},"K",[1421,2207,1423],{},[1460,2209,2210,2212],{"accent":1462},[1417,2211,1426],{},[1421,2213,1472],{"stretchy":1462},[1421,2215,1938],{},[1460,2217,2218,2220],{"accent":1462},[1417,2219,1429],{},[1421,2221,1472],{"stretchy":1462},[1474,2223,2224],{"encoding":1476},"K=\\overline A\\cdot \\overline B",[1398,2226,2228,2246,2292],{"className":2227,"ariaHidden":1462},[1481],[1398,2229,2231,2234,2237,2240,2243],{"className":2230},[1485],[1398,2232],{"className":2233,"style":1490},[1489],[1398,2235,2205],{"className":2236,"style":1526},[1494,1495],[1398,2238],{"className":2239,"style":1501},[1500],[1398,2241,1423],{"className":2242},[1505],[1398,2244],{"className":2245,"style":1501},[1500],[1398,2247,2249,2252,2283,2286,2289],{"className":2248},[1485],[1398,2250],{"className":2251,"style":1659},[1489],[1398,2253,2255],{"className":2254},[1494,1649],[1398,2256,2258],{"className":2257},[1599],[1398,2259,2261],{"className":2260},[1604],[1398,2262,2264,2275],{"className":2263,"style":1659},[1608],[1398,2265,2266,2269],{"style":1662},[1398,2267],{"className":2268,"style":1666},[1616],[1398,2270,2272],{"className":2271},[1494],[1398,2273,1426],{"className":2274},[1494,1495],[1398,2276,2277,2280],{"style":1713},[1398,2278],{"className":2279,"style":1666},[1616],[1398,2281],{"className":2282,"style":1721},[1720],[1398,2284],{"className":2285,"style":1530},[1500],[1398,2287,1938],{"className":2288},[1534],[1398,2290],{"className":2291,"style":1530},[1500],[1398,2293,2295,2298],{"className":2294},[1485],[1398,2296],{"className":2297,"style":1659},[1489],[1398,2299,2301],{"className":2300},[1494,1649],[1398,2302,2304],{"className":2303},[1599],[1398,2305,2307],{"className":2306},[1604],[1398,2308,2310,2321],{"className":2309,"style":1659},[1608],[1398,2311,2312,2315],{"style":1662},[1398,2313],{"className":2314,"style":1666},[1616],[1398,2316,2318],{"className":2317},[1494],[1398,2319,1429],{"className":2320,"style":1522},[1494,1495],[1398,2322,2323,2326],{"style":1713},[1398,2324],{"className":2325,"style":1666},[1616],[1398,2327],{"className":2328,"style":1721},[1720],[990,2330,2331,2334],{},[994,2332,2333],{},"用 P、G、K 表达加法器:",[1007,2335,2336],{},[990,2337,2338],{},[1398,2339,2341,2373],{"className":2340},[1401],[1398,2342,2344],{"className":2343},[1405],[1407,2345,2346],{"xmlns":1409},[1411,2347,2348,2370],{},[1414,2349,2350,2356,2358,2360,2362,2364],{},[1449,2351,2352,2354],{},[1417,2353,1432],{},[1417,2355,1469],{},[1421,2357,1423],{},[1417,2359,1931],{},[1421,2361,1435],{},[1417,2363,2114],{},[1449,2365,2366,2368],{},[1417,2367,1432],{},[1417,2369,1455],{},[1474,2371,2372],{"encoding":1476},"C_o = G + P C_i",[1398,2374,2376,2431,2449],{"className":2375,"ariaHidden":1462},[1481],[1398,2377,2379,2382,2422,2425,2428],{"className":2378},[1485],[1398,2380],{"className":2381,"style":1858},[1489],[1398,2383,2385,2388],{"className":2384},[1494],[1398,2386,1432],{"className":2387,"style":1526},[1494,1495],[1398,2389,2391],{"className":2390},[1595],[1398,2392,2394,2414],{"className":2393},[1599,1600],[1398,2395,2397,2411],{"className":2396},[1604],[1398,2398,2400],{"className":2399,"style":1688},[1608],[1398,2401,2402,2405],{"style":1612},[1398,2403],{"className":2404,"style":1617},[1616],[1398,2406,2408],{"className":2407},[1621,1622,1623,1624],[1398,2409,1469],{"className":2410},[1494,1495,1624],[1398,2412,1632],{"className":2413},[1631],[1398,2415,2417],{"className":2416},[1604],[1398,2418,2420],{"className":2419,"style":1639},[1608],[1398,2421],{},[1398,2423],{"className":2424,"style":1501},[1500],[1398,2426,1423],{"className":2427},[1505],[1398,2429],{"className":2430,"style":1501},[1500],[1398,2432,2434,2437,2440,2443,2446],{"className":2433},[1485],[1398,2435],{"className":2436,"style":1515},[1489],[1398,2438,1931],{"className":2439},[1494,1495],[1398,2441],{"className":2442,"style":1530},[1500],[1398,2444,1435],{"className":2445},[1534],[1398,2447],{"className":2448,"style":1530},[1500],[1398,2450,2452,2455,2458],{"className":2451},[1485],[1398,2453],{"className":2454,"style":1858},[1489],[1398,2456,2114],{"className":2457,"style":2139},[1494,1495],[1398,2459,2461,2464],{"className":2460},[1494],[1398,2462,1432],{"className":2463,"style":1526},[1494,1495],[1398,2465,2467],{"className":2466},[1595],[1398,2468,2470,2490],{"className":2469},[1599,1600],[1398,2471,2473,2487],{"className":2472},[1604],[1398,2474,2476],{"className":2475,"style":1609},[1608],[1398,2477,2478,2481],{"style":1612},[1398,2479],{"className":2480,"style":1617},[1616],[1398,2482,2484],{"className":2483},[1621,1622,1623,1624],[1398,2485,1455],{"className":2486},[1494,1495,1624],[1398,2488,1632],{"className":2489},[1631],[1398,2491,2493],{"className":2492},[1604],[1398,2494,2496],{"className":2495,"style":1639},[1608],[1398,2497],{},[1025,2499,2500,2501,2504],{},"如果我们知道每一位是 ",[994,2502,2503],{},"Generate \u002F Propagate \u002F Kill","，就可以提前推导高位进位，形成后面的：",[1007,2506,2507,2510,2513,2516],{},[990,2508,2509],{},"Carry Lookahead Adder",[990,2511,2512],{},"Carry Skip Adder",[990,2514,2515],{},"Carry Select Adder",[990,2517,2518],{},"Prefix Adder",[1366,2520,2522],{"id":2521},"mirror-adder","Mirror Adder",[1025,2524,2525],{},[1028,2526],{"alt":1028,"src":2527},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-08.png",[1025,2529,2530,2531],{},"核心公式",[1398,2532,2534,2576],{"className":2533},[1401],[1398,2535,2537],{"className":2536},[1405],[1407,2538,2539],{"xmlns":1409},[1411,2540,2541,2573],{},[1414,2542,2543,2549,2551,2553,2555,2557,2563,2565,2567,2569,2571],{},[1449,2544,2545,2547],{},[1417,2546,1432],{},[1417,2548,1469],{},[1421,2550,1423],{},[1417,2552,1426],{},[1417,2554,1429],{},[1421,2556,1435],{},[1449,2558,2559,2561],{},[1417,2560,1432],{},[1417,2562,1455],{},[1421,2564,1439],{"stretchy":1438},[1417,2566,1426],{},[1421,2568,1435],{},[1417,2570,1429],{},[1421,2572,1458],{"stretchy":1438},[1474,2574,2575],{"encoding":1476},"C_o = AB + C_i(A+B)",[1398,2577,2579,2634,2655,2716],{"className":2578,"ariaHidden":1462},[1481],[1398,2580,2582,2585,2625,2628,2631],{"className":2581},[1485],[1398,2583],{"className":2584,"style":1858},[1489],[1398,2586,2588,2591],{"className":2587},[1494],[1398,2589,1432],{"className":2590,"style":1526},[1494,1495],[1398,2592,2594],{"className":2593},[1595],[1398,2595,2597,2617],{"className":2596},[1599,1600],[1398,2598,2600,2614],{"className":2599},[1604],[1398,2601,2603],{"className":2602,"style":1688},[1608],[1398,2604,2605,2608],{"style":1612},[1398,2606],{"className":2607,"style":1617},[1616],[1398,2609,2611],{"className":2610},[1621,1622,1623,1624],[1398,2612,1469],{"className":2613},[1494,1495,1624],[1398,2615,1632],{"className":2616},[1631],[1398,2618,2620],{"className":2619},[1604],[1398,2621,2623],{"className":2622,"style":1639},[1608],[1398,2624],{},[1398,2626],{"className":2627,"style":1501},[1500],[1398,2629,1423],{"className":2630},[1505],[1398,2632],{"className":2633,"style":1501},[1500],[1398,2635,2637,2640,2643,2646,2649,2652],{"className":2636},[1485],[1398,2638],{"className":2639,"style":1515},[1489],[1398,2641,1426],{"className":2642},[1494,1495],[1398,2644,1429],{"className":2645,"style":1522},[1494,1495],[1398,2647],{"className":2648,"style":1530},[1500],[1398,2650,1435],{"className":2651},[1534],[1398,2653],{"className":2654,"style":1530},[1500],[1398,2656,2658,2661,2701,2704,2707,2710,2713],{"className":2657},[1485],[1398,2659],{"className":2660,"style":1544},[1489],[1398,2662,2664,2667],{"className":2663},[1494],[1398,2665,1432],{"className":2666,"style":1526},[1494,1495],[1398,2668,2670],{"className":2669},[1595],[1398,2671,2673,2693],{"className":2672},[1599,1600],[1398,2674,2676,2690],{"className":2675},[1604],[1398,2677,2679],{"className":2678,"style":1609},[1608],[1398,2680,2681,2684],{"style":1612},[1398,2682],{"className":2683,"style":1617},[1616],[1398,2685,2687],{"className":2686},[1621,1622,1623,1624],[1398,2688,1455],{"className":2689},[1494,1495,1624],[1398,2691,1632],{"className":2692},[1631],[1398,2694,2696],{"className":2695},[1604],[1398,2697,2699],{"className":2698,"style":1639},[1608],[1398,2700],{},[1398,2702,1439],{"className":2703},[1548],[1398,2705,1426],{"className":2706},[1494,1495],[1398,2708],{"className":2709,"style":1530},[1500],[1398,2711,1435],{"className":2712},[1534],[1398,2714],{"className":2715,"style":1530},[1500],[1398,2717,2719,2722,2725],{"className":2718},[1485],[1398,2720],{"className":2721,"style":1544},[1489],[1398,2723,1429],{"className":2724,"style":1522},[1494,1495],[1398,2726,1458],{"className":2727},[1645],[1741,2729,2730],{"id":2730},"电路实现",[1025,2732,2733],{},"红色网络实际先生成：",[1398,2735,2738],{"className":2736},[2737],"katex-display",[1398,2739,2741,2764],{"className":2740},[1401],[1398,2742,2744],{"className":2743},[1405],[1407,2745,2747],{"xmlns":1409,"display":2746},"block",[1411,2748,2749,2761],{},[1414,2750,2751],{},[1460,2752,2753,2759],{"accent":1462},[1449,2754,2755,2757],{},[1417,2756,1432],{},[1417,2758,1469],{},[1421,2760,1472],{"stretchy":1462},[1474,2762,2763],{"encoding":1476},"\\overline{C_o}",[1398,2765,2767],{"className":2766,"ariaHidden":1462},[1481],[1398,2768,2770,2774],{"className":2769},[1485],[1398,2771],{"className":2772,"style":2773},[1489],"height:1.0333em;vertical-align:-0.15em;",[1398,2775,2777],{"className":2776},[1494,1649],[1398,2778,2780,2845],{"className":2779},[1599,1600],[1398,2781,2783,2842],{"className":2782},[1604],[1398,2784,2786,2834],{"className":2785,"style":1659},[1608],[1398,2787,2788,2791],{"style":1662},[1398,2789],{"className":2790,"style":1666},[1616],[1398,2792,2794],{"className":2793},[1494],[1398,2795,2797,2800],{"className":2796},[1494],[1398,2798,1432],{"className":2799,"style":1526},[1494,1495],[1398,2801,2803],{"className":2802},[1595],[1398,2804,2806,2826],{"className":2805},[1599,1600],[1398,2807,2809,2823],{"className":2808},[1604],[1398,2810,2812],{"className":2811,"style":1688},[1608],[1398,2813,2814,2817],{"style":1612},[1398,2815],{"className":2816,"style":1617},[1616],[1398,2818,2820],{"className":2819},[1621,1622,1623,1624],[1398,2821,1469],{"className":2822},[1494,1495,1624],[1398,2824,1632],{"className":2825},[1631],[1398,2827,2829],{"className":2828},[1604],[1398,2830,2832],{"className":2831,"style":1639},[1608],[1398,2833],{},[1398,2835,2836,2839],{"style":1713},[1398,2837],{"className":2838,"style":1666},[1616],[1398,2840],{"className":2841,"style":1721},[1720],[1398,2843,1632],{"className":2844},[1631],[1398,2846,2848],{"className":2847},[1604],[1398,2849,2851],{"className":2850,"style":1639},[1608],[1398,2852],{},[1007,2854,2855,3001],{},[990,2856,2857,2858,2996],{},"上拉网络：负责让 ",[1398,2859,2861,2889],{"className":2860},[1401],[1398,2862,2864],{"className":2863},[1405],[1407,2865,2866],{"xmlns":1409},[1411,2867,2868,2886],{},[1414,2869,2870,2880,2882],{},[1460,2871,2872,2878],{"accent":1462},[1449,2873,2874,2876],{},[1417,2875,1432],{},[1417,2877,1469],{},[1421,2879,1472],{"stretchy":1462},[1421,2881,1423],{},[2883,2884,2885],"mn",{},"1",[1474,2887,2888],{"encoding":1476},"\\overline{C_o}=1",[1398,2890,2892,2986],{"className":2891,"ariaHidden":1462},[1481],[1398,2893,2895,2898,2977,2980,2983],{"className":2894},[1485],[1398,2896],{"className":2897,"style":2773},[1489],[1398,2899,2901],{"className":2900},[1494,1649],[1398,2902,2904,2969],{"className":2903},[1599,1600],[1398,2905,2907,2966],{"className":2906},[1604],[1398,2908,2910,2958],{"className":2909,"style":1659},[1608],[1398,2911,2912,2915],{"style":1662},[1398,2913],{"className":2914,"style":1666},[1616],[1398,2916,2918],{"className":2917},[1494],[1398,2919,2921,2924],{"className":2920},[1494],[1398,2922,1432],{"className":2923,"style":1526},[1494,1495],[1398,2925,2927],{"className":2926},[1595],[1398,2928,2930,2950],{"className":2929},[1599,1600],[1398,2931,2933,2947],{"className":2932},[1604],[1398,2934,2936],{"className":2935,"style":1688},[1608],[1398,2937,2938,2941],{"style":1612},[1398,2939],{"className":2940,"style":1617},[1616],[1398,2942,2944],{"className":2943},[1621,1622,1623,1624],[1398,2945,1469],{"className":2946},[1494,1495,1624],[1398,2948,1632],{"className":2949},[1631],[1398,2951,2953],{"className":2952},[1604],[1398,2954,2956],{"className":2955,"style":1639},[1608],[1398,2957],{},[1398,2959,2960,2963],{"style":1713},[1398,2961],{"className":2962,"style":1666},[1616],[1398,2964],{"className":2965,"style":1721},[1720],[1398,2967,1632],{"className":2968},[1631],[1398,2970,2972],{"className":2971},[1604],[1398,2973,2975],{"className":2974,"style":1639},[1608],[1398,2976],{},[1398,2978],{"className":2979,"style":1501},[1500],[1398,2981,1423],{"className":2982},[1505],[1398,2984],{"className":2985,"style":1501},[1500],[1398,2987,2989,2993],{"className":2988},[1485],[1398,2990],{"className":2991,"style":2992},[1489],"height:0.6444em;",[1398,2994,2885],{"className":2995},[1494],[1007,2997,2998],{},[990,2999,3000],{},"对应 Kill 和 “0”-Propagate",[990,3002,3003,3004,3140],{},"下拉网络：负责让 ",[1398,3005,3007,3034],{"className":3006},[1401],[1398,3008,3010],{"className":3009},[1405],[1407,3011,3012],{"xmlns":1409},[1411,3013,3014,3031],{},[1414,3015,3016,3026,3028],{},[1460,3017,3018,3024],{"accent":1462},[1449,3019,3020,3022],{},[1417,3021,1432],{},[1417,3023,1469],{},[1421,3025,1472],{"stretchy":1462},[1421,3027,1423],{},[2883,3029,3030],{},"0",[1474,3032,3033],{"encoding":1476},"\\overline{C_o}=0",[1398,3035,3037,3131],{"className":3036,"ariaHidden":1462},[1481],[1398,3038,3040,3043,3122,3125,3128],{"className":3039},[1485],[1398,3041],{"className":3042,"style":2773},[1489],[1398,3044,3046],{"className":3045},[1494,1649],[1398,3047,3049,3114],{"className":3048},[1599,1600],[1398,3050,3052,3111],{"className":3051},[1604],[1398,3053,3055,3103],{"className":3054,"style":1659},[1608],[1398,3056,3057,3060],{"style":1662},[1398,3058],{"className":3059,"style":1666},[1616],[1398,3061,3063],{"className":3062},[1494],[1398,3064,3066,3069],{"className":3065},[1494],[1398,3067,1432],{"className":3068,"style":1526},[1494,1495],[1398,3070,3072],{"className":3071},[1595],[1398,3073,3075,3095],{"className":3074},[1599,1600],[1398,3076,3078,3092],{"className":3077},[1604],[1398,3079,3081],{"className":3080,"style":1688},[1608],[1398,3082,3083,3086],{"style":1612},[1398,3084],{"className":3085,"style":1617},[1616],[1398,3087,3089],{"className":3088},[1621,1622,1623,1624],[1398,3090,1469],{"className":3091},[1494,1495,1624],[1398,3093,1632],{"className":3094},[1631],[1398,3096,3098],{"className":3097},[1604],[1398,3099,3101],{"className":3100,"style":1639},[1608],[1398,3102],{},[1398,3104,3105,3108],{"style":1713},[1398,3106],{"className":3107,"style":1666},[1616],[1398,3109],{"className":3110,"style":1721},[1720],[1398,3112,1632],{"className":3113},[1631],[1398,3115,3117],{"className":3116},[1604],[1398,3118,3120],{"className":3119,"style":1639},[1608],[1398,3121],{},[1398,3123],{"className":3124,"style":1501},[1500],[1398,3126,1423],{"className":3127},[1505],[1398,3129],{"className":3130,"style":1501},[1500],[1398,3132,3134,3137],{"className":3133},[1485],[1398,3135],{"className":3136,"style":2992},[1489],[1398,3138,3030],{"className":3139},[1494],[1007,3141,3142],{},[990,3143,3144],{},"对应 Generate 和 “1”-Propagate",[1741,3146,3147],{"id":3147},"优点",[1007,3149,3150,3225,3228,3231],{},[990,3151,3152,3153],{},"不显式生成 ",[1398,3154,3156,3177],{"className":3155},[1401],[1398,3157,3159],{"className":3158},[1405],[1407,3160,3161],{"xmlns":1409},[1411,3162,3163,3175],{},[1414,3164,3165,3167,3169,3171,3173],{},[1417,3166,2114],{},[1421,3168,1423],{},[1417,3170,1426],{},[1421,3172,2121],{},[1417,3174,1429],{},[1474,3176,2126],{"encoding":1476},[1398,3178,3180,3198,3216],{"className":3179,"ariaHidden":1462},[1481],[1398,3181,3183,3186,3189,3192,3195],{"className":3182},[1485],[1398,3184],{"className":3185,"style":1490},[1489],[1398,3187,2114],{"className":3188,"style":2139},[1494,1495],[1398,3190],{"className":3191,"style":1501},[1500],[1398,3193,1423],{"className":3194},[1505],[1398,3196],{"className":3197,"style":1501},[1500],[1398,3199,3201,3204,3207,3210,3213],{"className":3200},[1485],[1398,3202],{"className":3203,"style":1515},[1489],[1398,3205,1426],{"className":3206},[1494,1495],[1398,3208],{"className":3209,"style":1530},[1500],[1398,3211,2121],{"className":3212},[1534],[1398,3214],{"className":3215,"style":1530},[1500],[1398,3217,3219,3222],{"className":3218},[1485],[1398,3220],{"className":3221,"style":1490},[1489],[1398,3223,1429],{"className":3224,"style":1522},[1494,1495],[990,3226,3227],{},"直接把 Kill \u002F Propagate \u002F Generate 写进晶体管导通路径",[990,3229,3230],{},"晶体管数少：24T",[990,3232,3233],{},"Carry 路径更直接，适合 ripple-carry adder",[1025,3235,3236],{},[3237,3238,3239],"mark",{},[994,3240,3241],{},"Mirror Adder 是按进位行为设计晶体管网络：消进位、传进位、产生进位。",[1366,3243,3245],{"id":3244},"transmission-gate-full-adder","Transmission Gate Full Adder",[1025,3247,3248],{},"采用传输门的方式来进行全加器的设计",[1025,3250,3251],{},[1028,3252],{"alt":1028,"src":3253},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-09.png",[1366,3255,3257],{"id":3256},"complementary-pass-transistor-logic-互补传输晶体管逻辑","Complementary Pass Transistor Logic ｜ 互补传输晶体管逻辑",[1025,3259,3260],{},[1028,3261],{"alt":1028,"src":3262},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-10.png",[1025,3264,3265],{},"速度更快是因为级连数目比较少 但是会占用比较大的面积",[983,3267,3269],{"id":3268},"multi-bit-addition","Multi-bit Addition",[1366,3271,3273],{"id":3272},"ripple-carry-adder-串行进位加法器","Ripple-Carry Adder 串行进位加法器",[1025,3275,3276,3277,3280],{},"把多个 ",[994,3278,3279],{},"Full Adder，全加器"," 串起来：",[1025,3282,3283],{},[1028,3284],{"alt":1028,"src":3285},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-11.png",[1025,3287,3288,3289,3511],{},"关键路径",[1398,3290,3292,3332],{"className":3291},[1401],[1398,3293,3295],{"className":3294},[1405],[1407,3296,3297],{"xmlns":1409},[1411,3298,3299,3329],{},[1414,3300,3301,3307,3310,3316,3318,3324,3326],{},[1449,3302,3303,3305],{},[1417,3304,1432],{},[1417,3306,1455],{},[1421,3308,3309],{},"→",[1449,3311,3312,3314],{},[1417,3313,1432],{},[1417,3315,1469],{},[1421,3317,3309],{},[1449,3319,3320,3322],{},[1417,3321,1432],{},[1417,3323,1469],{},[1421,3325,3309],{},[1421,3327,3328],{},"⋯",[1474,3330,3331],{"encoding":1476},"C_i \\rightarrow C_o \\rightarrow C_o \\rightarrow \\cdots",[1398,3333,3335,3390,3445,3500],{"className":3334,"ariaHidden":1462},[1481],[1398,3336,3338,3341,3381,3384,3387],{"className":3337},[1485],[1398,3339],{"className":3340,"style":1858},[1489],[1398,3342,3344,3347],{"className":3343},[1494],[1398,3345,1432],{"className":3346,"style":1526},[1494,1495],[1398,3348,3350],{"className":3349},[1595],[1398,3351,3353,3373],{"className":3352},[1599,1600],[1398,3354,3356,3370],{"className":3355},[1604],[1398,3357,3359],{"className":3358,"style":1609},[1608],[1398,3360,3361,3364],{"style":1612},[1398,3362],{"className":3363,"style":1617},[1616],[1398,3365,3367],{"className":3366},[1621,1622,1623,1624],[1398,3368,1455],{"className":3369},[1494,1495,1624],[1398,3371,1632],{"className":3372},[1631],[1398,3374,3376],{"className":3375},[1604],[1398,3377,3379],{"className":3378,"style":1639},[1608],[1398,3380],{},[1398,3382],{"className":3383,"style":1501},[1500],[1398,3385,3309],{"className":3386},[1505],[1398,3388],{"className":3389,"style":1501},[1500],[1398,3391,3393,3396,3436,3439,3442],{"className":3392},[1485],[1398,3394],{"className":3395,"style":1858},[1489],[1398,3397,3399,3402],{"className":3398},[1494],[1398,3400,1432],{"className":3401,"style":1526},[1494,1495],[1398,3403,3405],{"className":3404},[1595],[1398,3406,3408,3428],{"className":3407},[1599,1600],[1398,3409,3411,3425],{"className":3410},[1604],[1398,3412,3414],{"className":3413,"style":1688},[1608],[1398,3415,3416,3419],{"style":1612},[1398,3417],{"className":3418,"style":1617},[1616],[1398,3420,3422],{"className":3421},[1621,1622,1623,1624],[1398,3423,1469],{"className":3424},[1494,1495,1624],[1398,3426,1632],{"className":3427},[1631],[1398,3429,3431],{"className":3430},[1604],[1398,3432,3434],{"className":3433,"style":1639},[1608],[1398,3435],{},[1398,3437],{"className":3438,"style":1501},[1500],[1398,3440,3309],{"className":3441},[1505],[1398,3443],{"className":3444,"style":1501},[1500],[1398,3446,3448,3451,3491,3494,3497],{"className":3447},[1485],[1398,3449],{"className":3450,"style":1858},[1489],[1398,3452,3454,3457],{"className":3453},[1494],[1398,3455,1432],{"className":3456,"style":1526},[1494,1495],[1398,3458,3460],{"className":3459},[1595],[1398,3461,3463,3483],{"className":3462},[1599,1600],[1398,3464,3466,3480],{"className":3465},[1604],[1398,3467,3469],{"className":3468,"style":1688},[1608],[1398,3470,3471,3474],{"style":1612},[1398,3472],{"className":3473,"style":1617},[1616],[1398,3475,3477],{"className":3476},[1621,1622,1623,1624],[1398,3478,1469],{"className":3479},[1494,1495,1624],[1398,3481,1632],{"className":3482},[1631],[1398,3484,3486],{"className":3485},[1604],[1398,3487,3489],{"className":3488,"style":1639},[1608],[1398,3490],{},[1398,3492],{"className":3493,"style":1501},[1500],[1398,3495,3309],{"className":3496},[1505],[1398,3498],{"className":3499,"style":1501},[1500],[1398,3501,3503,3507],{"className":3502},[1485],[1398,3504],{"className":3505,"style":3506},[1489],"height:0.313em;",[1398,3508,3328],{"className":3509},[3510],"minner",",延迟随位数线性增加.",[1025,3513,3514],{},"具体延迟计算",[1398,3516,3518],{"className":3517},[2737],[1398,3519,3521,3603],{"className":3520},[1401],[1398,3522,3524],{"className":3523},[1405],[1407,3525,3526],{"xmlns":1409,"display":2746},[1411,3527,3528,3600],{},[1414,3529,3530,3551,3553,3555,3558,3561,3563,3565,3583,3585],{},[1449,3531,3532,3535],{},[1417,3533,3534],{},"t",[1414,3536,3537,3540,3543,3545,3548],{},[1417,3538,3539],{},"a",[1417,3541,3542],{},"d",[1417,3544,3542],{},[1417,3546,3547],{},"e",[1417,3549,3550],{},"r",[1421,3552,1423],{},[1421,3554,1439],{"stretchy":1438},[1417,3556,3557],{},"N",[1421,3559,3560],{},"−",[2883,3562,2885],{},[1421,3564,1458],{"stretchy":1438},[1449,3566,3567,3569],{},[1417,3568,3534],{},[1414,3570,3571,3574,3576,3578,3580],{},[1417,3572,3573],{},"c",[1417,3575,3539],{},[1417,3577,3550],{},[1417,3579,3550],{},[1417,3581,3582],{},"y",[1421,3584,1435],{},[1449,3586,3587,3589],{},[1417,3588,3534],{},[1414,3590,3591,3594,3597],{},[1417,3592,3593],{},"s",[1417,3595,3596],{},"u",[1417,3598,3599],{},"m",[1474,3601,3602],{"encoding":1476},"t_{adder}=(N-1)t_{carry}+t_{sum}",[1398,3604,3606,3676,3698,3777],{"className":3605,"ariaHidden":1462},[1481],[1398,3607,3609,3613,3667,3670,3673],{"className":3608},[1485],[1398,3610],{"className":3611,"style":3612},[1489],"height:0.7651em;vertical-align:-0.15em;",[1398,3614,3616,3619],{"className":3615},[1494],[1398,3617,3534],{"className":3618},[1494,1495],[1398,3620,3622],{"className":3621},[1595],[1398,3623,3625,3659],{"className":3624},[1599,1600],[1398,3626,3628,3656],{"className":3627},[1604],[1398,3629,3632],{"className":3630,"style":3631},[1608],"height:0.3361em;",[1398,3633,3635,3638],{"style":3634},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1398,3636],{"className":3637,"style":1617},[1616],[1398,3639,3641],{"className":3640},[1621,1622,1623,1624],[1398,3642,3644,3647,3651],{"className":3643},[1494,1624],[1398,3645,3539],{"className":3646},[1494,1495,1624],[1398,3648,3650],{"className":3649},[1494,1495,1624],"dd",[1398,3652,3655],{"className":3653,"style":3654},[1494,1495,1624],"margin-right:0.0278em;","er",[1398,3657,1632],{"className":3658},[1631],[1398,3660,3662],{"className":3661},[1604],[1398,3663,3665],{"className":3664,"style":1639},[1608],[1398,3666],{},[1398,3668],{"className":3669,"style":1501},[1500],[1398,3671,1423],{"className":3672},[1505],[1398,3674],{"className":3675,"style":1501},[1500],[1398,3677,3679,3682,3685,3689,3692,3695],{"className":3678},[1485],[1398,3680],{"className":3681,"style":1544},[1489],[1398,3683,1439],{"className":3684},[1548],[1398,3686,3557],{"className":3687,"style":3688},[1494,1495],"margin-right:0.109em;",[1398,3690],{"className":3691,"style":1530},[1500],[1398,3693,3560],{"className":3694},[1534],[1398,3696],{"className":3697,"style":1530},[1500],[1398,3699,3701,3705,3708,3711,3768,3771,3774],{"className":3700},[1485],[1398,3702],{"className":3703,"style":3704},[1489],"height:1.0361em;vertical-align:-0.2861em;",[1398,3706,2885],{"className":3707},[1494],[1398,3709,1458],{"className":3710},[1645],[1398,3712,3714,3717],{"className":3713},[1494],[1398,3715,3534],{"className":3716},[1494,1495],[1398,3718,3720],{"className":3719},[1595],[1398,3721,3723,3759],{"className":3722},[1599,1600],[1398,3724,3726,3756],{"className":3725},[1604],[1398,3727,3729],{"className":3728,"style":1688},[1608],[1398,3730,3731,3734],{"style":3634},[1398,3732],{"className":3733,"style":1617},[1616],[1398,3735,3737],{"className":3736},[1621,1622,1623,1624],[1398,3738,3740,3743,3746,3749,3752],{"className":3739},[1494,1624],[1398,3741,3573],{"className":3742},[1494,1495,1624],[1398,3744,3539],{"className":3745},[1494,1495,1624],[1398,3747,3550],{"className":3748,"style":3654},[1494,1495,1624],[1398,3750,3550],{"className":3751,"style":3654},[1494,1495,1624],[1398,3753,3582],{"className":3754,"style":3755},[1494,1495,1624],"margin-right:0.0359em;",[1398,3757,1632],{"className":3758},[1631],[1398,3760,3762],{"className":3761},[1604],[1398,3763,3766],{"className":3764,"style":3765},[1608],"height:0.2861em;",[1398,3767],{},[1398,3769],{"className":3770,"style":1530},[1500],[1398,3772,1435],{"className":3773},[1534],[1398,3775],{"className":3776,"style":1530},[1500],[1398,3778,3780,3783],{"className":3779},[1485],[1398,3781],{"className":3782,"style":3612},[1489],[1398,3784,3786,3789],{"className":3785},[1494],[1398,3787,3534],{"className":3788},[1494,1495],[1398,3790,3792],{"className":3791},[1595],[1398,3793,3795,3824],{"className":3794},[1599,1600],[1398,3796,3798,3821],{"className":3797},[1604],[1398,3799,3801],{"className":3800,"style":1688},[1608],[1398,3802,3803,3806],{"style":3634},[1398,3804],{"className":3805,"style":1617},[1616],[1398,3807,3809],{"className":3808},[1621,1622,1623,1624],[1398,3810,3812,3815,3818],{"className":3811},[1494,1624],[1398,3813,3593],{"className":3814},[1494,1495,1624],[1398,3816,3596],{"className":3817},[1494,1495,1624],[1398,3819,3599],{"className":3820},[1494,1495,1624],[1398,3822,1632],{"className":3823},[1631],[1398,3825,3827],{"className":3826},[1604],[1398,3828,3830],{"className":3829,"style":1639},[1608],[1398,3831],{},[1025,3833,3834,3835,3931,3932,3935,3936,4021],{},"其中",[1398,3836,3838,3866],{"className":3837},[1401],[1398,3839,3841],{"className":3840},[1405],[1407,3842,3843],{"xmlns":1409},[1411,3844,3845,3863],{},[1414,3846,3847],{},[1449,3848,3849,3851],{},[1417,3850,3534],{},[1414,3852,3853,3855,3857,3859,3861],{},[1417,3854,3573],{},[1417,3856,3539],{},[1417,3858,3550],{},[1417,3860,3550],{},[1417,3862,3582],{},[1474,3864,3865],{"encoding":1476},"t_{carry}",[1398,3867,3869],{"className":3868,"ariaHidden":1462},[1481],[1398,3870,3872,3876],{"className":3871},[1485],[1398,3873],{"className":3874,"style":3875},[1489],"height:0.9012em;vertical-align:-0.2861em;",[1398,3877,3879,3882],{"className":3878},[1494],[1398,3880,3534],{"className":3881},[1494,1495],[1398,3883,3885],{"className":3884},[1595],[1398,3886,3888,3923],{"className":3887},[1599,1600],[1398,3889,3891,3920],{"className":3890},[1604],[1398,3892,3894],{"className":3893,"style":1688},[1608],[1398,3895,3896,3899],{"style":3634},[1398,3897],{"className":3898,"style":1617},[1616],[1398,3900,3902],{"className":3901},[1621,1622,1623,1624],[1398,3903,3905,3908,3911,3914,3917],{"className":3904},[1494,1624],[1398,3906,3573],{"className":3907},[1494,1495,1624],[1398,3909,3539],{"className":3910},[1494,1495,1624],[1398,3912,3550],{"className":3913,"style":3654},[1494,1495,1624],[1398,3915,3550],{"className":3916,"style":3654},[1494,1495,1624],[1398,3918,3582],{"className":3919,"style":3755},[1494,1495,1624],[1398,3921,1632],{"className":3922},[1631],[1398,3924,3926],{"className":3925},[1604],[1398,3927,3929],{"className":3928,"style":3765},[1608],[1398,3930],{},"是单个 full adder 中，",[994,3933,3934],{},"进位从输入传到输出","的延迟，即Ci→Co的延迟,",[1398,3937,3939,3963],{"className":3938},[1401],[1398,3940,3942],{"className":3941},[1405],[1407,3943,3944],{"xmlns":1409},[1411,3945,3946,3960],{},[1414,3947,3948],{},[1449,3949,3950,3952],{},[1417,3951,3534],{},[1414,3953,3954,3956,3958],{},[1417,3955,3593],{},[1417,3957,3596],{},[1417,3959,3599],{},[1474,3961,3962],{"encoding":1476},"t_{sum}",[1398,3964,3966],{"className":3965,"ariaHidden":1462},[1481],[1398,3967,3969,3972],{"className":3968},[1485],[1398,3970],{"className":3971,"style":3612},[1489],[1398,3973,3975,3978],{"className":3974},[1494],[1398,3976,3534],{"className":3977},[1494,1495],[1398,3979,3981],{"className":3980},[1595],[1398,3982,3984,4013],{"className":3983},[1599,1600],[1398,3985,3987,4010],{"className":3986},[1604],[1398,3988,3990],{"className":3989,"style":1688},[1608],[1398,3991,3992,3995],{"style":3634},[1398,3993],{"className":3994,"style":1617},[1616],[1398,3996,3998],{"className":3997},[1621,1622,1623,1624],[1398,3999,4001,4004,4007],{"className":4000},[1494,1624],[1398,4002,3593],{"className":4003},[1494,1495,1624],[1398,4005,3596],{"className":4006},[1494,1495,1624],[1398,4008,3599],{"className":4009},[1494,1495,1624],[1398,4011,1632],{"className":4012},[1631],[1398,4014,4016],{"className":4015},[1604],[1398,4017,4019],{"className":4018,"style":1639},[1608],[1398,4020],{},"则是最后一级 full adder 中，进位到达后产生 Sum 的延迟。",[1366,4023,4025],{"id":4024},"inversion-property-全加器的反向特性","Inversion Property ｜ 全加器的反向特性",[1025,4027,4028],{},[1028,4029],{"alt":1028,"src":4030},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-12.png",[1025,4032,4033],{},"全加器有这样的反相特性——如果把全加器的所有输入都取反，那么输出也会整体取反",[1398,4035,4037],{"className":4036},[2737],[1398,4038,4040,4110],{"className":4039},[1401],[1398,4041,4043],{"className":4042},[1405],[1407,4044,4045],{"xmlns":1409,"display":2746},[1411,4046,4047,4107],{},[1414,4048,4049,4055,4057,4059,4061,4063,4065,4071,4073,4075,4077,4079,4085,4087,4093,4095,4105],{},[1460,4050,4051,4053],{"accent":1462},[1417,4052,1419],{},[1421,4054,1472],{"stretchy":1462},[1421,4056,1439],{"stretchy":1438},[1417,4058,1426],{},[1421,4060,1797],{"separator":1462},[1417,4062,1429],{},[1421,4064,1797],{"separator":1462},[1449,4066,4067,4069],{},[1417,4068,1432],{},[1417,4070,1455],{},[1421,4072,1458],{"stretchy":1438},[1421,4074,1423],{},[1417,4076,1419],{},[1421,4078,1439],{"stretchy":1438},[1460,4080,4081,4083],{"accent":1462},[1417,4082,1426],{},[1421,4084,1472],{"stretchy":1462},[1421,4086,1797],{"separator":1462},[1460,4088,4089,4091],{"accent":1462},[1417,4090,1429],{},[1421,4092,1472],{"stretchy":1462},[1421,4094,1797],{"separator":1462},[1460,4096,4097,4103],{"accent":1462},[1449,4098,4099,4101],{},[1417,4100,1432],{},[1417,4102,1455],{},[1421,4104,1472],{"stretchy":1462},[1421,4106,1458],{"stretchy":1438},[1474,4108,4109],{"encoding":1476},"\\overline{S}(A,B,C_i)=S(\\overline A,\\overline B,\\overline 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418,4420,4422,4424,4426,4432,4434,4436,4442,4444,4450,4452,4458,4460,4470],{},[1460,4407,4408,4414],{"accent":1462},[1449,4409,4410,4412],{},[1417,4411,1432],{},[1417,4413,1469],{},[1421,4415,1472],{"stretchy":1462},[1421,4417,1439],{"stretchy":1438},[1417,4419,1426],{},[1421,4421,1797],{"separator":1462},[1417,4423,1429],{},[1421,4425,1797],{"separator":1462},[1449,4427,4428,4430],{},[1417,4429,1432],{},[1417,4431,1455],{},[1421,4433,1458],{"stretchy":1438},[1421,4435,1423],{},[1449,4437,4438,4440],{},[1417,4439,1432],{},[1417,4441,1469],{},[1421,4443,1439],{"stretchy":1438},[1460,4445,4446,4448],{"accent":1462},[1417,4447,1426],{},[1421,4449,1472],{"stretchy":1462},[1421,4451,1797],{"separator":1462},[1460,4453,4454,4456],{"accent":1462},[1417,4455,1429],{},[1421,4457,1472],{"stretchy":1462},[1421,4459,1797],{"separator":1462},[1460,4461,4462,4468],{"accent":1462},[1449,4463,4464,4466],{},[1417,4465,1432],{},[1417,4467,1455],{},[1421,4469,1472],{"stretchy":1462},[1421,4471,1458],{"stretchy":1438},[1474,4473,4474],{"encoding":1476},"\\overline{C_o}(A,B,C_i)=C_o(\\overline A,\\overline B,\\overline {C_i})",[1398,4476,4478,4636],{"className":4477,"ariaHidden":1462},[1481],[1398,4479,4481,4484,4563,4566,4569,4572,4575,4578,4581,4584,4624,4627,4630,4633],{"className":4480},[1485],[1398,4482],{"className":4483,"style":1585},[1489],[1398,4485,4487],{"className":4486},[1494,1649],[1398,4488,4490,4555],{"className":4489},[1599,1600],[1398,4491,4493,4552],{"className":4492},[1604],[1398,4494,4496,4544],{"className":4495,"style":1659},[1608],[1398,4497,4498,4501],{"style":1662},[1398,4499],{"className":4500,"style":1666},[1616],[1398,4502,4504],{"className":4503},[1494],[1398,4505,4507,4510],{"className":4506},[1494],[1398,4508,1432],{"className":4509,"style":1526},[1494,1495],[1398,4511,4513],{"className":4512},[1595],[1398,4514,4516,4536],{"className":4515},[1599,1600],[1398,4517,4519,4533],{"className":4518},[1604],[1398,4520,4522],{"className":4521,"style":1688},[1608],[1398,4523,4524,4527],{"style":1612},[1398,4525],{"className":4526,"style":1617},[1616],[1398,4528,4530],{"className":4529},[1621,1622,1623,1624],[1398,4531,1469],{"className":4532},[1494,1495,1624],[1398,4534,1632],{"className":4535},[1631],[1398,4537,4539],{"className":4538},[1604],[1398,4540,4542],{"className":4541,"style":1639},[1608],[1398,4543],{},[1398,4545,4546,4549],{"style":1713},[1398,4547],{"className":4548,"style":1666},[1616],[1398,4550],{"className":4551,"style":1721},[1720],[1398,4553,1632],{"className":4554},[1631],[1398,4556,4558],{"className":4557},[1604],[1398,4559,4561],{"className":4560,"style":1639},[1608],[1398,4562],{},[1398,4564,1439],{"className":4565},[1548],[1398,4567,1426],{"className":4568},[1494,1495],[1398,4570,1797],{"className":4571},[1819],[1398,4573],{"className":4574,"style":1823},[1500],[1398,4576,1429],{"className":4577,"style":1522},[1494,1495],[1398,4579,1797],{"className":4580},[1819],[1398,4582],{"className":4583,"style":1823},[1500],[1398,4585,4587,4590],{"className":4586},[1494],[1398,4588,1432],{"className":4589,"style":1526},[1494,1495],[1398,4591,4593],{"className":4592},[1595],[1398,4594,4596,4616],{"className":4595},[1599,1600],[1398,4597,4599,4613],{"className":4598},[1604],[1398,4600,4602],{"className":4601,"style":1609},[1608],[1398,4603,4604,4607],{"style":1612},[1398,4605],{"className":4606,"style":1617},[1616],[1398,4608,4610],{"className":4609},[1621,1622,1623,1624],[1398,4611,1455],{"className":4612},[1494,1495,1624],[1398,4614,1632],{"className":4615},[1631],[1398,4617,4619],{"className":4618},[1604],[1398,4620,4622],{"className":4621,"style":1639},[1608],[1398,4623],{},[1398,4625,1458],{"className":4626},[1645],[1398,4628],{"className":4629,"style":1501},[1500],[1398,4631,1423],{"className":4632},[1505],[1398,4634],{"className":4635,"style":1501},[1500],[1398,4637,4639,4642,4682,4685,4716,4719,4722,4753,4756,4759,4838],{"className":4638},[1485],[1398,4640],{"className":4641,"style":1585},[1489],[1398,4643,4645,4648],{"className":4644},[1494],[1398,4646,1432],{"className":4647,"style":1526},[1494,1495],[1398,4649,4651],{"className":4650},[1595],[1398,4652,4654,4674],{"className":4653},[1599,1600],[1398,4655,4657,4671],{"className":4656},[1604],[1398,4658,4660],{"className":4659,"style":1688},[1608],[1398,4661,4662,4665],{"style":1612},[1398,4663],{"className":4664,"style":1617},[1616],[1398,4666,4668],{"className":4667},[1621,1622,1623,1624],[1398,4669,1469],{"className":4670},[1494,1495,1624],[1398,4672,1632],{"className":4673},[1631],[1398,4675,4677],{"className":4676},[1604],[1398,4678,4680],{"className":4679,"style":1639},[1608],[1398,4681],{},[1398,4683,1439],{"className":4684},[1548],[1398,4686,4688],{"className":4687},[1494,1649],[1398,4689,4691],{"className":4690},[1599],[1398,4692,4694],{"className":4693},[1604],[1398,4695,4697,4708],{"className":4696,"style":1659},[1608],[1398,4698,4699,4702],{"style":1662},[1398,4700],{"className":4701,"style":1666},[1616],[1398,4703,4705],{"className":4704},[1494],[1398,4706,1426],{"className":4707},[1494,1495],[1398,4709,4710,4713],{"style":1713},[1398,4711],{"className":4712,"style":1666},[1616],[1398,4714],{"className":4715,"style":1721},[1720],[1398,4717,1797],{"className":4718},[1819],[1398,4720],{"className":4721,"style":1823},[1500],[1398,4723,4725],{"className":4724},[1494,1649],[1398,4726,4728],{"className":4727},[1599],[1398,4729,4731],{"className":4730},[1604],[1398,4732,4734,4745],{"className":4733,"style":1659},[1608],[1398,4735,4736,4739],{"style":1662},[1398,4737],{"className":4738,"style":1666},[1616],[1398,4740,4742],{"className":4741},[1494],[1398,4743,1429],{"className":4744,"style":1522},[1494,1495],[1398,4746,4747,4750],{"style":1713},[1398,4748],{"className":4749,"style":1666},[1616],[1398,4751],{"className":4752,"style":1721},[1720],[1398,4754,1797],{"className":4755},[1819],[1398,4757],{"className":4758,"style":1823},[1500],[1398,4760,4762],{"className":4761},[1494,1649],[1398,4763,4765,4830],{"className":4764},[1599,1600],[1398,4766,4768,4827],{"className":4767},[1604],[1398,4769,4771,4819],{"className":4770,"style":1659},[1608],[1398,4772,4773,4776],{"style":1662},[1398,4774],{"className":4775,"style":1666},[1616],[1398,4777,4779],{"className":4778},[1494],[1398,4780,4782,4785],{"className":4781},[1494],[1398,4783,1432],{"className":4784,"style":1526},[1494,1495],[1398,4786,4788],{"className":4787},[1595],[1398,4789,4791,4811],{"className":4790},[1599,1600],[1398,4792,4794,4808],{"className":4793},[1604],[1398,4795,4797],{"className":4796,"style":1609},[1608],[1398,4798,4799,4802],{"style":1612},[1398,4800],{"className":4801,"style":1617},[1616],[1398,4803,4805],{"className":4804},[1621,1622,1623,1624],[1398,4806,1455],{"className":4807},[1494,1495,1624],[1398,4809,1632],{"className":4810},[1631],[1398,4812,4814],{"className":4813},[1604],[1398,4815,4817],{"className":4816,"style":1639},[1608],[1398,4818],{},[1398,4820,4821,4824],{"style":1713},[1398,4822],{"className":4823,"style":1666},[1616],[1398,4825],{"className":4826,"style":1721},[1720],[1398,4828,1632],{"className":4829},[1631],[1398,4831,4833],{"className":4832},[1604],[1398,4834,4836],{"className":4835,"style":1639},[1608],[1398,4837],{},[1398,4839,1458],{"className":4840},[1645],[1025,4842,4843,4844,4847,4848,4851],{},"真实 CMOS 全加器的 carry 输出往往",[994,4845,4846],{},"天然是反相","的，如果每一级都加反相器恢复极性，会拖慢 carry critical path；所以",[994,4849,4850],{},"让 even \u002F odd 全加器交替使用反相 carry","，省掉 carry 路径上的反相器",[1025,4853,4854],{},[1028,4855],{"alt":1028,"src":4856},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-13.png",[1025,4858,4859,4860,4863],{},"具体实施操作如下图所示",[3237,4861,4862],{},"（从右往左看）","：",[1025,4865,4866],{},[1028,4867],{"alt":1028,"src":4868},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-14.png",[1025,4870,4871],{},"A2,B2 需要以反相信号形式进入 odd cell，这样输出的S2才是正值",[1025,4873,4874,4877,4882,4912],{},[3237,4875,4876],{},"注意：",[3237,4878,4879],{},[994,4880,4881],{},"在",[1398,4883,4885,4899],{"className":4884},[1401],[1398,4886,4888],{"className":4887},[1405],[1407,4889,4890],{"xmlns":1409},[1411,4891,4892,4896],{},[1414,4893,4894],{},[1421,4895,2121],{},[1474,4897,4898],{"encoding":1476},"\\oplus",[1398,4900,4902],{"className":4901,"ariaHidden":1462},[1481],[1398,4903,4905,4909],{"className":4904},[1485],[1398,4906],{"className":4907,"style":4908},[1489],"height:0.6667em;vertical-align:-0.0833em;",[1398,4910,2121],{"className":4911},[1494],[3237,4913,4914],{},[994,4915,4916],{},"符号上的圆圈表示反相输入，并不代表有反相器存在！！",[1366,4918,4920],{"id":4919},"manchester-carry-chain-曼彻斯特加法链","Manchester Carry Chain | 曼彻斯特加法链",[1025,4922,4923],{},[1028,4924],{"alt":1028,"src":4925},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-15.png",[1025,4927,4928],{},"此页左边电路就是在实现这个逻辑：",[1007,4930,4931,5168,5440],{},[990,4932,4933,5026,5027,5096,5097,5167],{},[1398,4934,4936,4958],{"className":4935},[1401],[1398,4937,4939],{"className":4938},[1405],[1407,4940,4941],{"xmlns":1409},[1411,4942,4943,4955],{},[1414,4944,4945,4951,4953],{},[1449,4946,4947,4949],{},[1417,4948,2114],{},[1417,4950,1455],{},[1421,4952,1423],{},[2883,4954,2885],{},[1474,4956,4957],{"encoding":1476},"P_i=1",[1398,4959,4961,5017],{"className":4960,"ariaHidden":1462},[1481],[1398,4962,4964,4967,5008,5011,5014],{"className":4963},[1485],[1398,4965],{"className":4966,"style":1858},[1489],[1398,4968,4970,4973],{"className":4969},[1494],[1398,4971,2114],{"className":4972,"style":2139},[1494,1495],[1398,4974,4976],{"className":4975},[1595],[1398,4977,4979,5000],{"className":4978},[1599,1600],[1398,4980,4982,4997],{"className":4981},[1604],[1398,4983,4985],{"className":4984,"style":1609},[1608],[1398,4986,4988,4991],{"style":4987},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1398,4989],{"className":4990,"style":1617},[1616],[1398,4992,4994],{"className":4993},[1621,1622,1623,1624],[1398,4995,1455],{"className":4996},[1494,1495,1624],[1398,4998,1632],{"className":4999},[1631],[1398,5001,5003],{"className":5002},[1604],[1398,5004,5006],{"className":5005,"style":1639},[1608],[1398,5007],{},[1398,5009],{"className":5010,"style":1501},[1500],[1398,5012,1423],{"className":5013},[1505],[1398,5015],{"className":5016,"style":1501},[1500],[1398,5018,5020,5023],{"className":5019},[1485],[1398,5021],{"className":5022,"style":2992},[1489],[1398,5024,2885],{"className":5025},[1494],"：传输门打开，直接把 ",[1398,5028,5030,5047],{"className":5029},[1401],[1398,5031,5033],{"className":5032},[1405],[1407,5034,5035],{"xmlns":1409},[1411,5036,5037,5045],{},[1414,5038,5039],{},[1449,5040,5041,5043],{},[1417,5042,1432],{},[1417,5044,1455],{},[1474,5046,1848],{"encoding":1476},[1398,5048,5050],{"className":5049,"ariaHidden":1462},[1481],[1398,5051,5053,5056],{"className":5052},[1485],[1398,5054],{"className":5055,"style":1858},[1489],[1398,5057,5059,5062],{"className":5058},[1494],[1398,5060,1432],{"className":5061,"style":1526},[1494,1495],[1398,5063,5065],{"className":5064},[1595],[1398,5066,5068,5088],{"className":5067},[1599,1600],[1398,5069,5071,5085],{"className":5070},[1604],[1398,5072,5074],{"className":5073,"style":1609},[1608],[1398,5075,5076,5079],{"style":1612},[1398,5077],{"className":5078,"style":1617},[1616],[1398,5080,5082],{"className":5081},[1621,1622,1623,1624],[1398,5083,1455],{"className":5084},[1494,1495,1624],[1398,5086,1632],{"className":5087},[1631],[1398,5089,5091],{"className":5090},[1604],[1398,5092,5094],{"className":5093,"style":1639},[1608],[1398,5095],{}," 传到 ",[1398,5098,5100,5118],{"className":5099},[1401],[1398,5101,5103],{"className":5102},[1405],[1407,5104,5105],{"xmlns":1409},[1411,5106,5107,5115],{},[1414,5108,5109],{},[1449,5110,5111,5113],{},[1417,5112,1432],{},[1417,5114,1469],{},[1474,5116,5117],{"encoding":1476},"C_o",[1398,5119,5121],{"className":5120,"ariaHidden":1462},[1481],[1398,5122,5124,5127],{"className":5123},[1485],[1398,5125],{"className":5126,"style":1858},[1489],[1398,5128,5130,5133],{"className":5129},[1494],[1398,5131,1432],{"className":5132,"style":1526},[1494,1495],[1398,5134,5136],{"className":5135},[1595],[1398,5137,5139,5159],{"className":5138},[1599,1600],[1398,5140,5142,5156],{"className":5141},[1604],[1398,5143,5145],{"className":5144,"style":1688},[1608],[1398,5146,5147,5150],{"style":1612},[1398,5148],{"className":5149,"style":1617},[1616],[1398,5151,5153],{"className":5152},[1621,1622,1623,1624],[1398,5154,1469],{"className":5155},[1494,1495,1624],[1398,5157,1632],{"className":5158},[1631],[1398,5160,5162],{"className":5161},[1604],[1398,5163,5165],{"className":5164,"style":1639},[1608],[1398,5166],{},"；",[990,5169,5170,5262,5263,5347,5348,5167],{},[1398,5171,5173,5195],{"className":5172},[1401],[1398,5174,5176],{"className":5175},[1405],[1407,5177,5178],{"xmlns":1409},[1411,5179,5180,5192],{},[1414,5181,5182,5188,5190],{},[1449,5183,5184,5186],{},[1417,5185,1931],{},[1417,5187,1455],{},[1421,5189,1423],{},[2883,5191,2885],{},[1474,5193,5194],{"encoding":1476},"G_i=1",[1398,5196,5198,5253],{"className":5197,"ariaHidden":1462},[1481],[1398,5199,5201,5204,5244,5247,5250],{"className":5200},[1485],[1398,5202],{"className":5203,"style":1858},[1489],[1398,5205,5207,5210],{"className":5206},[1494],[1398,5208,1931],{"className":5209},[1494,1495],[1398,5211,5213],{"className":5212},[1595],[1398,5214,5216,5236],{"className":5215},[1599,1600],[1398,5217,5219,5233],{"className":5218},[1604],[1398,5220,5222],{"className":5221,"style":1609},[1608],[1398,5223,5224,5227],{"style":3634},[1398,5225],{"className":5226,"style":1617},[1616],[1398,5228,5230],{"className":5229},[1621,1622,1623,1624],[1398,5231,1455],{"className":5232},[1494,1495,1624],[1398,5234,1632],{"className":5235},[1631],[1398,5237,5239],{"className":5238},[1604],[1398,5240,5242],{"className":5241,"style":1639},[1608],[1398,5243],{},[1398,5245],{"className":5246,"style":1501},[1500],[1398,5248,1423],{"className":5249},[1505],[1398,5251],{"className":5252,"style":1501},[1500],[1398,5254,5256,5259],{"className":5255},[1485],[1398,5257],{"className":5258,"style":2992},[1489],[1398,5260,2885],{"className":5261},[1494],"：上拉到 ",[1398,5264,5266,5290],{"className":5265},[1401],[1398,5267,5269],{"className":5268},[1405],[1407,5270,5271],{"xmlns":1409},[1411,5272,5273,5287],{},[1414,5274,5275],{},[1449,5276,5277,5280],{},[1417,5278,5279],{},"V",[1414,5281,5282,5285],{},[1417,5283,5284],{},"D",[1417,5286,5284],{},[1474,5288,5289],{"encoding":1476},"V_{DD}",[1398,5291,5293],{"className":5292,"ariaHidden":1462},[1481],[1398,5294,5296,5299],{"className":5295},[1485],[1398,5297],{"className":5298,"style":1858},[1489],[1398,5300,5302,5305],{"className":5301},[1494],[1398,5303,5279],{"className":5304,"style":1530},[1494,1495],[1398,5306,5308],{"className":5307},[1595],[1398,5309,5311,5339],{"className":5310},[1599,1600],[1398,5312,5314,5336],{"className":5313},[1604],[1398,5315,5318],{"className":5316,"style":5317},[1608],"height:0.3283em;",[1398,5319,5321,5324],{"style":5320},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1398,5322],{"className":5323,"style":1617},[1616],[1398,5325,5327],{"className":5326},[1621,1622,1623,1624],[1398,5328,5330,5333],{"className":5329},[1494,1624],[1398,5331,5284],{"className":5332,"style":3654},[1494,1495,1624],[1398,5334,5284],{"className":5335,"style":3654},[1494,1495,1624],[1398,5337,1632],{"className":5338},[1631],[1398,5340,5342],{"className":5341},[1604],[1398,5343,5345],{"className":5344,"style":1639},[1608],[1398,5346],{},"，强制 ",[1398,5349,5351,5373],{"className":5350},[1401],[1398,5352,5354],{"className":5353},[1405],[1407,5355,5356],{"xmlns":1409},[1411,5357,5358,5370],{},[1414,5359,5360,5366,5368],{},[1449,5361,5362,5364],{},[1417,5363,1432],{},[1417,5365,1469],{},[1421,5367,1423],{},[2883,5369,2885],{},[1474,5371,5372],{"encoding":1476},"C_o=1",[1398,5374,5376,5431],{"className":5375,"ariaHidden":1462},[1481],[1398,5377,5379,5382,5422,5425,5428],{"className":5378},[1485],[1398,5380],{"className":5381,"style":1858},[1489],[1398,5383,5385,5388],{"className":5384},[1494],[1398,5386,1432],{"className":5387,"style":1526},[1494,1495],[1398,5389,5391],{"className":5390},[1595],[1398,5392,5394,5414],{"className":5393},[1599,1600],[1398,5395,5397,5411],{"className":5396},[1604],[1398,5398,5400],{"className":5399,"style":1688},[1608],[1398,5401,5402,5405],{"style":1612},[1398,5403],{"className":5404,"style":1617},[1616],[1398,5406,5408],{"className":5407},[1621,1622,1623,1624],[1398,5409,1469],{"className":5410},[1494,1495,1624],[1398,5412,1632],{"className":5413},[1631],[1398,5415,5417],{"className":5416},[1604],[1398,5418,5420],{"className":5419,"style":1639},[1608],[1398,5421],{},[1398,5423],{"className":5424,"style":1501},[1500],[1398,5426,1423],{"className":5427},[1505],[1398,5429],{"className":5430,"style":1501},[1500],[1398,5432,5434,5437],{"className":5433},[1485],[1398,5435],{"className":5436,"style":2992},[1489],[1398,5438,2885],{"className":5439},[1494],[990,5441,5442,5535,5536,5628],{},[1398,5443,5445,5467],{"className":5444},[1401],[1398,5446,5448],{"className":5447},[1405],[1407,5449,5450],{"xmlns":1409},[1411,5451,5452,5464],{},[1414,5453,5454,5460,5462],{},[1449,5455,5456,5458],{},[1417,5457,5284],{},[1417,5459,1455],{},[1421,5461,1423],{},[2883,5463,2885],{},[1474,5465,5466],{"encoding":1476},"D_i=1",[1398,5468,5470,5526],{"className":5469,"ariaHidden":1462},[1481],[1398,5471,5473,5476,5517,5520,5523],{"className":5472},[1485],[1398,5474],{"className":5475,"style":1858},[1489],[1398,5477,5479,5482],{"className":5478},[1494],[1398,5480,5284],{"className":5481,"style":3654},[1494,1495],[1398,5483,5485],{"className":5484},[1595],[1398,5486,5488,5509],{"className":5487},[1599,1600],[1398,5489,5491,5506],{"className":5490},[1604],[1398,5492,5494],{"className":5493,"style":1609},[1608],[1398,5495,5497,5500],{"style":5496},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1398,5498],{"className":5499,"style":1617},[1616],[1398,5501,5503],{"className":5502},[1621,1622,1623,1624],[1398,5504,1455],{"className":5505},[1494,1495,1624],[1398,5507,1632],{"className":5508},[1631],[1398,5510,5512],{"className":5511},[1604],[1398,5513,5515],{"className":5514,"style":1639},[1608],[1398,5516],{},[1398,5518],{"className":5519,"style":1501},[1500],[1398,5521,1423],{"className":5522},[1505],[1398,5524],{"className":5525,"style":1501},[1500],[1398,5527,5529,5532],{"className":5528},[1485],[1398,5530],{"className":5531,"style":2992},[1489],[1398,5533,2885],{"className":5534},[1494],"：下拉到 GND，强制 ",[1398,5537,5539,5561],{"className":5538},[1401],[1398,5540,5542],{"className":5541},[1405],[1407,5543,5544],{"xmlns":1409},[1411,5545,5546,5558],{},[1414,5547,5548,5554,5556],{},[1449,5549,5550,5552],{},[1417,5551,1432],{},[1417,5553,1469],{},[1421,5555,1423],{},[2883,5557,3030],{},[1474,5559,5560],{"encoding":1476},"C_o=0",[1398,5562,5564,5619],{"className":5563,"ariaHidden":1462},[1481],[1398,5565,5567,5570,5610,5613,5616],{"className":5566},[1485],[1398,5568],{"className":5569,"style":1858},[1489],[1398,5571,5573,5576],{"className":5572},[1494],[1398,5574,1432],{"className":5575,"style":1526},[1494,1495],[1398,5577,5579],{"className":5578},[1595],[1398,5580,5582,5602],{"className":5581},[1599,1600],[1398,5583,5585,5599],{"className":5584},[1604],[1398,5586,5588],{"className":5587,"style":1688},[1608],[1398,5589,5590,5593],{"style":1612},[1398,5591],{"className":5592,"style":1617},[1616],[1398,5594,5596],{"className":5595},[1621,1622,1623,1624],[1398,5597,1469],{"className":5598},[1494,1495,1624],[1398,5600,1632],{"className":5601},[1631],[1398,5603,5605],{"className":5604},[1604],[1398,5606,5608],{"className":5607,"style":1639},[1608],[1398,5609],{},[1398,5611],{"className":5612,"style":1501},[1500],[1398,5614,1423],{"className":5615},[1505],[1398,5617],{"className":5618,"style":1501},[1500],[1398,5620,5622,5625],{"className":5621},[1485],[1398,5623],{"className":5624,"style":2992},[1489],[1398,5626,3030],{"className":5627},[1494],"。",[1025,5630,5631,5632],{},"右边本质上是在动态逻辑里实现：",[1398,5633,5635,5683],{"className":5634},[1401],[1398,5636,5638],{"className":5637},[1405],[1407,5639,5640],{"xmlns":1409},[1411,5641,5642,5680],{},[1414,5643,5644,5654,5656,5662,5664,5670],{},[1460,5645,5646,5652],{"accent":1462},[1449,5647,5648,5650],{},[1417,5649,1432],{},[1417,5651,1469],{},[1421,5653,1472],{"stretchy":1462},[1421,5655,1423],{},[1449,5657,5658,5660],{},[1417,5659,5284],{},[1417,5661,1455],{},[1421,5663,1435],{},[1449,5665,5666,5668],{},[1417,5667,2114],{},[1417,5669,1455],{},[1460,5671,5672,5678],{"accent":1462},[1449,5673,5674,5676],{},[1417,5675,1432],{},[1417,5677,1455],{},[1421,5679,1472],{"stretchy":1462},[1474,5681,5682],{"encoding":1476},"\\overline{C_o}=D_i+P_i\\overline{C_i}",[1398,5684,5686,5780,5835],{"className":5685,"ariaHidden":1462},[1481],[1398,5687,5689,5692,5771,5774,5777],{"className":5688},[1485],[1398,5690],{"className":5691,"style":2773},[1489],[1398,5693,5695],{"className":5694},[1494,1649],[1398,5696,5698,5763],{"className":5697},[1599,1600],[1398,5699,5701,5760],{"className":5700},[1604],[1398,5702,5704,5752],{"className":5703,"style":1659},[1608],[1398,5705,5706,5709],{"style":1662},[1398,5707],{"className":5708,"style":1666},[1616],[1398,5710,5712],{"className":5711},[1494],[1398,5713,5715,5718],{"className":5714},[1494],[1398,5716,1432],{"className":5717,"style":1526},[1494,1495],[1398,5719,5721],{"className":5720},[1595],[1398,5722,5724,5744],{"className":5723},[1599,1600],[1398,5725,5727,5741],{"className":5726},[1604],[1398,5728,5730],{"className":5729,"style":1688},[1608],[1398,5731,5732,5735],{"style":1612},[1398,5733],{"className":5734,"style":1617},[1616],[1398,5736,5738],{"className":5737},[1621,1622,1623,1624],[1398,5739,1469],{"className":5740},[1494,1495,1624],[1398,5742,1632],{"className":5743},[1631],[1398,5745,5747],{"className":5746},[1604],[1398,5748,5750],{"className":5749,"style":1639},[1608],[1398,5751],{},[1398,5753,5754,5757],{"style":1713},[1398,5755],{"className":5756,"style":1666},[1616],[1398,5758],{"className":5759,"style":1721},[1720],[1398,5761,1632],{"className":5762},[1631],[1398,5764,5766],{"className":5765},[1604],[1398,5767,5769],{"className":5768,"style":1639},[1608],[1398,5770],{},[1398,5772],{"className":5773,"style":1501},[1500],[1398,5775,1423],{"className":5776},[1505],[1398,5778],{"className":5779,"style":1501},[1500],[1398,5781,5783,5786,5826,5829,5832],{"className":5782},[1485],[1398,5784],{"className":5785,"style":1858},[1489],[1398,5787,5789,5792],{"className":5788},[1494],[1398,5790,5284],{"className":5791,"style":3654},[1494,1495],[1398,5793,5795],{"className":5794},[1595],[1398,5796,5798,5818],{"className":5797},[1599,1600],[1398,5799,5801,5815],{"className":5800},[1604],[1398,5802,5804],{"className":5803,"style":1609},[1608],[1398,5805,5806,5809],{"style":5496},[1398,5807],{"className":5808,"style":1617},[1616],[1398,5810,5812],{"className":5811},[1621,1622,1623,1624],[1398,5813,1455],{"className":5814},[1494,1495,1624],[1398,5816,1632],{"className":5817},[1631],[1398,5819,5821],{"className":5820},[1604],[1398,5822,5824],{"className":5823,"style":1639},[1608],[1398,5825],{},[1398,5827],{"className":5828,"style":1530},[1500],[1398,5830,1435],{"className":5831},[1534],[1398,5833],{"className":5834,"style":1530},[1500],[1398,5836,5838,5841,5881],{"className":5837},[1485],[1398,5839],{"className":5840,"style":2773},[1489],[1398,5842,5844,5847],{"className":5843},[1494],[1398,5845,2114],{"className":5846,"style":2139},[1494,1495],[1398,584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cell 复制 4 次，形成 4-bit carry chain",[1398,5969,5971],{"className":5970},[2737],[1398,5972,5974,6052],{"className":5973},[1401],[1398,5975,5977],{"className":5976},[1405],[1407,5978,5979],{"xmlns":1409,"display":2746},[1411,5980,5981,6049],{},[1414,5982,5983,5999,6001,6011,6013,6023,6025,6036,6038],{},[1460,5984,5985,5997],{"accent":1462},[1449,5986,5987,5989],{},[1417,5988,1432],{},[1414,5990,5991,5993,5995],{},[1417,5992,1455],{},[1421,5994,1797],{"separator":1462},[2883,5996,3030],{},[1421,5998,1472],{"stretchy":1462},[1421,6000,3309],{},[1460,6002,6003,6009],{"accent":1462},[1449,6004,6005,6007],{},[1417,6006,1432],{},[2883,6008,3030],{},[1421,6010,1472],{"stretchy":1462},[1421,6012,3309],{},[1460,6014,6015,6021],{"accent":1462},[1449,6016,6017,6019],{},[1417,6018,1432],{},[2883,6020,2885],{},[1421,6022,1472],{"stretchy":1462},[1421,6024,3309],{},[1460,6026,6027,6034],{"accent":1462},[1449,6028,6029,6031],{},[1417,6030,1432],{},[2883,6032,6033],{},"2",[1421,6035,1472],{"stretchy":1462},[1421,6037,3309],{},[1460,6039,6040,6047],{"accent":1462},[1449,6041,6042,6044],{},[1417,6043,1432],{},[2883,6045,6046],{},"3",[1421,6048,1472],{"stretchy":1462},[1474,6050,6051],{"encoding":1476},"\\overline{C_{i,0}} \\rightarrow \\overline{C_0} \\rightarrow \\overline{C_1} \\rightarrow \\overline{C_2} \\rightarrow \\overline{C_3}",[1398,6053,6055,6159,6254,6348,6442],{"className":6054,"ariaHidden":1462},[1481],[1398,6056,6058,6062,6150,6153,6156],{"className":6057},[1485],[1398,6059],{"className":6060,"style":6061},[1489],"height:1.1694em;vertical-align:-0.2861em;",[1398,6063,6065],{"className":6064},[1494,1649],[1398,6066,6068,6142],{"className":6067},[1599,1600],[1398,6069,6071,6139],{"className":6070},[1604],[1398,6072,6074,6131],{"className":6073,"style":1659},[1608],[1398,6075,6076,6079],{"style":1662},[1398,6077],{"className":6078,"style":1666},[1616],[1398,6080,6082],{"className":6081},[1494],[1398,6083,6085,6088],{"className":6084},[1494],[1398,6086,1432],{"className":6087,"style":1526},[1494,1495],[1398,6089,6091],{"className":6090},[1595],[1398,6092,6094,6123],{"className":6093},[1599,1600],[1398,6095,6097,6120],{"className":6096},[1604],[1398,6098,6100],{"className":6099,"style":1609},[1608],[1398,6101,6102,6105],{"style":1612},[1398,6103],{"className":6104,"style":1617},[1616],[1398,6106,6108],{"className":6107},[1621,1622,1623,1624],[1398,6109,6111,6114,6117],{"className":6110},[1494,1624],[1398,6112,1455],{"className":6113},[1494,1495,1624],[1398,6115,1797],{"className":6116},[1819,1624],[1398,6118,3030],{"className":6119},[1494,1624],[1398,6121,1632],{"className":6122},[1631],[1398,6124,6126],{"className":6125},[1604],[1398,6127,6129],{"className":6128,"style":3765},[1608],[1398,6130],{},[1398,6132,6133,6136],{"style":1713},[1398,6134],{"className":6135,"style":1666},[1616],[1398,6137],{"className":6138,"style":1721},[1720],[1398,6140,1632],{"className":6141},[1631],[1398,6143,6145],{"className":6144},[1604],[1398,6146,6148],{"className":6147,"style":3765},[1608],[1398,6149],{},[1398,6151],{"className":6152,"style":1501},[1500],[1398,6154,3309],{"className":6155},[1505],[1398,6157],{"className":6158,"style":1501},[1500],[1398,6160,6162,6165,6245,6248,6251],{"className":6161},[1485],[1398,6163],{"className":6164,"style":2773},[1489],[1398,6166,6168],{"className":6167},[1494,1649],[1398,6169,6171,6237],{"className":6170},[1599,1600],[1398,6172,6174,6234],{"className":6173},[1604],[1398,6175,6177,6226],{"className":6176,"style":1659},[1608],[1398,6178,6179,6182],{"style":1662},[1398,6180],{"className":6181,"style":1666},[1616],[1398,6183,6185],{"className":6184},[1494],[1398,6186,6188,6191],{"className":6187},[1494],[1398,6189,1432],{"className":6190,"style":1526},[1494,1495],[1398,6192,6194],{"className":6193},[1595],[1398,6195,6197,6218],{"className":6196},[1599,1600],[1398,6198,6200,6215],{"className":6199},[1604],[1398,6201,6204],{"className":6202,"style":6203},[1608],"height:0.3011em;",[1398,6205,6206,6209],{"style":1612},[1398,6207],{"className":6208,"style":1617},[1616],[1398,6210,6212],{"className":6211},[1621,1622,1623,1624],[1398,6213,3030],{"className":6214},[1494,1624],[1398,6216,1632],{"className":6217},[1631],[1398,6219,6221],{"className":6220},[1604],[1398,6222,6224],{"className":6223,"style":1639},[1608],[1398,6225],{},[1398,6227,6228,6231],{"style":1713},[1398,6229],{"className":6230,"style":1666},[1616],[1398,6232],{"className":6233,"style":1721},[1720],[1398,6235,1632],{"className":6236},[1631],[1398,6238,6240],{"className":6239},[1604],[1398,6241,6243],{"className":6242,"style":1639},[1608],[1398,6244],{},[1398,6246],{"className":6247,"style":1501},[1500],[1398,6249,3309],{"className":6250},[1505],[1398,6252],{"className":6253,"style":1501},[1500],[1398,6255,6257,6260,6339,6342,6345],{"className":6256},[1485],[1398,6258],{"className":6259,"style":2773},[1489],[1398,6261,6263],{"className":6262},[1494,1649],[1398,6264,6266,6331],{"className":6265},[1599,1600],[1398,6267,6269,6328],{"className":6268},[1604],[1398,6270,6272,6320],{"className":6271,"style":1659},[1608],[1398,6273,6274,6277],{"style":1662},[1398,6275],{"className":6276,"style":1666},[1616],[1398,6278,6280],{"className":6279},[1494],[1398,6281,6283,6286],{"className":6282},[1494],[1398,6284,1432],{"className":6285,"style":1526},[1494,1495],[1398,6287,6289],{"className":6288},[1595],[1398,6290,6292,6312],{"className":6291},[1599,1600],[1398,6293,6295,6309],{"className":6294},[1604],[1398,6296,6298],{"className":6297,"style":6203},[1608],[1398,6299,6300,6303],{"style":1612},[1398,6301],{"className":6302,"style":1617},[1616],[1398,6304,6306],{"className":6305},[1621,1622,1623,1624],[1398,6307,2885],{"className":6308},[1494,1624],[1398,6310,1632],{"className":6311},[1631],[1398,6313,6315],{"className":6314},[1604],[1398,6316,6318],{"className":6317,"style":1639},[1608],[1398,6319],{},[1398,6321,6322,6325],{"style":1713},[1398,6323],{"className":6324,"style":1666},[1616],[1398,6326],{"className":6327,"style":1721},[1720],[1398,6329,1632],{"className":6330},[1631],[1398,6332,6334],{"className":6333},[1604],[1398,6335,6337],{"className":6336,"style":1639},[1608],[1398,6338],{},[1398,6340],{"className":6341,"style":1501},[1500],[1398,6343,3309],{"className":6344},[1505],[1398,6346],{"className":6347,"style":1501},[1500],[1398,6349,6351,6354,6433,6436,6439],{"className":6350},[1485],[1398,6352],{"className":6353,"style":2773},[1489],[1398,6355,6357],{"className":6356},[1494,1649],[1398,6358,6360,6425],{"className":6359},[1599,1600],[1398,6361,6363,6422],{"className":6362},[1604],[1398,6364,6366,6414],{"className":6365,"style":1659},[1608],[1398,6367,6368,6371],{"style":1662},[1398,6369],{"className":6370,"style":1666},[1616],[1398,6372,6374],{"className":6373},[1494],[1398,6375,6377,6380],{"className":6376},[1494],[1398,6378,1432],{"className":6379,"style":1526},[1494,1495],[1398,6381,6383],{"className":6382},[1595],[1398,6384,6386,6406],{"className":6385},[1599,1600],[1398,6387,6389,6403],{"className":6388},[1604],[1398,6390,6392],{"className":6391,"style":6203},[1608],[1398,6393,6394,6397],{"style":1612},[1398,6395],{"className":6396,"style":1617},[1616],[1398,6398,6400],{"className":6399},[1621,1622,1623,1624],[1398,6401,6033],{"className":6402},[1494,1624],[1398,6404,1632],{"className":6405},[1631],[1398,6407,6409],{"className":6408},[1604],[1398,6410,6412],{"className":6411,"style":1639},[1608],[1398,6413],{},[1398,6415,6416,6419],{"style":1713},[1398,6417],{"className":6418,"style":1666},[1616],[1398,6420],{"className":6421,"style":1721},[1720],[1398,6423,1632],{"className":6424},[1631],[1398,6426,6428],{"className":6427},[1604],[1398,6429,6431],{"className":6430,"style":1639},[1608],[1398,6432],{},[1398,6434],{"className":6435,"style":1501},[1500],[1398,6437,3309],{"className":6438},[1505],[1398,6440],{"className":6441,"style":1501},[1500],[1398,6443,6445,6448],{"className":6444},[1485],[1398,6446],{"className":6447,"style":2773},[1489],[1398,6449,6451],{"className":6450},[1494,1649],[1398,6452,6454,6519],{"className":6453},[1599,1600],[1398,6455,6457,6516],{"className":6456},[1604],[1398,6458,6460,6508],{"className":6459,"style":1659},[1608],[1398,6461,6462,6465],{"style":1662},[1398,6463],{"className":6464,"style":1666},[1616],[1398,6466,6468],{"className":6467},[1494],[1398,6469,6471,6474],{"className":6470},[1494],[1398,6472,1432],{"className":6473,"style":1526},[1494,1495],[1398,6475,6477],{"className":6476},[1595],[1398,6478,6480,6500],{"className":6479},[1599,1600],[1398,6481,6483,6497],{"className":6482},[1604],[1398,6484,6486],{"className":6485,"style":6203},[1608],[1398,6487,6488,6491],{"style":1612},[1398,6489],{"className":6490,"style":1617},[1616],[1398,6492,6494],{"className":6493},[1621,1622,1623,1624],[1398,6495,6046],{"className":6496},[1494,1624],[1398,6498,1632],{"className":6499},[1631],[1398,6501,6503],{"className":6502},[1604],[1398,6504,6506],{"className":6505,"style":1639},[1608],[1398,6507],{},[1398,6509,6510,6513],{"style":1713},[1398,6511],{"className":6512,"style":1666},[1616],[1398,6514],{"className":6515,"style":1721},[1720],[1398,6517,1632],{"className":6518},[1631],[1398,6520,6522],{"className":6521},[1604],[1398,6523,6525],{"className":6524,"style":1639},[1608],[1398,6526],{},[1025,6528,6529],{},"普通 ripple-carry adder 每一位都要经过一个完整 FA 的 carry 逻辑：",[1398,6531,6533],{"className":6532},[2737],[1398,6534,6536,6628],{"className":6535},[1401],[1398,6537,6539],{"className":6538},[1405],[1407,6540,6541],{"xmlns":1409,"display":2746},[1411,6542,6543,6625],{},[1414,6544,6545,6551,6553,6556,6558,6560,6572,6575,6581,6583,6585,6587,6589,6601,6607,6609,6611,6613,6615,6617,6619,6621,6623],{},[1449,6546,6547,6549],{},[1417,6548,1432],{},[1417,6550,1455],{},[1421,6552,3309],{},[1417,6554,6555],{},"F",[1417,6557,1426],{},[1421,6559,3309],{},[1449,6561,6562,6564],{},[1417,6563,1432],{},[1414,6565,6566,6568,6570],{},[1417,6567,1455],{},[1421,6569,1435],{},[2883,6571,2885],{},[1500,6573],{"linebreak":6574},"newline",[1449,6576,6577,6579],{},[1417,6578,1432],{},[1417,6580,1455],{},[1421,6582,3309],{},[1417,6584,6555],{},[1417,6586,1426],{},[1421,6588,3309],{},[1449,6590,6591,6593],{},[1417,6592,1432],{},[1414,6594,6595,6597,6599],{},[1417,6596,1455],{},[1421,6598,1435],{},[2883,6600,2885],{},[1449,6602,6603,6605],{},[1417,6604,1432],{},[1417,6606,1455],{},[1500,6608],{"linebreak":6574},[1421,6610,3309],{},[1417,6612,6555],{},[1417,6614,1426],{},[1421,6616,3309],{},[1417,6618,1432],{},[1417,6620,1455],{},[1421,6622,1435],{},[2883,6624,2885],{},[1474,6626,6627],{"encoding":1476},"C_i→FA→C_{i+1} \\\\    C_i \\rightarrow FA \\rightarrow C_{i+1}C_i \\\\ →FA→Ci+1",[1398,6629,6631,6686,6707,6764,6767,6822,6843,6938,6941,6954,6975,6996],{"className":6630,"ariaHidden":1462},[1481],[1398,6632,6634,6637,6677,6680,6683],{"className":6633},[1485],[1398,6635],{"className":6636,"style":1858},[1489],[1398,6638,6640,6643],{"className":6639},[1494],[1398,6641,1432],{"className":6642,"style":1526},[1494,1495],[1398,6644,6646],{"className":6645},[1595],[1398,6647,6649,6669],{"className":6648},[1599,1600],[1398,6650,6652,6666],{"className":6651},[1604],[1398,6653,6655],{"className":6654,"style":1609},[1608],[1398,6656,6657,6660],{"style":1612},[1398,6658],{"className":6659,"style":1617},[1616],[1398,6661,6663],{"className":6662},[1621,1622,1623,1624],[1398,6664,1455],{"className":6665},[1494,1495,1624],[1398,6667,1632],{"className":6668},[1631],[1398,6670,6672],{"className":6671},[1604],[1398,6673,6675],{"className":6674,"style":1639},[1608],[1398,6676],{},[1398,6678],{"className":6679,"style":1501},[1500],[1398,6681,3309],{"className":6682},[1505],[1398,6684],{"className":6685,"style":1501},[1500],[1398,6687,6689,6692,6695,6698,6701,6704],{"className":6688},[1485],[1398,6690],{"className":6691,"style":1490},[1489],[1398,6693,6555],{"className":6694,"style":2139},[1494,1495],[1398,6696,1426],{"className":6697},[1494,1495],[1398,6699],{"className":6700,"style":1501},[1500],[1398,6702,3309],{"className":6703},[1505],[1398,6705],{"className":6706,"style":1501},[1500],[1398,6708,6710,6714],{"className":6709},[1485],[1398,6711],{"className":6712,"style":6713},[1489],"height:0.8917em;vertical-align:-0.2083em;",[1398,6715,6717,6720],{"className":6716},[1494],[1398,6718,1432],{"className":6719,"style":1526},[1494,1495],[1398,6721,6723],{"className":6722},[1595],[1398,6724,6726,6755],{"className":6725},[1599,1600],[1398,6727,6729,6752],{"className":6728},[1604],[1398,6730,6732],{"className":6731,"style":1609},[1608],[1398,6733,6734,6737],{"style":1612},[1398,6735],{"className":6736,"style":1617},[1616],[1398,6738,6740],{"className":6739},[1621,1622,1623,1624],[1398,6741,6743,6746,6749],{"className":6742},[1494,1624],[1398,6744,1455],{"className":6745},[1494,1495,1624],[1398,6747,1435],{"className":6748},[1534,1624],[1398,6750,2885],{"className":6751},[1494,1624],[1398,6753,1632],{"className":6754},[1631],[1398,6756,6758],{"className":6757},[1604],[1398,6759,6762],{"className":6760,"style":6761},[1608],"height:0.2083em;",[1398,6763],{},[1398,6765],{"className":6766},[1500,6574],[1398,6768,6770,6773,6813,6816,6819],{"className":6769},[1485],[1398,6771],{"className":6772,"style":1858},[1489],[1398,6774,6776,6779],{"className":6775},[1494],[1398,6777,1432],{"className":6778,"style":1526},[1494,1495],[1398,6780,6782],{"className":6781},[1595],[1398,6783,6785,6805],{"className":6784},[1599,1600],[1398,6786,6788,6802],{"className":6787},[1604],[1398,6789,6791],{"className":6790,"style":1609},[1608],[1398,6792,6793,6796],{"style":1612},[1398,6794],{"className":6795,"style":1617},[1616],[1398,6797,6799],{"className":6798},[1621,1622,1623,1624],[1398,6800,1455],{"className":6801},[1494,1495,1624],[1398,6803,1632],{"className":6804},[1631],[1398,6806,6808],{"className":6807},[1604],[1398,6809,6811],{"className":6810,"style":1639},[1608],[1398,6812],{},[1398,6814],{"className":6815,"style":1501},[1500],[1398,6817,3309],{"className":6818},[1505],[1398,6820],{"className":6821,"style":1501},[1500],[1398,6823,6825,6828,6831,6834,6837,6840],{"className":6824},[1485],[1398,6826],{"className":6827,"style":1490},[1489],[1398,6829,6555],{"className":6830,"style":2139},[1494,1495],[1398,6832,1426],{"className":6833},[1494,1495],[1398,6835],{"className":6836,"style":1501},[1500],[1398,6838,3309],{"className":6839},[1505],[1398,6841],{"className":6842,"style":1501},[1500],[1398,6844,6846,6849,6898],{"className":6845},[1485],[1398,6847],{"className":6848,"style":6713},[1489],[1398,6850,6852,6855],{"className":6851},[1494],[1398,6853,1432],{"className":6854,"style":1526},[1494,1495],[1398,6856,6858],{"className":6857},[1595],[1398,6859,6861,6890],{"className":6860},[1599,1600],[1398,6862,6864,6887],{"className":6863},[1604],[1398,6865,6867],{"className":6866,"style":1609},[1608],[1398,6868,6869,6872],{"style":1612},[1398,6870],{"className":6871,"style":1617},[1616],[1398,6873,6875],{"className":6874},[1621,1622,1623,1624],[1398,6876,6878,6881,6884],{"className":6877},[1494,1624],[1398,6879,1455],{"className":6880},[1494,1495,1624],[1398,6882,1435],{"className":6883},[1534,1624],[1398,6885,2885],{"className":6886},[1494,1624],[1398,6888,1632],{"className":6889},[1631],[1398,6891,6893],{"className":6892},[1604],[1398,6894,6896],{"className":6895,"style":6761},[1608],[1398,6897],{},[1398,6899,6901,6904],{"className":6900},[1494],[1398,6902,1432],{"className":6903,"style":1526},[1494,1495],[1398,6905,6907],{"className":6906},[1595],[1398,6908,6910,6930],{"className":6909},[1599,1600],[1398,6911,6913,6927],{"className":6912},[1604],[1398,6914,6916],{"className":6915,"style":1609},[1608],[1398,6917,6918,6921],{"style":1612},[1398,6919],{"className":6920,"style":1617},[1616],[1398,6922,6924],{"className":6923},[1621,1622,1623,1624],[1398,6925,1455],{"className":6926},[1494,1495,1624],[1398,6928,1632],{"className":6929},[1631],[1398,6931,6933],{"className":6932},[1604],[1398,6934,6936],{"className":6935,"style":1639},[1608],[1398,6937],{},[1398,6939],{"className":6940},[1500,6574],[1398,6942,6944,6948,6951],{"className":6943},[1485],[1398,6945],{"className":6946,"style":6947},[1489],"height:0.3669em;",[1398,6949,3309],{"className":6950},[1505],[1398,6952],{"className":6953,"style":1501},[1500],[1398,6955,6957,6960,6963,6966,6969,6972],{"className":6956},[1485],[1398,6958],{"className":6959,"style":1490},[1489],[1398,6961,6555],{"className":6962,"style":2139},[1494,1495],[1398,6964,1426],{"className":6965},[1494,1495],[1398,6967],{"className":6968,"style":1501},[1500],[1398,6970,3309],{"className":6971},[1505],[1398,6973],{"className":6974,"style":1501},[1500],[1398,6976,6978,6981,6984,6987,6990,6993],{"className":6977},[1485],[1398,6979],{"className":6980,"style":1515},[1489],[1398,6982,1432],{"className":6983,"style":1526},[1494,1495],[1398,6985,1455],{"className":6986},[1494,1495],[1398,6988],{"className":6989,"style":1530},[1500],[1398,6991,1435],{"className":6992},[1534],[1398,6994],{"className":6995,"style":1530},[1500],[1398,6997,6999,7002],{"className":6998},[1485],[1398,7000],{"className":7001,"style":2992},[1489],[1398,7003,2885],{"className":7004},[1494],[1025,7006,7007,7008,7133],{},"而Manchester Carry Chain 的思路是：先把 ",[1398,7009,7011,7037],{"className":7010},[1401],[1398,7012,7014],{"className":7013},[1405],[1407,7015,7016],{"xmlns":1409},[1411,7017,7018,7034],{},[1414,7019,7020,7026,7028],{},[1449,7021,7022,7024],{},[1417,7023,1426],{},[1417,7025,1455],{},[1421,7027,1797],{"separator":1462},[1449,7029,7030,7032],{},[1417,7031,1429],{},[1417,7033,1455],{},[1474,7035,7036],{"encoding":1476},"A_i,B_i",[1398,7038,7040],{"className":7039,"ariaHidden":1462},[1481],[1398,7041,7043,7046,7086,7089,7092],{"className":7042},[1485],[1398,7044],{"className":7045,"style":1812},[1489],[1398,7047,7049,7052],{"className":7048},[1494],[1398,7050,1426],{"className":7051},[1494,1495],[1398,7053,7055],{"className":7054},[1595],[1398,7056,7058,7078],{"className":7057},[1599,1600],[1398,7059,7061,7075],{"className":7060},[1604],[1398,7062,7064],{"className":7063,"style":1609},[1608],[1398,7065,7066,7069],{"style":3634},[1398,7067],{"className":7068,"style":1617},[1616],[1398,7070,7072],{"className":7071},[1621,1622,1623,1624],[1398,7073,1455],{"className":7074},[1494,1495,1624],[1398,7076,1632],{"className":7077},[1631],[1398,7079,7081],{"className":7080},[1604],[1398,7082,7084],{"className":7083,"style":1639},[1608],[1398,7085],{},[1398,7087,1797],{"className":7088},[1819],[1398,7090],{"className":7091,"style":1823},[1500],[1398,7093,7095,7098],{"className":7094},[1494],[1398,7096,1429],{"className":7097,"style":1522},[1494,1495],[1398,7099,7101],{"className":7100},[1595],[1398,7102,7104,7125],{"className":7103},[1599,1600],[1398,7105,7107,7122],{"className":7106},[1604],[1398,7108,7110],{"className":7109,"style":1609},[1608],[1398,7111,7113,7116],{"style":7112},"top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;",[1398,7114],{"className":7115,"style":1617},[1616],[1398,7117,7119],{"className":7118},[1621,1622,1623,1624],[1398,7120,1455],{"className":7121},[1494,1495,1624],[1398,7123,1632],{"className":7124},[1631],[1398,7126,7128],{"className":7127},[1604],[1398,7129,7131],{"className":7130,"style":1639},[1608],[1398,7132],{}," 提前变成控制信号",[1398,7135,7137],{"className":7136},[2737],[1398,7138,7140,7172],{"className":7139},[1401],[1398,7141,7143],{"className":7142},[1405],[1407,7144,7145],{"xmlns":1409,"display":2746},[1411,7146,7147,7169],{},[1414,7148,7149,7155,7157,7163],{},[1449,7150,7151,7153],{},[1417,7152,1931],{},[1417,7154,1455],{},[1421,7156,1423],{},[1449,7158,7159,7161],{},[1417,7160,1426],{},[1417,7162,1455],{},[1449,7164,7165,7167],{},[1417,7166,1429],{},[1417,7168,1455],{},[1474,7170,7171],{"encoding":1476},"G_i=A_iB_i",[1398,7173,7175,7230],{"className":7174,"ariaHidden":1462},[1481],[1398,7176,7178,7181,7221,7224,7227],{"className":7177},[1485],[1398,7179],{"className":7180,"style":1858},[1489],[1398,7182,7184,7187],{"className":7183},[1494],[1398,7185,1931],{"className":7186},[1494,1495],[1398,7188,7190],{"className":7189},[1595],[1398,7191,7193,7213],{"className":7192},[1599,1600],[1398,7194,7196,7210],{"className":7195},[1604],[1398,7197,7199],{"className":7198,"style":1609},[1608],[1398,7200,7201,7204],{"style":3634},[1398,7202],{"className":7203,"style":1617},[1616],[1398,7205,7207],{"className":7206},[1621,1622,1623,1624],[1398,7208,1455],{"className":7209},[1494,1495,1624],[1398,7211,1632],{"className":7212},[1631],[1398,7214,7216],{"className":7215},[1604],[1398,7217,7219],{"className":7218,"style":1639},[1608],[1398,7220],{},[1398,7222],{"className":7223,"style":1501},[1500],[1398,7225,1423],{"className":7226},[1505],[1398,7228],{"className":7229,"style":1501},[1500],[1398,7231,7233,7236,7276],{"className":7232},[1485],[1398,7234],{"className":7235,"style":1858},[1489],[1398,7237,7239,7242],{"className":7238},[1494],[1398,7240,1426],{"className":7241},[1494,1495],[1398,7243,7245],{"className":7244},[1595],[1398,7246,7248,7268],{"className":7247},[1599,1600],[1398,7249,7251,7265],{"className":7250},[1604],[1398,7252,7254],{"className":7253,"style":1609},[1608],[1398,7255,7256,7259],{"style":3634},[1398,7257],{"className":7258,"style":1617},[1616],[1398,7260,7262],{"className":7261},[1621,1622,1623,1624],[1398,7263,1455],{"className":7264},[1494,1495,1624],[1398,7266,1632],{"className":7267},[1631],[1398,7269,7271],{"className":7270},[1604],[1398,7272,7274],{"className":7273,"style":1639},[1608],[1398,7275],{},[1398,7277,7279,7282],{"className":7278},[1494],[1398,7280,1429],{"className":7281,"style":1522},[1494,1495],[1398,7283,7285],{"className":7284},[1595],[1398,7286,7288,7308],{"className":7287},[1599,1600],[1398,7289,7291,7305],{"className":7290},[1604],[1398,7292,7294],{"className":7293,"style":1609},[1608],[1398,7295,7296,7299],{"style":7112},[1398,7297],{"className":7298,"style":1617},[1616],[1398,7300,7302],{"className":7301},[1621,1622,1623,1624],[1398,7303,1455],{"className":7304},[1494,1495,1624],[1398,7306,1632],{"className":7307},[1631],[1398,7309,7311],{"className":7310},[1604],[1398,7312,7314],{"className":7313,"style":1639},[1608],[1398,7315],{},[1398,7317,7319],{"className":7318},[2737],[1398,7320,7322,7356],{"className":7321},[1401],[1398,7323,7325],{"className":7324},[1405],[1407,7326,7327],{"xmlns":1409,"display":2746},[1411,7328,7329,7353],{},[1414,7330,7331,7337,7339,7345,7347],{},[1449,7332,7333,7335],{},[1417,7334,2114],{},[1417,7336,1455],{},[1421,7338,1423],{},[1449,7340,7341,7343],{},[1417,7342,1426],{},[1417,7344,1455],{},[1421,7346,2121],{},[1449,7348,7349,7351],{},[1417,7350,1429],{},[1417,7352,1455],{},[1474,7354,7355],{"encoding":1476},"P_i=A_i\\oplus B_i",[1398,7357,7359,7414,7469],{"className":7358,"ariaHidden":1462},[1481],[1398,7360,7362,7365,7405,7408,7411],{"className":7361},[1485],[1398,7363],{"className":7364,"style":1858},[1489],[1398,7366,7368,7371],{"className":7367},[1494],[1398,7369,2114],{"className":7370,"style":2139},[1494,1495],[1398,7372,7374],{"className":7373},[1595],[1398,7375,7377,7397],{"className":7376},[1599,1600],[1398,7378,7380,7394],{"className":7379},[1604],[1398,7381,7383],{"className":7382,"style":1609},[1608],[1398,7384,7385,7388],{"style":4987},[1398,7386],{"className":7387,"style":1617},[1616],[1398,7389,7391],{"className":7390},[1621,1622,1623,1624],[1398,7392,1455],{"className":7393},[1494,1495,1624],[1398,7395,1632],{"className":7396},[1631],[1398,7398,7400],{"className":7399},[1604],[1398,7401,7403],{"className":7402,"style":1639},[1608],[1398,7404],{},[1398,7406],{"className":7407,"style":1501},[1500],[1398,7409,1423],{"className":7410},[1505],[1398,7412],{"className":7413,"style":1501},[1500],[1398,7415,7417,7420,7460,7463,7466],{"className":7416},[1485],[1398,7418],{"className":7419,"style":1858},[1489],[1398,7421,7423,7426],{"className":7422},[1494],[1398,7424,1426],{"className":7425},[1494,1495],[1398,7427,7429],{"className":7428},[1595],[1398,7430,7432,7452],{"className":7431},[1599,1600],[1398,7433,7435,7449],{"className":7434},[1604],[1398,7436,7438],{"className":7437,"style":1609},[1608],[1398,7439,7440,7443],{"style":3634},[1398,7441],{"className":7442,"style":1617},[1616],[1398,7444,7446],{"className":7445},[1621,1622,1623,1624],[1398,7447,1455],{"className":7448},[1494,1495,1624],[1398,7450,1632],{"className":7451},[1631],[1398,7453,7455],{"className":7454},[1604],[1398,7456,7458],{"className":7457,"style":1639},[1608],[1398,7459],{},[1398,7461],{"className":7462,"style":1530},[1500],[1398,7464,2121],{"className":7465},[1534],[1398,7467],{"className":7468,"style":1530},[1500],[1398,7470,7472,7475],{"className":7471},[1485],[1398,7473],{"className":7474,"style":1858},[1489],[1398,7476,7478,7481],{"className":7477},[1494],[1398,7479,1429],{"className":7480,"style":1522},[1494,1495],[1398,7482,7484],{"className":7483},[1595],[1398,7485,7487,7507],{"className":7486},[1599,1600],[1398,7488,7490,7504],{"className":7489},[1604],[1398,7491,7493],{"className":7492,"style":1609},[1608],[1398,7494,7495,7498],{"style":7112},[1398,7496],{"className":7497,"style":1617},[1616],[1398,7499,7501],{"className":7500},[1621,1622,1623,1624],[1398,7502,1455],{"className":7503},[1494,1495,1624],[1398,7505,1632],{"className":7506},[1631],[1398,7508,7510],{"className":7509},[1604],[1398,7511,7513],{"className":7512,"style":1639},[1608],[1398,7514],{},[1398,7516,7518],{"className":7517},[2737],[1398,7519,7521,7561],{"className":7520},[1401],[1398,7522,7524],{"className":7523},[1405],[1407,7525,7526],{"xmlns":1409,"display":2746},[1411,7527,7528,7558],{},[1414,7529,7530,7536,7538,7548],{},[1449,7531,7532,7534],{},[1417,7533,5284],{},[1417,7535,1455],{},[1421,7537,1423],{},[1460,7539,7540,7546],{"accent":1462},[1449,7541,7542,7544],{},[1417,7543,1426],{},[1417,7545,1455],{},[1421,7547,1472],{"stretchy":1462},[1460,7549,7550,7556],{"accent":1462},[1449,7551,7552,7554],{},[1417,7553,1429],{},[1417,7555,1455],{},[1421,7557,1472],{"stretchy":1462},[1474,7559,7560],{"encoding":1476},"D_i=\\overline{A_i}\\overline{B_i}",[1398,7562,7564,7619],{"className":7563,"ariaHidden":1462},[1481],[1398,7565,7567,7570,7610,7613,7616],{"className":7566},[1485],[1398,7568],{"className":7569,"style":1858},[1489],[1398,7571,7573,7576],{"className":7572},[1494],[1398,7574,5284],{"className":7575,"style":3654},[1494,1495],[1398,7577,7579],{"className":7578},[1595],[1398,7580,7582,7602],{"className":7581},[1599,1600],[1398,7583,7585,7599],{"className":7584},[1604],[1398,7586,7588],{"className":7587,"style":1609},[1608],[1398,7589,7590,7593],{"style":5496},[1398,7591],{"className":7592,"style":1617},[1616],[1398,7594,7596],{"className":7595},[1621,1622,1623,1624],[1398,7597,1455],{"className":7598},[1494,1495,1624],[1398,7600,1632],{"className":7601},[1631],[1398,7603,7605],{"className":7604},[1604],[1398,7606,7608],{"className":7607,"style":1639},[1608],[1398,7609],{},[1398,7611],{"className":7612,"style":1501},[1500],[1398,7614,1423],{"className":7615},[1505],[1398,7617],{"className":7618,"style":1501},[1500],[1398,7620,7622,7625,7704],{"className":7621},[1485],[1398,7623],{"className":7624,"style":2773},[1489],[1398,7626,7628],{"className":7627},[1494,1649],[1398,7629,7631,7696],{"className":7630},[1599,1600],[1398,7632,7634,7693],{"className":7633},[1604],[1398,7635,7637,7685],{"className":7636,"style":1659},[1608],[1398,7638,7639,7642],{"style":1662},[1398,7640],{"className":7641,"style":1666},[1616],[1398,7643,7645],{"className":7644},[1494],[1398,7646,7648,7651],{"className":7647},[1494],[1398,7649,1426],{"className":7650},[1494,1495],[1398,7652,7654],{"className":7653},[1595],[1398,7655,7657,7677],{"className":7656},[1599,1600],[1398,7658,7660,7674],{"className":7659},[1604],[1398,7661,7663],{"className":7662,"style":1609},[1608],[1398,7664,7665,7668],{"style":3634},[1398,7666],{"className":7667,"style":1617},[1616],[1398,7669,7671],{"className":7670},[1621,1622,1623,1624],[1398,7672,1455],{"className":7673},[1494,1495,1624],[1398,7675,1632],{"className":7676},[1631],[1398,7678,7680],{"className":7679},[1604],[1398,7681,7683],{"className":7682,"style":1639},[1608],[1398,7684],{},[1398,7686,7687,7690],{"style":1713},[1398,7688],{"className":7689,"style":1666},[1616],[1398,7691],{"className":7692,"style":1721},[1720],[1398,7694,1632],{"className":7695},[1631],[1398,7697,7699],{"className":7698},[1604],[1398,7700,7702],{"className":7701,"style":1639},[1608],[1398,7703],{},[1398,7705,7707],{"className":7706},[1494,1649],[1398,7708,7710,7775],{"className":7709},[1599,1600],[1398,7711,7713,7772],{"className":7712},[1604],[1398,7714,7716,7764],{"className":7715,"style":1659},[1608],[1398,7717,7718,7721],{"style":1662},[1398,7719],{"className":7720,"style":1666},[1616],[1398,7722,7724],{"className":7723},[1494],[1398,7725,7727,7730],{"className":7726},[1494],[1398,7728,1429],{"className":7729,"style":1522},[1494,1495],[1398,7731,7733],{"className":7732},[1595],[1398,7734,7736,7756],{"className":7735},[1599,1600],[1398,7737,7739,7753],{"className":7738},[1604],[1398,7740,7742],{"className":7741,"style":1609},[1608],[1398,7743,7744,7747],{"style":7112},[1398,7745],{"className":7746,"style":1617},[1616],[1398,7748,7750],{"className":7749},[1621,1622,1623,1624],[1398,7751,1455],{"className":7752},[1494,1495,1624],[1398,7754,1632],{"className":7755},[1631],[1398,7757,7759],{"className":7758},[1604],[1398,7760,7762],{"className":7761,"style":1639},[1608],[1398,7763],{},[1398,7765,7766,7769],{"style":1713},[1398,7767],{"className":7768,"style":1666},[1616],[1398,7770],{"className":7771,"style":1721},[1720],[1398,7773,1632],{"className":7774},[1631],[1398,7776,7778],{"className":7777},[1604],[1398,7779,7781],{"className":7780,"style":1639},[1608],[1398,7782],{},[1025,7784,7785,7786,7789],{},"这些都先预计算好（",[994,7787,7788],{},"在 carry 到来之前就可以算好","），然后再来计算carry链",[1025,7791,7792,7795,7800],{},[3237,7793,7794],{},"但是如果所有位都是 propagate，那 carry 还是要穿过很多 pass transistor。链太长时，RC 延迟会变大，信号也可能变弱，",[3237,7796,7797],{},[994,7798,7799],{},"所以 Manchester carry chain 通常适合做一小段高速 carry 链。","  长位宽还要配合分段、buffer、carry-bypass、carry-lookahead 等结构。",[1366,7802,7804],{"id":7803},"carry-bypass-adder-进位旁路跳过加法器","Carry-Bypass Adder ｜ 进位旁路\u002F跳过加法器",[1025,7806,7807],{},[1028,7808],{"alt":1028,"src":7809},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-17.png",[1025,7811,7812,7813,7894],{},"这个核心思想就是，如果P=1,那进位的输入就等于输出，如果有连续的一个block都是P=1的话，那么实际上就可以直接旁路一开始的",[1398,7814,7816,7839],{"className":7815},[1401],[1398,7817,7819],{"className":7818},[1405],[1407,7820,7821],{"xmlns":1409},[1411,7822,7823,7836],{},[1414,7824,7825,7827,7829],{},[1417,7826,1432],{},[1417,7828,1455],{},[1449,7830,7831,7834],{},[1417,7832,7833],{},"n",[2883,7835,3030],{},[1474,7837,7838],{"encoding":1476},"Cin_0",[1398,7840,7842],{"className":7841,"ariaHidden":1462},[1481],[1398,7843,7845,7848,7851,7854],{"className":7844},[1485],[1398,7846],{"className":7847,"style":1858},[1489],[1398,7849,1432],{"className":7850,"style":1526},[1494,1495],[1398,7852,1455],{"className":7853},[1494,1495],[1398,7855,7857,7860],{"className":7856},[1494],[1398,7858,7833],{"className":7859},[1494,1495],[1398,7861,7863],{"className":7862},[1595],[1398,7864,7866,7886],{"className":7865},[1599,1600],[1398,7867,7869,7883],{"className":7868},[1604],[1398,7870,7872],{"className":7871,"style":6203},[1608],[1398,7873,7874,7877],{"style":3634},[1398,7875],{"className":7876,"style":1617},[1616],[1398,7878,7880],{"className":7879},[1621,1622,1623,1624],[1398,7881,3030],{"className":7882},[1494,1624],[1398,7884,1632],{"className":7885},[1631],[1398,7887,7889],{"className":7888},[1604],[1398,7890,7892],{"className":7891,"style":1639},[1608],[1398,7893],{},"，直接传输过来，节省了四个FA的运算时间（以上图作为例子）",[1025,7896,7897],{},[994,7898,7899],{},"如果整个 block（比如选取四个FA作为一个Block） 都是 propagate，就直接跳过；否则说明 block 内部某一位会产生或杀死进位，就走普通 ripple 结果。",[1025,7901,7902],{},[1028,7903],{"alt":1028,"src":7904},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-18.png",[1025,7906,7907],{},"那么这个延迟时间计算：",[1398,7909,7911],{"className":7910},[2737],[1398,7912,7914,8061],{"className":7913},[1401],[1398,7915,7917],{"className":7916},[1405],[1407,7918,7919],{"xmlns":1409,"display":2746},[1411,7920,7921,8058],{},[1414,7922,7923,7939,7941,7957,7959,7962,7978,7980,7997,8016,8018,8020,8022,8024,8026,8028,8044,8046],{},[1449,7924,7925,7927],{},[1417,7926,3534],{},[1414,7928,7929,7931,7933,7935,7937],{},[1417,7930,3539],{},[1417,7932,3542],{},[1417,7934,3542],{},[1417,7936,3547],{},[1417,7938,3550],{},[1421,7940,1423],{},[1449,7942,7943,7945],{},[1417,7944,3534],{},[1414,7946,7947,7949,7951,7953,7955],{},[1417,7948,3593],{},[1417,7950,3547],{},[1417,7952,3534],{},[1417,7954,3596],{},[1417,7956,1025],{},[1421,7958,1435],{},[1417,7960,7961],{},"M",[1449,7963,7964,7966],{},[1417,7965,3534],{},[1414,7967,7968,7970,7972,7974,7976],{},[1417,7969,3573],{},[1417,7971,3539],{},[1417,7973,3550],{},[1417,7975,3550],{},[1417,7977,3582],{},[1421,7979,1435],{},[1414,7981,7982,7984,7991,7993,7995],{},[1421,7983,1439],{"fence":1462},[7985,7986,7987,7989],"mfrac",{},[1417,7988,3557],{},[1417,7990,7961],{},[1421,7992,3560],{},[2883,7994,6033],{},[1421,7996,1458],{"fence":1462},[1449,7998,7999,8001],{},[1417,8000,3534],{},[1414,8002,8003,8006,8008,8010,8012,8014],{},[1417,8004,8005],{},"b",[1417,8007,3582],{},[1417,8009,1025],{},[1417,8011,3539],{},[1417,8013,3593],{},[1417,8015,3593],{},[1421,8017,1435],{},[1421,8019,1439],{"stretchy":1438},[1417,8021,7961],{},[1421,8023,3560],{},[2883,8025,2885],{},[1421,8027,1458],{"stretchy":1438},[1449,8029,8030,8032],{},[1417,8031,3534],{},[1414,8033,8034,8036,8038,8040,8042],{},[1417,8035,3573],{},[1417,8037,3539],{},[1417,8039,3550],{},[1417,8041,3550],{},[1417,8043,3582],{},[1421,8045,1435],{},[1449,8047,8048,8050],{},[1417,8049,3534],{},[1414,8051,8052,8054,8056],{},[1417,8053,3593],{},[1417,8055,3596],{},[1417,8057,3599],{},[1474,8059,8060],{"encoding":1476},"t_{adder}=t_{setup}+Mt_{carry}+\\left(\\frac{N}{M}-2\\right)t_{bypass}+(M-1)t_{carry}+t_{sum}",[1398,8062,8064,8128,8197,8271,8445,8466,8542],{"className":8063,"ariaHidden":1462},[1481],[1398,8065,8067,8070,8119,8122,8125],{"className":8066},[1485],[1398,8068],{"className":8069,"style":3612},[1489],[1398,8071,8073,8076],{"className":8072},[1494],[1398,8074,3534],{"className":8075},[1494,1495],[1398,8077,8079],{"className":8078},[1595],[1398,8080,8082,8111],{"className":8081},[1599,1600],[1398,8083,8085,8108],{"className":8084},[1604],[1398,8086,8088],{"className":8087,"style":3631},[1608],[1398,8089,8090,8093],{"style":3634},[1398,8091],{"className":8092,"style":1617},[1616],[1398,8094,8096],{"className":8095},[1621,1622,1623,1624],[1398,8097,8099,8102,8105],{"className":8098},[1494,1624],[1398,8100,3539],{"className":8101},[1494,1495,1624],[1398,8103,3650],{"className":8104},[1494,1495,1624],[1398,8106,3655],{"className":8107,"style":3654},[1494,1495,1624],[1398,8109,1632],{"className":8110},[1631],[1398,8112,8114],{"className":8113},[1604],[1398,8115,8117],{"className":8116,"style":1639},[1608],[1398,8118],{},[1398,8120],{"className":8121,"style":1501},[1500],[1398,8123,1423],{"className":8124},[1505],[1398,8126],{"className":8127,"style":1501},[1500],[1398,8129,8131,8134,8188,8191,8194],{"className":8130},[1485],[1398,8132],{"className":8133,"style":3875},[1489],[1398,8135,8137,8140],{"className":8136},[1494],[1398,8138,3534],{"className":8139},[1494,1495],[1398,8141,8143],{"className":8142},[1595],[1398,8144,8146,8180],{"className":8145},[1599,1600],[1398,8147,8149,8177],{"className":8148},[1604],[1398,8150,8153],{"className":8151,"style":8152},[1608],"height:0.2806em;",[1398,8154,8155,8158],{"style":3634},[1398,8156],{"className":8157,"style":1617},[1616],[1398,8159,8161],{"className":8160},[1621,1622,1623,1624],[1398,8162,8164,8168,8171,8174],{"className":8163},[1494,1624],[1398,8165,8167],{"className":8166},[1494,1495,1624],"se",[1398,8169,3534],{"className":8170},[1494,1495,1624],[1398,8172,3596],{"className":8173},[1494,1495,1624],[1398,8175,1025],{"className":8176},[1494,1495,1624],[1398,8178,1632],{"className":8179},[1631],[1398,8181,8183],{"className":8182},[1604],[1398,8184,8186],{"className":8185,"style":3765},[1608],[1398,8187],{},[1398,8189],{"className":8190,"style":1530},[1500],[1398,8192,1435],{"className":8193},[1534],[1398,8195],{"className":8196,"style":1530},[1500],[1398,8198,8200,8204,8207,8262,8265,8268],{"className":8199},[1485],[1398,8201],{"className":8202,"style":8203},[1489],"height:0.9694em;vertical-align:-0.2861em;",[1398,8205,7961],{"className":8206,"style":3688},[1494,1495],[1398,8208,8210,8213],{"className":8209},[1494],[1398,8211,3534],{"className":8212},[1494,1495],[1398,8214,8216],{"className":8215},[1595],[1398,8217,8219,8254],{"className":8218},[1599,1600],[1398,8220,8222,8251],{"className":8221},[1604],[1398,8223,8225],{"className":8224,"style":1688},[1608],[1398,8226,8227,8230],{"style":3634},[1398,8228],{"className":8229,"style":1617},[1616],[1398,8231,8233],{"className":8232},[1621,1622,1623,1624],[1398,8234,8236,8239,8242,8245,8248],{"className":8235},[1494,1624],[1398,8237,3573],{"className":8238},[1494,1495,1624],[1398,8240,3539],{"className":8241},[1494,1495,1624],[1398,8243,3550],{"className":8244,"style":3654},[1494,1495,1624],[1398,8246,3550],{"className":8247,"style":3654},[1494,1495,1624],[1398,8249,3582],{"className":8250,"style":3755},[1494,1495,1624],[1398,8252,1632],{"className":8253},[1631],[1398,8255,8257],{"className":8256},[1604],[1398,8258,8260],{"className":8259,"style":3765},[1608],[1398,8261],{},[1398,8263],{"className":8264,"style":1530},[1500],[1398,8266,1435],{"className":8267},[1534],[1398,8269],{"className":8270,"style":1530},[1500],[1398,8272,8274,8278,8377,8380,8436,8439,8442],{"className":8273},[1485],[1398,8275],{"className":8276,"style":8277},[1489],"height:2.4em;vertical-align:-0.95em;",[1398,8279,8281,8290,8359,8362,8365,8368,8371],{"className":8280},[3510],[1398,8282,8286],{"className":8283,"style":8285},[1548,8284],"delimcenter","top:0em;",[1398,8287,1439],{"className":8288},[8289,1623],"delimsizing",[1398,8291,8293,8297,8356],{"className":8292},[1494],[1398,8294],{"className":8295},[1548,8296],"nulldelimiter",[1398,8298,8300],{"className":8299},[7985],[1398,8301,8303,8347],{"className":8302},[1599,1600],[1398,8304,8306,8344],{"className":8305},[1604],[1398,8307,8310,8322,8332],{"className":8308,"style":8309},[1608],"height:1.3603em;",[1398,8311,8313,8316],{"style":8312},"top:-2.314em;",[1398,8314],{"className":8315,"style":1666},[1616],[1398,8317,8319],{"className":8318},[1494],[1398,8320,7961],{"className":8321,"style":3688},[1494,1495],[1398,8323,8325,8328],{"style":8324},"top:-3.23em;",[1398,8326],{"className":8327,"style":1666},[1616],[1398,8329],{"className":8330,"style":1721},[8331],"frac-line",[1398,8333,8335,8338],{"style":8334},"top:-3.677em;",[1398,8336],{"className":8337,"style":1666},[1616],[1398,8339,8341],{"className":8340},[1494],[1398,8342,3557],{"className":8343,"style":3688},[1494,1495],[1398,8345,1632],{"className":8346},[1631],[1398,8348,8350],{"className":8349},[1604],[1398,8351,8354],{"className":8352,"style":8353},[1608],"height:0.686em;",[1398,8355],{},[1398,8357],{"className":8358},[1645,8296],[1398,8360],{"className":8361,"style":1530},[1500],[1398,8363,3560],{"className":8364},[1534],[1398,8366],{"className":8367,"style":1530},[1500],[1398,8369,6033],{"className":8370},[1494],[1398,8372,8374],{"className":8373,"style":8285},[1645,8284],[1398,8375,1458],{"className":8376},[8289,1623],[1398,8378],{"className":8379,"style":1823},[1500],[1398,8381,8383,8386],{"className":8382},[1494],[1398,8384,3534],{"className":8385},[1494,1495],[1398,8387,8389],{"className":8388},[1595],[1398,8390,8392,8428],{"className":8391},[1599,1600],[1398,8393,8395,8425],{"className":8394},[1604],[1398,8396,8398],{"className":8397,"style":3631},[1608],[1398,8399,8400,8403],{"style":3634},[1398,8401],{"className":8402,"style":1617},[1616],[1398,8404,8406],{"className":8405},[1621,1622,1623,1624],[1398,8407,8409,8412,8415,8418,8421],{"className":8408},[1494,1624],[1398,8410,8005],{"className":8411},[1494,1495,1624],[1398,8413,3582],{"className":8414,"style":3755},[1494,1495,1624],[1398,8416,1025],{"className":8417},[1494,1495,1624],[1398,8419,3539],{"className":8420},[1494,1495,1624],[1398,8422,8424],{"className":8423},[1494,1495,1624],"ss",[1398,8426,1632],{"className":8427},[1631],[1398,8429,8431],{"className":8430},[1604],[1398,8432,8434],{"className":8433,"style":3765},[1608],[1398,8435],{},[1398,8437],{"className":8438,"style":1530},[1500],[1398,8440,1435],{"className":8441},[1534],[1398,8443],{"className":8444,"style":1530},[1500],[1398,8446,8448,8451,8454,8457,8460,8463],{"className":8447},[1485],[1398,8449],{"className":8450,"style":1544},[1489],[1398,8452,1439],{"className":8453},[1548],[1398,8455,7961],{"className":8456,"style":3688},[1494,1495],[1398,8458],{"className":8459,"style":1530},[1500],[1398,8461,3560],{"className":8462},[1534],[1398,8464],{"className":8465,"style":1530},[1500],[1398,8467,8469,8472,8475,8478,8533,8536,8539],{"className":8468},[1485],[1398,8470],{"className":8471,"style":3704},[1489],[1398,8473,2885],{"className":8474},[1494],[1398,8476,1458],{"className":8477},[1645],[1398,8479,8481,8484],{"className":8480},[1494],[1398,8482,3534],{"className":8483},[1494,1495],[1398,8485,8487],{"className":8486},[1595],[1398,8488,8490,8525],{"className":8489},[1599,1600],[1398,8491,8493,8522],{"className":8492},[1604],[1398,8494,8496],{"className":8495,"style":1688},[1608],[1398,8497,8498,8501],{"style":3634},[1398,8499],{"className":8500,"style":1617},[1616],[1398,8502,8504],{"className":8503},[1621,1622,1623,1624],[1398,8505,8507,8510,8513,8516,8519],{"className":8506},[1494,1624],[1398,8508,3573],{"className":8509},[1494,1495,1624],[1398,8511,3539],{"className":8512},[1494,1495,1624],[1398,8514,3550],{"className":8515,"style":3654},[1494,1495,1624],[1398,8517,3550],{"className":8518,"style":3654},[1494,1495,1624],[1398,8520,3582],{"className":8521,"style":3755},[1494,1495,1624],[1398,8523,1632],{"className":8524},[1631],[1398,8526,8528],{"className":8527},[1604],[1398,8529,8531],{"className":8530,"style":3765},[1608],[1398,8532],{},[1398,8534],{"className":8535,"style":1530},[1500],[1398,8537,1435],{"className":8538},[1534],[1398,8540],{"className":8541,"style":1530},[1500],[1398,8543,8545,8548],{"className":8544},[1485],[1398,8546],{"className":8547,"style":3612},[1489],[1398,8549,8551,8554],{"className":8550},[1494],[1398,8552,3534],{"className":8553},[1494,1495],[1398,8555,8557],{"className":8556},[1595],[1398,8558,8560,8589],{"className":8559},[1599,1600],[1398,8561,8563,8586],{"className":8562},[1604],[1398,8564,8566],{"className":8565,"style":1688},[1608],[1398,8567,8568,8571],{"style":3634},[1398,8569],{"className":8570,"style":1617},[1616],[1398,8572,8574],{"className":8573},[1621,1622,1623,1624],[1398,8575,8577,8580,8583],{"className":8576},[1494,1624],[1398,8578,3593],{"className":8579},[1494,1495,1624],[1398,8581,3596],{"className":8582},[1494,1495,1624],[1398,8584,3599],{"className":8585},[1494,1495,1624],[1398,8587,1632],{"className":8588},[1631],[1398,8590,8592],{"className":8591},[1604],[1398,8593,8595],{"className":8594,"style":1639},[1608],[1398,8596],{},[1025,8598,8599],{},"这里：",[1007,8601,8602,8633,8664,8902,8999,9099],{},[990,8603,8604,8632],{},[1398,8605,8607,8620],{"className":8606},[1401],[1398,8608,8610],{"className":8609},[1405],[1407,8611,8612],{"xmlns":1409},[1411,8613,8614,8618],{},[1414,8615,8616],{},[1417,8617,3557],{},[1474,8619,3557],{"encoding":1476},[1398,8621,8623],{"className":8622,"ariaHidden":1462},[1481],[1398,8624,8626,8629],{"className":8625},[1485],[1398,8627],{"className":8628,"style":1490},[1489],[1398,8630,3557],{"className":8631,"style":3688},[1494,1495],"：总位数，比如 16 bit；",[990,8634,8635,8663],{},[1398,8636,8638,8651],{"className":8637},[1401],[1398,8639,8641],{"className":8640},[1405],[1407,8642,8643],{"xmlns":1409},[1411,8644,8645,8649],{},[1414,8646,8647],{},[1417,8648,7961],{},[1474,8650,7961],{"encoding":1476},[1398,8652,8654],{"className":8653,"ariaHidden":1462},[1481],[1398,8655,8657,8660],{"className":8656},[1485],[1398,8658],{"className":8659,"style":1490},[1489],[1398,8661,7961],{"className":8662,"style":3688},[1494,1495],"：每个 block 的位数，比如 4 bit；",[990,8665,8666,8758,8759,8901],{},[1398,8667,8669,8697],{"className":8668},[1401],[1398,8670,8672],{"className":8671},[1405],[1407,8673,8674],{"xmlns":1409},[1411,8675,8676,8694],{},[1414,8677,8678],{},[1449,8679,8680,8682],{},[1417,8681,3534],{},[1414,8683,8684,8686,8688,8690,8692],{},[1417,8685,3593],{},[1417,8687,3547],{},[1417,8689,3534],{},[1417,8691,3596],{},[1417,8693,1025],{},[1474,8695,8696],{"encoding":1476},"t_{setup}",[1398,8698,8700],{"className":8699,"ariaHidden":1462},[1481],[1398,8701,8703,8706],{"className":8702},[1485],[1398,8704],{"className":8705,"style":3875},[1489],[1398,8707,8709,8712],{"className":8708},[1494],[1398,8710,3534],{"className":8711},[1494,1495],[1398,8713,8715],{"className":8714},[1595],[1398,8716,8718,8750],{"className":8717},[1599,1600],[1398,8719,8721,8747],{"className":8720},[1604],[1398,8722,8724],{"className":8723,"style":8152},[1608],[1398,8725,8726,8729],{"style":3634},[1398,8727],{"className":8728,"style":1617},[1616],[1398,8730,8732],{"className":8731},[1621,1622,1623,1624],[1398,8733,8735,8738,8741,8744],{"className":8734},[1494,1624],[1398,8736,8167],{"className":8737},[1494,1495,1624],[1398,8739,3534],{"className":8740},[1494,1495,1624],[1398,8742,3596],{"className":8743},[1494,1495,1624],[1398,8745,1025],{"className":8746},[1494,1495,1624],[1398,8748,1632],{"className":8749},[1631],[1398,8751,8753],{"className":8752},[1604],[1398,8754,8756],{"className":8755,"style":3765},[1608],[1398,8757],{},"：提前算 ",[1398,8760,8762,8794],{"className":8761},[1401],[1398,8763,8765],{"className":8764},[1405],[1407,8766,8767],{"xmlns":1409},[1411,8768,8769,8791],{},[1414,8770,8771,8777,8779,8785,8787,8789],{},[1449,8772,8773,8775],{},[1417,8774,2114],{},[1417,8776,1455],{},[1421,8778,1797],{"separator":1462},[1449,8780,8781,8783],{},[1417,8782,1931],{},[1417,8784,1455],{},[1421,8786,1797],{"separator":1462},[1417,8788,1429],{},[1417,8790,2114],{},[1474,8792,8793],{"encoding":1476},"P_i,G_i,BP",[1398,8795,8797],{"className":8796,"ariaHidden":1462},[1481],[1398,8798,8800,8803,8843,8846,8849,8889,8892,8895,8898],{"className":8799},[1485],[1398,8801],{"className":8802,"style":1812},[1489],[1398,8804,8806,8809],{"className":8805},[1494],[1398,8807,2114],{"className":8808,"style":2139},[1494,1495],[1398,8810,8812],{"className":8811},[1595],[1398,8813,8815,8835],{"className":8814},[1599,1600],[1398,8816,8818,8832],{"className":8817},[1604],[1398,8819,8821],{"className":8820,"style":1609},[1608],[1398,8822,8823,8826],{"style":4987},[1398,8824],{"className":8825,"style":1617},[1616],[1398,8827,8829],{"className":8828},[1621,1622,1623,1624],[1398,8830,1455],{"className":8831},[1494,1495,1624],[1398,8833,1632],{"className":8834},[1631],[1398,8836,8838],{"className":8837},[1604],[1398,8839,8841],{"className":8840,"style":1639},[1608],[1398,8842],{},[1398,8844,1797],{"className":8845},[1819],[1398,8847],{"className":8848,"style":1823},[1500],[1398,8850,8852,8855],{"className":8851},[1494],[1398,8853,1931],{"className":8854},[1494,1495],[1398,8856,8858],{"className":8857},[1595],[1398,8859,8861,8881],{"className":8860},[1599,1600],[1398,8862,8864,8878],{"className":8863},[1604],[1398,8865,8867],{"className":8866,"style":1609},[1608],[1398,8868,8869,8872],{"style":3634},[1398,8870],{"className":8871,"style":1617},[1616],[1398,8873,8875],{"className":8874},[1621,1622,1623,1624],[1398,8876,1455],{"className":8877},[1494,1495,1624],[1398,8879,1632],{"className":8880},[1631],[1398,8882,8884],{"className":8883},[1604],[1398,8885,8887],{"className":8886,"style":1639},[1608],[1398,8888],{},[1398,8890,1797],{"className":8891},[1819],[1398,8893],{"className":8894,"style":1823},[1500],[1398,8896,1429],{"className":8897,"style":1522},[1494,1495],[1398,8899,2114],{"className":8900,"style":2139},[1494,1495]," 的时间；",[990,8903,8904,8998],{},[1398,8905,8907,8934],{"className":8906},[1401],[1398,8908,8910],{"className":8909},[1405],[1407,8911,8912],{"xmlns":1409},[1411,8913,8914,8932],{},[1414,8915,8916],{},[1449,8917,8918,8920],{},[1417,8919,3534],{},[1414,8921,8922,8924,8926,8928,8930],{},[1417,8923,3573],{},[1417,8925,3539],{},[1417,8927,3550],{},[1417,8929,3550],{},[1417,8931,3582],{},[1474,8933,3865],{"encoding":1476},[1398,8935,8937],{"className":8936,"ariaHidden":1462},[1481],[1398,8938,8940,8943],{"className":8939},[1485],[1398,8941],{"className":8942,"style":3875},[1489],[1398,8944,8946,8949],{"className":8945},[1494],[1398,8947,3534],{"className":8948},[1494,1495],[1398,8950,8952],{"className":8951},[1595],[1398,8953,8955,8990],{"className":8954},[1599,1600],[1398,8956,8958,8987],{"className":8957},[1604],[1398,8959,8961],{"className":8960,"style":1688},[1608],[1398,8962,8963,8966],{"style":3634},[1398,8964],{"className":8965,"style":1617},[1616],[1398,8967,8969],{"className":8968},[1621,1622,1623,1624],[1398,8970,8972,8975,8978,8981,8984],{"className":8971},[1494,1624],[1398,8973,3573],{"className":8974},[1494,1495,1624],[1398,8976,3539],{"className":8977},[1494,1495,1624],[1398,8979,3550],{"className":8980,"style":3654},[1494,1495,1624],[1398,8982,3550],{"className":8983,"style":3654},[1494,1495,1624],[1398,8985,3582],{"className":8986,"style":3755},[1494,1495,1624],[1398,8988,1632],{"className":8989},[1631],[1398,8991,8993],{"className":8992},[1604],[1398,8994,8996],{"className":8995,"style":3765},[1608],[1398,8997],{},"：carry 经过一位 FA 的时间；",[990,9000,9001,9098],{},[1398,9002,9004,9034],{"className":9003},[1401],[1398,9005,9007],{"className":9006},[1405],[1407,9008,9009],{"xmlns":1409},[1411,9010,9011,9031],{},[1414,9012,9013],{},[1449,9014,9015,9017],{},[1417,9016,3534],{},[1414,9018,9019,9021,9023,9025,9027,9029],{},[1417,9020,8005],{},[1417,9022,3582],{},[1417,9024,1025],{},[1417,9026,3539],{},[1417,9028,3593],{},[1417,9030,3593],{},[1474,9032,9033],{"encoding":1476},"t_{bypass}",[1398,9035,9037],{"className":9036,"ariaHidden":1462},[1481],[1398,9038,9040,9043],{"className":9039},[1485],[1398,9041],{"className":9042,"style":3875},[1489],[1398,9044,9046,9049],{"className":9045},[1494],[1398,9047,3534],{"className":9048},[1494,1495],[1398,9050,9052],{"className":9051},[1595],[1398,9053,9055,9090],{"className":9054},[1599,1600],[1398,9056,9058,9087],{"className":9057},[1604],[1398,9059,9061],{"className":9060,"style":3631},[1608],[1398,9062,9063,9066],{"style":3634},[1398,9064],{"className":9065,"style":1617},[1616],[1398,9067,9069],{"className":9068},[1621,1622,1623,1624],[1398,9070,9072,9075,9078,9081,9084],{"className":9071},[1494,1624],[1398,9073,8005],{"className":9074},[1494,1495,1624],[1398,9076,3582],{"className":9077,"style":3755},[1494,1495,1624],[1398,9079,1025],{"className":9080},[1494,1495,1624],[1398,9082,3539],{"className":9083},[1494,1495,1624],[1398,9085,8424],{"className":9086},[1494,1495,1624],[1398,9088,1632],{"className":9089},[1631],[1398,9091,9093],{"className":9092},[1604],[1398,9094,9096],{"className":9095,"style":3765},[1608],[1398,9097],{},"：carry 经过一个 bypass MUX 的时间；",[990,9100,9101,9185],{},[1398,9102,9104,9127],{"className":9103},[1401],[1398,9105,9107],{"className":9106},[1405],[1407,9108,9109],{"xmlns":1409},[1411,9110,9111,9125],{},[1414,9112,9113],{},[1449,9114,9115,9117],{},[1417,9116,3534],{},[1414,9118,9119,9121,9123],{},[1417,9120,3593],{},[1417,9122,3596],{},[1417,9124,3599],{},[1474,9126,3962],{"encoding":1476},[1398,9128,9130],{"className":9129,"ariaHidden":1462},[1481],[1398,9131,9133,9136],{"className":9132},[1485],[1398,9134],{"className":9135,"style":3612},[1489],[1398,9137,9139,9142],{"className":9138},[1494],[1398,9140,3534],{"className":9141},[1494,1495],[1398,9143,9145],{"className":9144},[1595],[1398,9146,9148,9177],{"className":9147},[1599,1600],[1398,9149,9151,9174],{"className":9150},[1604],[1398,9152,9154],{"className":9153,"style":1688},[1608],[1398,9155,9156,9159],{"style":3634},[1398,9157],{"className":9158,"style":1617},[1616],[1398,9160,9162],{"className":9161},[1621,1622,1623,1624],[1398,9163,9165,9168,9171],{"className":9164},[1494,1624],[1398,9166,3593],{"className":9167},[1494,1495,1624],[1398,9169,3596],{"className":9170},[1494,1495,1624],[1398,9172,3599],{"className":9173},[1494,1495,1624],[1398,9175,1632],{"className":9176},[1631],[1398,9178,9180],{"className":9179},[1604],[1398,9181,9183],{"className":9182,"style":1639},[1608],[1398,9184],{},"：最后生成 sum 的时间。",[9187,9188,9190,9193,9500,9506,10267],"alert",{"type":9189},"tip",[1025,9191,9192],{},"这个公式怎么得出来的（为什么上面的这个式子是最坏情况）：",[1025,9194,9195,9267,9268,9340,9341],{},[1398,9196,9198,9219],{"className":9197},[1401],[1398,9199,9201],{"className":9200},[1405],[1407,9202,9203],{"xmlns":1409},[1411,9204,9205,9217],{},[1414,9206,9207,9209,9211,9213,9215],{},[1417,9208,2114],{},[1421,9210,1423],{},[1417,9212,1426],{},[1421,9214,2121],{},[1417,9216,1429],{},[1474,9218,2126],{"encoding":1476},[1398,9220,9222,9240,9258],{"className":9221,"ariaHidden":1462},[1481],[1398,9223,9225,9228,9231,9234,9237],{"className":9224},[1485],[1398,9226],{"className":9227,"style":1490},[1489],[1398,9229,2114],{"className":9230,"style":2139},[1494,1495],[1398,9232],{"className":9233,"style":1501},[1500],[1398,9235,1423],{"className":9236},[1505],[1398,9238],{"className":9239,"style":1501},[1500],[1398,9241,9243,9246,9249,9252,9255],{"className":9242},[1485],[1398,9244],{"className":9245,"style":1515},[1489],[1398,9247,1426],{"className":9248},[1494,1495],[1398,9250],{"className":9251,"style":1530},[1500],[1398,9253,2121],{"className":9254},[1534],[1398,9256],{"className":9257,"style":1530},[1500],[1398,9259,9261,9264],{"className":9260},[1485],[1398,9262],{"className":9263,"style":1490},[1489],[1398,9265,1429],{"className":9266,"style":1522},[1494,1495],", ",[1398,9269,9271,9292],{"className":9270},[1401],[1398,9272,9274],{"className":9273},[1405],[1407,9275,9276],{"xmlns":1409},[1411,9277,9278,9290],{},[1414,9279,9280,9282,9284,9286,9288],{},[1417,9281,1931],{},[1421,9283,1423],{},[1417,9285,1426],{},[1421,9287,1938],{},[1417,9289,1429],{},[1474,9291,1943],{"encoding":1476},[1398,9293,9295,9313,9331],{"className":9294,"ariaHidden":1462},[1481],[1398,9296,9298,9301,9304,9307,9310],{"className":9297},[1485],[1398,9299],{"className":9300,"style":1490},[1489],[1398,9302,1931],{"className":9303},[1494,1495],[1398,9305],{"className":9306,"style":1501},[1500],[1398,9308,1423],{"className":9309},[1505],[1398,9311],{"className":9312,"style":1501},[1500],[1398,9314,9316,9319,9322,9325,9328],{"className":9315},[1485],[1398,9317],{"className":9318,"style":1490},[1489],[1398,9320,1426],{"className":9321},[1494,1495],[1398,9323],{"className":9324,"style":1530},[1500],[1398,9326,1938],{"className":9327},[1534],[1398,9329],{"className":9330,"style":1530},[1500],[1398,9332,9334,9337],{"className":9333},[1485],[1398,9335],{"className":9336,"style":1490},[1489],[1398,9338,1429],{"className":9339,"style":1522},[1494,1495],"，",[1398,9342,9344,9375],{"className":9343},[1401],[1398,9345,9347],{"className":9346},[1405],[1407,9348,9349],{"xmlns":1409},[1411,9350,9351,9373],{},[1414,9352,9353,9359,9361,9363,9365,9367],{},[1449,9354,9355,9357],{},[1417,9356,1432],{},[1417,9358,1469],{},[1421,9360,1423],{},[1417,9362,1931],{},[1421,9364,1435],{},[1417,9366,2114],{},[1449,9368,9369,9371],{},[1417,9370,1432],{},[1417,9372,1455],{},[1474,9374,2372],{"encoding":1476},[1398,9376,9378,9433,9451],{"className":9377,"ariaHidden":1462},[1481],[1398,9379,9381,9384,9424,9427,9430],{"className":9380},[1485],[1398,9382],{"className":9383,"style":1858},[1489],[1398,9385,9387,9390],{"className":9386},[1494],[1398,9388,1432],{"className":9389,"style":1526},[1494,1495],[1398,9391,9393],{"className":9392},[1595],[1398,9394,9396,9416],{"className":9395},[1599,1600],[1398,9397,9399,9413],{"className":9398},[1604],[1398,9400,9402],{"className":9401,"style":1688},[1608],[1398,9403,9404,9407],{"style":1612},[1398,9405],{"className":9406,"style":1617},[1616],[1398,9408,9410],{"className":9409},[1621,1622,1623,1624],[1398,9411,1469],{"className":9412},[1494,1495,1624],[1398,9414,1632],{"className":9415},[1631],[1398,9417,9419],{"className":9418},[1604],[1398,9420,9422],{"className":9421,"style":1639},[1608],[1398,9423],{},[1398,9425],{"className":9426,"style":1501},[1500],[1398,9428,1423],{"className":9429},[1505],[1398,9431],{"className":9432,"style":1501},[1500],[1398,9434,9436,9439,9442,9445,9448],{"className":9435},[1485],[1398,9437],{"className":9438,"style":1515},[1489],[1398,9440,1931],{"className":9441},[1494,1495],[1398,9443],{"className":9444,"style":1530},[1500],[1398,9446,1435],{"className":9447},[1534],[1398,9449],{"className":9450,"style":1530},[1500],[1398,9452,9454,9457,9460],{"className":9453},[1485],[1398,9455],{"className":9456,"style":1858},[1489],[1398,9458,2114],{"className":9459,"style":2139},[1494,1495],[1398,9461,9463,9466],{"className":9462},[1494],[1398,9464,1432],{"className":9465,"style":1526},[1494,1495],[1398,9467,9469],{"className":9468},[1595],[1398,9470,9472,9492],{"className":9471},[1599,1600],[1398,9473,9475,9489],{"className":9474},[1604],[1398,9476,9478],{"className":9477,"style":1609},[1608],[1398,9479,9480,9483],{"style":1612},[1398,9481],{"className":9482,"style":1617},[1616],[1398,9484,9486],{"className":9485},[1621,1622,1623,1624],[1398,9487,1455],{"className":9488},[1494,1495,1624],[1398,9490,1632],{"className":9491},[1631],[1398,9493,9495],{"className":9494},[1604],[1398,9496,9498],{"className":9497,"style":1639},[1608],[1398,9499],{},[1025,9501,9502,9503],{},"如果P=1，那么G=0一定成立，所以这个时候Cin =  Cout，",[3237,9504,9505],{},"但如果P=0，那么Co=G,此时就和这一级之前的加法器电路完全无关了，前面的延时不会被加进来",[1025,9507,9508,9509,9512,9513,9698,9699,9916,9917,10049,10050,10181,10182,10266],{},"所以说，",[3237,9510,9511],{},"如果考虑Carry Bypass最坏情况下，应该是，第一个FA电路是P=0，无跳过的；剩下中间N\u002FM-2个FA加法器都走Bypass路径（最后一个加法器不用管进位输出了）","，那么这样时间就好算了：\n",[1398,9514,9516,9564],{"className":9515},[1401],[1398,9517,9519],{"className":9518},[1405],[1407,9520,9521],{"xmlns":1409},[1411,9522,9523,9561],{},[1414,9524,9525,9541,9543,9545],{},[1449,9526,9527,9529],{},[1417,9528,3534],{},[1414,9530,9531,9533,9535,9537,9539],{},[1417,9532,3593],{},[1417,9534,3547],{},[1417,9536,3534],{},[1417,9538,3596],{},[1417,9540,1025],{},[1421,9542,1435],{},[1417,9544,7961],{},[1449,9546,9547,9549],{},[1417,9548,3534],{},[1414,9550,9551,9553,9555,9557,9559],{},[1417,9552,3573],{},[1417,9554,3539],{},[1417,9556,3550],{},[1417,9558,3550],{},[1417,9560,3582],{},[1474,9562,9563],{"encoding":1476},"t_{setup}+Mt_{carry}",[1398,9565,9567,9634],{"className":9566,"ariaHidden":1462},[1481],[1398,9568,9570,9573,9625,9628,9631],{"className":9569},[1485],[1398,9571],{"className":9572,"style":3875},[1489],[1398,9574,9576,9579],{"className":9575},[1494],[1398,9577,3534],{"className":9578},[1494,1495],[1398,9580,9582],{"className":9581},[1595],[1398,9583,9585,9617],{"className":9584},[1599,1600],[1398,9586,9588,9614],{"className":9587},[1604],[1398,9589,9591],{"className":9590,"style":8152},[1608],[1398,9592,9593,9596],{"style":3634},[1398,9594],{"className":9595,"style":1617},[1616],[1398,9597,9599],{"className":9598},[1621,1622,1623,1624],[1398,9600,9602,9605,9608,9611],{"className":9601},[1494,1624],[1398,9603,8167],{"className":9604},[1494,1495,1624],[1398,9606,3534],{"className":9607},[1494,1495,1624],[1398,9609,3596],{"className":9610},[1494,1495,1624],[1398,9612,1025],{"className":9613},[1494,1495,1624],[1398,9615,1632],{"className":9616},[1631],[1398,9618,9620],{"className":9619},[1604],[1398,9621,9623],{"className":9622,"style":3765},[1608],[1398,9624],{},[1398,9626],{"className":9627,"style":1530},[1500],[1398,9629,1435],{"className":9630},[1534],[1398,9632],{"className":9633,"style":1530},[1500],[1398,9635,9637,9640,9643],{"className":9636},[1485],[1398,9638],{"className":9639,"style":8203},[1489],[1398,9641,7961],{"className":9642,"style":3688},[1494,1495],[1398,9644,9646,9649],{"className":9645},[1494],[1398,9647,3534],{"className":9648},[1494,1495],[1398,9650,9652],{"className":9651},[1595],[1398,9653,9655,9690],{"className":9654},[1599,1600],[1398,9656,9658,9687],{"className":9657},[1604],[1398,9659,9661],{"className":9660,"style":1688},[1608],[1398,9662,9663,9666],{"style":3634},[1398,9664],{"className":9665,"style":1617},[1616],[1398,9667,9669],{"className":9668},[1621,1622,1623,1624],[1398,9670,9672,9675,9678,9681,9684],{"className":9671},[1494,1624],[1398,9673,3573],{"className":9674},[1494,1495,1624],[1398,9676,3539],{"className":9677},[1494,1495,1624],[1398,9679,3550],{"className":9680,"style":3654},[1494,1495,1624],[1398,9682,3550],{"className":9683,"style":3654},[1494,1495,1624],[1398,9685,3582],{"className":9686,"style":3755},[1494,1495,1624],[1398,9688,1632],{"className":9689},[1631],[1398,9691,9693],{"className":9692},[1604],[1398,9694,9696],{"className":9695,"style":3765},[1608],[1398,9697],{}," 是第一个FA的时间，",[1398,9700,9702,9748],{"className":9701},[1401],[1398,9703,9705],{"className":9704},[1405],[1407,9706,9707],{"xmlns":1409},[1411,9708,9709,9745],{},[1414,9710,9711,9727],{},[1414,9712,9713,9715,9721,9723,9725],{},[1421,9714,1439],{"fence":1462},[7985,9716,9717,9719],{},[1417,9718,3557],{},[1417,9720,7961],{},[1421,9722,3560],{},[2883,9724,6033],{},[1421,9726,1458],{"fence":1462},[1449,9728,9729,9731],{},[1417,9730,3534],{},[1414,9732,9733,9735,9737,9739,9741,9743],{},[1417,9734,8005],{},[1417,9736,3582],{},[1417,9738,1025],{},[1417,9740,3539],{},[1417,9742,3593],{},[1417,9744,3593],{},[1474,9746,9747],{"encoding":1476},"\\left(\\frac{N}{M}-2\\right)t_{bypass}",[1398,9749,9751],{"className":9750,"ariaHidden":1462},[1481],[1398,9752,9754,9758,9858,9861],{"className":9753},[1485],[1398,9755],{"className":9756,"style":9757},[1489],"height:1.2223em;vertical-align:-0.35em;",[1398,9759,9761,9768,9840,9843,9846,9849,9852],{"className":9760},[3510],[1398,9762,9764],{"className":9763,"style":8285},[1548,8284],[1398,9765,1439],{"className":9766},[8289,9767],"size1",[1398,9769,9771,9774,9837],{"className":9770},[1494],[1398,9772],{"className":9773},[1548,8296],[1398,9775,9777],{"className":9776},[7985],[1398,9778,9780,9828],{"className":9779},[1599,1600],[1398,9781,9783,9825],{"className":9782},[1604],[1398,9784,9787,9802,9810],{"className":9785,"style":9786},[1608],"height:0.8723em;",[1398,9788,9790,9793],{"style":9789},"top:-2.655em;",[1398,9791],{"className":9792,"style":1666},[1616],[1398,9794,9796],{"className":9795},[1621,1622,1623,1624],[1398,9797,9799],{"className":9798},[1494,1624],[1398,9800,7961],{"className":9801,"style":3688},[1494,1495,1624],[1398,9803,9804,9807],{"style":8324},[1398,9805],{"className":9806,"style":1666},[1616],[1398,9808],{"className":9809,"style":1721},[8331],[1398,9811,9813,9816],{"style":9812},"top:-3.394em;",[1398,9814],{"className":9815,"style":1666},[1616],[1398,9817,9819],{"className":9818},[1621,1622,1623,1624],[1398,9820,9822],{"className":9821},[1494,1624],[1398,9823,3557],{"className":9824,"style":3688},[1494,1495,1624],[1398,9826,1632],{"className":9827},[1631],[1398,9829,9831],{"className":9830},[1604],[1398,9832,9835],{"className":9833,"style":9834},[1608],"height:0.345em;",[1398,9836],{},[1398,9838],{"className":9839},[1645,8296],[1398,9841],{"className":9842,"style":1530},[1500],[1398,9844,3560],{"className":9845},[1534],[1398,9847],{"className":9848,"style":1530},[1500],[1398,9850,6033],{"className":9851},[1494],[1398,9853,9855],{"className":9854,"style":8285},[1645,8284],[1398,9856,1458],{"className":9857},[8289,9767],[1398,9859],{"className":9860,"style":1823},[1500],[1398,9862,9864,9867],{"className":9863},[1494],[1398,9865,3534],{"className":9866},[1494,1495],[1398,9868,9870],{"className":9869},[1595],[1398,9871,9873,9908],{"className":9872},[1599,1600],[1398,9874,9876,9905],{"className":9875},[1604],[1398,9877,9879],{"className":9878,"style":3631},[1608],[1398,9880,9881,9884],{"style":3634},[1398,9882],{"className":9883,"style":1617},[1616],[1398,9885,9887],{"className":9886},[1621,1622,1623,1624],[1398,9888,9890,9893,9896,9899,9902],{"className":9889},[1494,1624],[1398,9891,8005],{"className":9892},[1494,1495,1624],[1398,9894,3582],{"className":9895,"style":3755},[1494,1495,1624],[1398,9897,1025],{"className":9898},[1494,1495,1624],[1398,9900,3539],{"className":9901},[1494,1495,1624],[1398,9903,8424],{"className":9904},[1494,1495,1624],[1398,9906,1632],{"className":9907},[1631],[1398,9909,9911],{"className":9910},[1604],[1398,9912,9914],{"className":9913,"style":3765},[1608],[1398,9915],{},"是中间N\u002FM-2个FA加法器 的时间，",[1398,9918,9920,9958],{"className":9919},[1401],[1398,9921,9923],{"className":9922},[1405],[1407,9924,9925],{"xmlns":1409},[1411,9926,9927,9955],{},[1414,9928,9929,9931,9933,9935,9937,9939],{},[1421,9930,1439],{"stretchy":1438},[1417,9932,7961],{},[1421,9934,3560],{},[2883,9936,2885],{},[1421,9938,1458],{"stretchy":1438},[1449,9940,9941,9943],{},[1417,9942,3534],{},[1414,9944,9945,9947,9949,9951,9953],{},[1417,9946,3573],{},[1417,9948,3539],{},[1417,9950,3550],{},[1417,9952,3550],{},[1417,9954,3582],{},[1474,9956,9957],{"encoding":1476},"(M-1)t_{carry}",[1398,9959,9961,9982],{"className":9960,"ariaHidden":1462},[1481],[1398,9962,9964,9967,9970,9973,9976,9979],{"className":9963},[1485],[1398,9965],{"className":9966,"style":1544},[1489],[1398,9968,1439],{"className":9969},[1548],[1398,9971,7961],{"className":9972,"style":3688},[1494,1495],[1398,9974],{"className":9975,"style":1530},[1500],[1398,9977,3560],{"className":9978},[1534],[1398,9980],{"className":9981,"style":1530},[1500],[1398,9983,9985,9988,9991,9994],{"className":9984},[1485],[1398,9986],{"className":9987,"style":3704},[1489],[1398,9989,2885],{"className":9990},[1494],[1398,9992,1458],{"className":9993},[1645],[1398,9995,9997,10000],{"className":9996},[1494],[1398,9998,3534],{"className":9999},[1494,1495],[1398,10001,10003],{"className":10002},[1595],[1398,10004,10006,10041],{"className":10005},[1599,1600],[1398,10007,10009,10038],{"className":10008},[1604],[1398,10010,10012],{"className":10011,"style":1688},[1608],[1398,10013,10014,10017],{"style":3634},[1398,10015],{"className":10016,"style":1617},[1616],[1398,10018,10020],{"className":10019},[1621,1622,1623,1624],[1398,10021,10023,10026,10029,10032,10035],{"className":10022},[1494,1624],[1398,10024,3573],{"className":10025},[1494,1495,1624],[1398,10027,3539],{"className":10028},[1494,1495,1624],[1398,10030,3550],{"className":10031,"style":3654},[1494,1495,1624],[1398,10033,3550],{"className":10034,"style":3654},[1494,1495,1624],[1398,10036,3582],{"className":10037,"style":3755},[1494,1495,1624],[1398,10039,1632],{"className":10040},[1631],[1398,10042,10044],{"className":10043},[1604],[1398,10045,10047],{"className":10046,"style":3765},[1608],[1398,10048],{},"是对于最后一个加法器，实际上只需要计算剩余的M-1 个位就可以了，第M位是用来计算输出的进位的，但这个不在我们考虑范围内（我们只考虑sum的结果，不考虑sum的进位），所以是",[1398,10051,10053,10090],{"className":10052},[1401],[1398,10054,10056],{"className":10055},[1405],[1407,10057,10058],{"xmlns":1409},[1411,10059,10060,10088],{},[1414,10061,10062,10064,10066,10068,10070,10072],{},[1421,10063,1439],{"stretchy":1438},[1417,10065,7961],{},[1421,10067,3560],{},[2883,10069,2885],{},[1421,10071,1458],{"stretchy":1438},[1449,10073,10074,10076],{},[1417,10075,3534],{},[1414,10077,10078,10080,10082,10084,10086],{},[1417,10079,3573],{},[1417,10081,3539],{},[1417,10083,3550],{},[1417,10085,3550],{},[1417,10087,3582],{},[1474,10089,9957],{"encoding":1476},[1398,10091,10093,10114],{"className":10092,"ariaHidden":1462},[1481],[1398,10094,10096,10099,10102,10105,10108,10111],{"className":10095},[1485],[1398,10097],{"className":10098,"style":1544},[1489],[1398,10100,1439],{"className":10101},[1548],[1398,10103,7961],{"className":10104,"style":3688},[1494,1495],[1398,10106],{"className":10107,"style":1530},[1500],[1398,10109,3560],{"className":10110},[1534],[1398,10112],{"className":10113,"style":1530},[1500],[1398,10115,10117,10120,10123,10126],{"className":10116},[1485],[1398,10118],{"className":10119,"style":3704},[1489],[1398,10121,2885],{"className":10122},[1494],[1398,10124,1458],{"className":10125},[1645],[1398,10127,10129,10132],{"className":10128},[1494],[1398,10130,3534],{"className":10131},[1494,1495],[1398,10133,10135],{"className":10134},[1595],[1398,10136,10138,10173],{"className":10137},[1599,1600],[1398,10139,10141,10170],{"className":10140},[1604],[1398,10142,10144],{"className":10143,"style":1688},[1608],[1398,10145,10146,10149],{"style":3634},[1398,10147],{"className":10148,"style":1617},[1616],[1398,10150,10152],{"className":10151},[1621,1622,1623,1624],[1398,10153,10155,10158,10161,10164,10167],{"className":10154},[1494,1624],[1398,10156,3573],{"className":10157},[1494,1495,1624],[1398,10159,3539],{"className":10160},[1494,1495,1624],[1398,10162,3550],{"className":10163,"style":3654},[1494,1495,1624],[1398,10165,3550],{"className":10166,"style":3654},[1494,1495,1624],[1398,10168,3582],{"className":10169,"style":3755},[1494,1495,1624],[1398,10171,1632],{"className":10172},[1631],[1398,10174,10176],{"className":10175},[1604],[1398,10177,10179],{"className":10178,"style":3765},[1608],[1398,10180],{},",最后再加上sum的计算时间",[1398,10183,10185,10208],{"className":10184},[1401],[1398,10186,10188],{"className":10187},[1405],[1407,10189,10190],{"xmlns":1409},[1411,10191,10192,10206],{},[1414,10193,10194],{},[1449,10195,10196,10198],{},[1417,10197,3534],{},[1414,10199,10200,10202,10204],{},[1417,10201,3593],{},[1417,10203,3596],{},[1417,10205,3599],{},[1474,10207,3962],{"encoding":1476},[1398,10209,10211],{"className":10210,"ariaHidden":1462},[1481],[1398,10212,10214,10217],{"className":10213},[1485],[1398,10215],{"className":10216,"style":3612},[1489],[1398,10218,10220,10223],{"className":10219},[1494],[1398,10221,3534],{"className":10222},[1494,1495],[1398,10224,10226],{"className":10225},[1595],[1398,10227,10229,10258],{"className":10228},[1599,1600],[1398,10230,10232,10255],{"className":10231},[1604],[1398,10233,10235],{"className":10234,"style":1688},[1608],[1398,10236,10237,10240],{"style":3634},[1398,10238],{"className":10239,"style":1617},[1616],[1398,10241,10243],{"className":10242},[1621,1622,1623,1624],[1398,10244,10246,10249,10252],{"className":10245},[1494,1624],[1398,10247,3593],{"className":10248},[1494,1495,1624],[1398,10250,3596],{"className":10251},[1494,1495,1624],[1398,10253,3599],{"className":10254},[1494,1495,1624],[1398,10256,1632],{"className":10257},[1631],[1398,10259,10261],{"className":10260},[1604],[1398,10262,10264],{"className":10263,"style":1639},[1608],[1398,10265],{},",结果就是",[1398,10268,10270],{"className":10269},[2737],[1398,10271,10273,10416],{"className":10272},[1401],[1398,10274,10276],{"className":10275},[1405],[1407,10277,10278],{"xmlns":1409,"display":2746},[1411,10279,10280,10414],{},[1414,10281,10282,10298,10300,10316,10318,10320,10336,10338,10354,10372,10374,10376,10378,10380,10382,10384,10400,10402],{},[1449,10283,10284,10286],{},[1417,10285,3534],{},[1414,10287,10288,10290,10292,10294,10296],{},[1417,10289,3539],{},[1417,10291,3542],{},[1417,10293,3542],{},[1417,10295,3547],{},[1417,10297,3550],{},[1421,10299,1423],{},[1449,10301,10302,10304],{},[1417,10303,3534],{},[1414,10305,10306,10308,10310,10312,10314],{},[1417,10307,3593],{},[1417,10309,3547],{},[1417,10311,3534],{},[1417,10313,3596],{},[1417,10315,1025],{},[1421,10317,1435],{},[1417,10319,7961],{},[1449,10321,10322,10324],{},[1417,10323,3534],{},[1414,10325,10326,10328,10330,10332,10334],{},[1417,10327,3573],{},[1417,10329,3539],{},[1417,10331,3550],{},[1417,10333,3550],{},[1417,10335,3582],{},[1421,10337,1435],{},[1414,10339,10340,10342,10348,10350,10352],{},[1421,10341,1439],{"fence":1462},[7985,10343,10344,10346],{},[1417,10345,3557],{},[1417,10347,7961],{},[1421,10349,3560],{},[2883,10351,6033],{},[1421,10353,1458],{"fence":1462},[1449,10355,10356,10358],{},[1417,10357,3534],{},[1414,10359,10360,10362,10364,10366,10368,10370],{},[1417,10361,8005],{},[1417,10363,3582],{},[1417,10365,1025],{},[1417,10367,3539],{},[1417,10369,3593],{},[1417,10371,3593],{},[1421,10373,1435],{},[1421,10375,1439],{"stretchy":1438},[1417,10377,7961],{},[1421,10379,3560],{},[2883,10381,2885],{},[1421,10383,1458],{"stretchy":1438},[1449,10385,10386,10388],{},[1417,10387,3534],{},[1414,10389,10390,10392,10394,10396,10398],{},[1417,10391,3573],{},[1417,10393,3539],{},[1417,10395,3550],{},[1417,10397,3550],{},[1417,10399,3582],{},[1421,10401,1435],{},[1449,10403,10404,10406],{},[1417,10405,3534],{},[1414,10407,10408,10410,10412],{},[1417,10409,3593],{},[1417,10411,3596],{},[1417,10413,3599],{},[1474,10415,8060],{"encoding":1476},[1398,10417,10419,10483,10550,10623,10785,10806,10882],{"className":10418,"ariaHidden":1462},[1481],[1398,10420,10422,10425,10474,10477,10480],{"className":10421},[1485],[1398,10423],{"className":10424,"style":3612},[1489],[1398,10426,10428,10431],{"className":10427},[1494],[1398,10429,3534],{"className":10430},[1494,1495],[1398,10432,10434],{"className":10433},[1595],[1398,10435,10437,10466],{"className":10436},[1599,1600],[1398,10438,10440,10463],{"className":10439},[1604],[1398,10441,10443],{"className":10442,"style":3631},[1608],[1398,10444,10445,10448],{"style":3634},[1398,10446],{"className":10447,"style":1617},[1616],[1398,10449,10451],{"className":10450},[1621,1622,1623,1624],[1398,10452,10454,10457,10460],{"className":10453},[1494,1624],[1398,10455,3539],{"className":10456},[1494,1495,1624],[1398,10458,3650],{"className":10459},[1494,1495,1624],[1398,10461,3655],{"className":10462,"style":3654},[1494,1495,1624],[1398,10464,1632],{"className":10465},[1631],[1398,10467,10469],{"className":10468},[1604],[1398,10470,10472],{"className":10471,"style":1639},[1608],[1398,10473],{},[1398,10475],{"className":10476,"style":1501},[1500],[1398,10478,1423],{"className":10479},[1505],[1398,10481],{"className":10482,"style":1501},[1500],[1398,10484,10486,10489,10541,10544,10547],{"className":10485},[1485],[1398,10487],{"className":10488,"style":3875},[1489],[1398,10490,10492,10495],{"className":10491},[1494],[1398,10493,3534],{"className":10494},[1494,1495],[1398,10496,10498],{"className":10497},[1595],[1398,10499,10501,10533],{"className":10500},[1599,1600],[1398,10502,10504,10530],{"className":10503},[1604],[1398,10505,10507],{"className":10506,"style":8152},[1608],[1398,10508,10509,10512],{"style":3634},[1398,10510],{"className":10511,"style":1617},[1616],[1398,10513,10515],{"className":10514},[1621,1622,1623,1624],[1398,10516,10518,10521,10524,10527],{"className":10517},[1494,1624],[1398,10519,8167],{"className":10520},[1494,1495,1624],[1398,10522,3534],{"className":10523},[1494,1495,1624],[1398,10525,3596],{"className":10526},[1494,1495,1624],[1398,10528,1025],{"className":10529},[1494,1495,1624],[1398,10531,1632],{"className":10532},[1631],[1398,10534,10536],{"className":10535},[1604],[1398,10537,10539],{"className":10538,"style":3765},[1608],[1398,10540],{},[1398,10542],{"className":10543,"style":1530},[1500],[1398,10545,1435],{"className":10546},[1534],[1398,10548],{"className":10549,"style":1530},[1500],[1398,10551,10553,10556,10559,10614,10617,10620],{"className":10552},[1485],[1398,10554],{"className":10555,"style":8203},[1489],[1398,10557,7961],{"className":10558,"style":3688},[1494,1495],[1398,10560,10562,10565],{"className":10561},[1494],[1398,10563,3534],{"className":10564},[1494,1495],[1398,10566,10568],{"className":10567},[1595],[1398,10569,10571,10606],{"className":10570},[1599,1600],[1398,10572,10574,10603],{"className":10573},[1604],[1398,10575,10577],{"className":10576,"style":1688},[1608],[1398,10578,10579,10582],{"style":3634},[1398,10580],{"className":10581,"style":1617},[1616],[1398,10583,10585],{"className":10584},[1621,1622,1623,1624],[1398,10586,10588,10591,10594,10597,10600],{"className":10587},[1494,1624],[1398,10589,3573],{"className":10590},[1494,1495,1624],[1398,10592,3539],{"className":10593},[1494,1495,1624],[1398,10595,3550],{"className":10596,"style":3654},[1494,1495,1624],[1398,10598,3550],{"className":10599,"style":3654},[1494,1495,1624],[1398,10601,3582],{"className":10602,"style":3755},[1494,1495,1624],[1398,10604,1632],{"className":10605},[1631],[1398,10607,10609],{"className":10608},[1604],[1398,10610,10612],{"className":10611,"style":3765},[1608],[1398,10613],{},[1398,10615],{"className":10616,"style":1530},[1500],[1398,10618,1435],{"className":10619},[1534],[1398,10621],{"className":10622,"style":1530},[1500],[1398,10624,10626,10629,10718,10721,10776,10779,10782],{"className":10625},[1485],[1398,10627],{"className":10628,"style":8277},[1489],[1398,10630,10632,10638,10700,10703,10706,10709,10712],{"className":10631},[3510],[1398,10633,10635],{"className":10634,"style":8285},[1548,8284],[1398,10636,1439],{"className":10637},[8289,1623],[1398,10639,10641,10644,10697],{"className":10640},[14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sName":10919},[1494,1495,1624],[1398,10921,3596],{"className":10922},[1494,1495,1624],[1398,10924,3599],{"className":10925},[1494,1495,1624],[1398,10927,1632],{"className":10928},[1631],[1398,10930,10932],{"className":10931},[1604],[1398,10933,10935],{"className":10934,"style":1639},[1608],[1398,10936],{},[1741,10938,10940],{"id":10939},"carry-ripple-vs-carry-bypass-对比图","Carry Ripple vs Carry Bypass 对比图",[1025,10942,10943],{},[1028,10944],{"alt":1028,"src":10945},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-19.png",[1025,10947,10948,10949],{},"Carry-bypass adder 也会随 (N) 增长，但斜率小一些，因为中间有些 block 可以 bypass；但是 carry-bypass 有额外开销：",[1398,10950,10952,11005],{"className":10951},[1401],[1398,10953,10955],{"className":10954},[1405],[1407,10956,10957],{"xmlns":1409},[1411,10958,10959,11002],{},[1414,10960,10961,10977,10979,10983,10985,10987,10990,10992,10994,10996,10999],{},[1449,10962,10963,10965],{},[1417,10964,3534],{},[1414,10966,10967,10969,10971,10973,10975],{},[1417,10968,3593],{},[1417,10970,3547],{},[1417,10972,3534],{},[1417,10974,3596],{},[1417,10976,1025],{},[1421,10978,1797],{"separator":1462},[10980,10981,10982],"mtext",{}," ",[1417,10984,1429],{},[1417,10986,2114],{},[10980,10988,10989],{}," 逻辑",[1421,10991,1797],{"separator":1462},[10980,10993,10982],{},[1417,10995,7961],{},[1417,10997,10998],{},"U",[1417,11000,11001],{},"X",[1474,11003,11004],{"encoding":1476},"t_{setup},\\ BP\\text{ 逻辑},\\ MUX",[1398,11006,11008],{"className":11007,"ariaHidden":1462},[1481],[1398,11009,11011,11014,11066,11069,11072,11075,11078,11081,11093,11096,11099,11102,11105,11108],{"className":11010},[1485],[1398,11012],{"className":11013,"style":8203},[1489],[1398,11015,11017,11020],{"className":11016},[1494],[1398,11018,3534],{"className":11019},[1494,1495],[1398,11021,11023],{"className":11022},[1595],[1398,11024,11026,11058],{"className":11025},[1599,1600],[1398,11027,11029,11055],{"className":11028},[1604],[1398,11030,11032],{"className":11031,"style":8152},[1608],[1398,11033,11034,11037],{"style":3634},[1398,11035],{"className":11036,"style":1617},[1616],[1398,11038,11040],{"className":11039},[1621,1622,1623,1624],[1398,11041,11043,11046,11049,11052],{"className":11042},[1494,1624],[1398,11044,8167],{"className":11045},[1494,1495,1624],[1398,11047,3534],{"className":11048},[1494,1495,1624],[1398,11050,3596],{"className":11051},[1494,1495,1624],[1398,11053,1025],{"className":11054},[1494,1495,1624],[1398,11056,1632],{"className":11057},[1631],[1398,11059,11061],{"className":11060},[1604],[1398,11062,11064],{"className":11063,"style":3765},[1608],[1398,11065],{},[1398,11067,1797],{"className":11068},[1819],[1398,11070,10982],{"className":11071},[1500],[1398,11073],{"className":11074,"style":1823},[1500],[1398,11076,1429],{"className":11077,"style":1522},[1494,1495],[1398,11079,2114],{"className":11080,"style":2139},[1494,1495],[1398,11082,11085,11088],{"className":11083},[1494,11084],"text",[1398,11086,10982],{"className":11087},[1494],[1398,11089,11092],{"className":11090},[1494,11091],"cjk_fallback","逻辑",[1398,11094,1797],{"className":11095},[1819],[1398,11097,10982],{"className":11098},[1500],[1398,11100],{"className":11101,"style":1823},[1500],[1398,11103,7961],{"className":11104,"style":3688},[1494,1495],[1398,11106,10998],{"className":11107,"style":3688},[1494,1495],[1398,11109,11001],{"className":11110,"style":11111},[1494,1495],"margin-right:0.0785em;",[1025,11113,11114,11115,4863,11169],{},"所以在位数很小时，它不一定比 ripple 快。图上标的 ",[1398,11116,11118,11139],{"className":11117},[1401],[1398,11119,11121],{"className":11120},[1405],[1407,11122,11123],{"xmlns":1409},[1411,11124,11125,11136],{},[1414,11126,11127,11130,11133],{},[2883,11128,11129],{},"4",[1421,11131,11132],{},"∼",[2883,11134,11135],{},"8",[1474,11137,11138],{"encoding":1476},"4\\sim8",[1398,11140,11142,11160],{"className":11141,"ariaHidden":1462},[1481],[1398,11143,11145,11148,11151,11154,11157],{"className":11144},[1485],[1398,11146],{"className":11147,"style":2992},[1489],[1398,11149,11129],{"className":11150},[1494],[1398,11152],{"className":11153,"style":1501},[1500],[1398,11155,11132],{"className":11156},[1505],[1398,11158],{"className":11159,"style":1501},[1500],[1398,11161,11163,11166],{"className":11162},[1485],[1398,11164],{"className":11165,"style":2992},[1489],[1398,11167,11135],{"className":11168},[1494],[994,11170,11171],{},"通常位数大到一定程度后，carry-bypass 才开始明显优于 ripple。",[1366,11173,11175],{"id":11174},"carry-select-adder-进位选择加法器","Carry-Select Adder ｜ 进位选择加法器",[1025,11177,11178,11179],{},"核心思想：",[3237,11180,11181],{},"不等 carry 到了以后再算；先假设 carry-in=0 和 carry-in=1，把两种结果都提前算好。等真实 carry 到达时，用 MUX 选正确的结果——用面积换时间。",[1745,11183,11184],{"style":1747},[1749,11185,11186],{},[1752,11187,1755,11188,1755,11196],{"style":1754},[1757,11189,11191,1755],{"style":11190},"width: 45.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,11192,11193],{},[1028,11194],{"alt":1028,"src":11195},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-20.png",[1757,11197,11199,1755],{"style":11198},"width: 54.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,11200,11201],{},[1028,11202],{"alt":1028,"src":11203},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-21.png",[1741,11205,11207],{"id":11206},"critical-path-分析-关键路径分析","Critical Path 分析  ｜ 关键路径分析",[1025,11209,11210,11211,11312],{},"图里把 16-bit 分成 4 个 4-bit block，",[1398,11212,11214,11251],{"className":11213},[1401],[1398,11215,11217],{"className":11216},[1405],[1407,11218,11219],{"xmlns":1409},[1411,11220,11221,11248],{},[1414,11222,11223,11226,11228,11231,11234,11236,11238,11241,11243,11245],{},[10980,11224,11225],{},"Bit 0–3",[1421,11227,1797],{"separator":1462},[1500,11229],{"width":11230},"1em",[10980,11232,11233],{},"Bit 4–7",[1421,11235,1797],{"separator":1462},[1500,11237],{"width":11230},[10980,11239,11240],{},"Bit 8–11",[1421,11242,1797],{"separator":1462},[1500,11244],{"width":11230},[10980,11246,11247],{},"Bit 12–15",[1474,11249,11250],{"encoding":1476},"\\text{Bit 0–3},\\quad \\text{Bit 4–7},\\quad \\text{Bit 8–11},\\quad \\text{Bit 12–15}",[1398,11252,11254],{"className":11253,"ariaHidden":1462},[1481],[1398,11255,11257,11260,11266,11269,11273,11276,11282,11285,11288,11291,11297,11300,11303,11306],{"className":11256},[1485],[1398,11258],{"className":11259,"style":1812},[1489],[1398,11261,11263],{"className":11262},[1494,11084],[1398,11264,11225],{"className":11265},[1494],[1398,11267,1797],{"className":11268},[1819],[1398,11270],{"className":11271,"style":11272},[1500],"margin-right:1em;",[1398,11274],{"className":11275,"style":1823},[1500],[1398,11277,11279],{"className":11278},[1494,11084],[1398,11280,11233],{"className":11281},[1494],[1398,11283,1797],{"className":11284},[1819],[1398,11286],{"className":11287,"style":11272},[1500],[1398,11289],{"className":11290,"style":1823},[1500],[1398,11292,11294],{"className":11293},[1494,11084],[1398,11295,11240],{"className":11296},[1494],[1398,11298,1797],{"className":11299},[1819],[1398,11301],{"className":11302,"style":11272},[1500],[1398,11304],{"className":11305,"style":1823},[1500],[1398,11307,11309],{"className":11308},[1494,11084],[1398,11310,11247],{"className":11311},[1494],",每个 block 都提前算两套结果, 所以除了第一个 block 以外，后面 block 的内部 carry 结果其实都已经准备好了，关键路径实际上转换为：",[1398,11314,11316],{"className":11315},[2737],[1398,11317,11319,11356],{"className":11318},[1401],[1398,11320,11322],{"className":11321},[1405],[1407,11323,11324],{"xmlns":1409,"display":2746},[1411,11325,11326,11353],{},[1414,11327,11328,11331,11333,11336,11338,11340,11342,11344,11346,11348,11350],{},[10980,11329,11330],{},"第一个 block 内部 carry 传播",[1421,11332,3309],{},[10980,11334,11335],{},"MUX",[1421,11337,3309],{},[10980,11339,11335],{},[1421,11341,3309],{},[10980,11343,11335],{},[1421,11345,3309],{},[10980,11347,11335],{},[1421,11349,3309],{},[10980,11351,11352],{},"最高位 sum",[1474,11354,11355],{"encoding":1476},"\\text{第一个 block 内部 carry 传播} \\rightarrow \\text{MUX} \\rightarrow \\text{MUX} \\rightarrow \\text{MUX} \\rightarrow \\text{MUX} \\rightarrow \\text{最高位 sum}",[1398,11357,11359,11397,11418,11439,11460,11481],{"className":11358,"ariaHidden":1462},[1481],[1398,11360,11362,11365,11388,11391,11394],{"className":11361},[1485],[1398,11363],{"className":11364,"style":2033},[1489],[1398,11366,11368,11372,11376,11380,11384],{"className":11367},[1494,11084],[1398,11369,11371],{"className":11370},[1494,11091],"第一个",[1398,11373,11375],{"className":11374},[1494]," block ",[1398,11377,11379],{"className":11378},[1494,11091],"内部",[1398,11381,11383],{"className":11382},[1494]," carry ",[1398,11385,11387],{"className":11386},[1494,11091],"传播",[1398,11389],{"className":11390,"style":1501},[1500],[1398,11392,3309],{"className":11393},[1505],[1398,11395],{"className":11396,"style":1501},[1500],[1398,11398,11400,11403,11409,11412,11415],{"className":11399},[1485],[1398,11401],{"className":11402,"style":1490},[1489],[1398,11404,11406],{"className":11405},[1494,11084],[1398,11407,11335],{"className":11408},[1494],[1398,11410],{"className":11411,"style":1501},[1500],[1398,11413,3309],{"className":11414},[1505],[1398,11416],{"className":11417,"style":1501},[1500],[1398,11419,11421,11424,11430,11433,11436],{"className":11420},[1485],[1398,11422],{"className":11423,"style":1490},[1489],[1398,11425,11427],{"className":11426},[1494,11084],[1398,11428,11335],{"className":11429},[1494],[1398,11431],{"className":11432,"style":1501},[1500],[1398,11434,3309],{"className":11435},[1505],[1398,11437],{"className":11438,"style":1501},[1500],[1398,11440,11442,11445,11451,11454,11457],{"className":11441},[1485],[1398,11443],{"className":11444,"style":1490},[1489],[1398,11446,11448],{"className":11447},[1494,11084],[1398,11449,11335],{"className":11450},[1494],[1398,11452],{"className":11453,"style":1501},[1500],[1398,11455,3309],{"className":11456},[1505],[1398,11458],{"className":11459,"style":1501},[1500],[1398,11461,11463,11466,11472,11475,11478],{"className":11462},[1485],[1398,11464],{"className":11465,"style":1490},[1489],[1398,11467,11469],{"className":11468},[1494,11084],[1398,11470,11335],{"className":11471},[1494],[1398,11473],{"className":11474,"style":1501},[1500],[1398,11476,3309],{"className":11477},[1505],[1398,11479],{"className":11480,"style":1501},[1500],[1398,11482,11484,11487],{"className":11483},[1485],[1398,11485],{"className":11486,"style":1490},[1489],[1398,11488,11490,11494],{"className":11489},[1494,11084],[1398,11491,11493],{"className":11492},[1494,11091],"最高位",[1398,11495,11497],{"className":11496},[1494]," sum",[1025,11499,11500],{},"从而有",[1398,11502,11504],{"className":11503},[2737],[1398,11505,11507,11605],{"className":11506},[1401],[1398,11508,11510],{"className":11509},[1405],[1407,11511,11512],{"xmlns":1409,"display":2746},[1411,11513,11514,11602],{},[1414,11515,11516,11529,11531,11547,11549,11551,11567,11569,11575,11588,11590],{},[1449,11517,11518,11521],{},[1417,11519,11520],{},"T",[1414,11522,11523,11525,11527],{},[1417,11524,3539],{},[1417,11526,3542],{},[1417,11528,3542],{},[1421,11530,1423],{},[1449,11532,11533,11535],{},[1417,11534,3534],{},[1414,11536,11537,11539,11541,11543,11545],{},[1417,11538,3593],{},[1417,11540,3547],{},[1417,11542,3534],{},[1417,11544,3596],{},[1417,11546,1025],{},[1421,11548,1435],{},[1417,11550,7961],{},[1449,11552,11553,11555],{},[1417,11554,3534],{},[1414,11556,11557,11559,11561,11563,11565],{},[1417,11558,3573],{},[1417,11560,3539],{},[1417,11562,3550],{},[1417,11564,3550],{},[1417,11566,3582],{},[1421,11568,1435],{},[7985,11570,11571,11573],{},[1417,11572,3557],{},[1417,11574,7961],{},[1449,11576,11577,11579],{},[1417,11578,3534],{},[1414,11580,11581,11583,11585],{},[1417,11582,3599],{},[1417,11584,3596],{},[1417,11586,11587],{},"x",[1421,11589,1435],{},[1449,11591,11592,11594],{},[1417,11593,3534],{},[1414,11595,11596,11598,11600],{},[1417,11597,3593],{},[1417,11599,3596],{},[1417,11601,3599],{},[1474,11603,11604],{"encoding":1476},"T_{add}=t_{setup}+Mt_{carry}+\\frac{N}{M}t_{mux}+t_{sum}",[1398,11606,11608,11669,11736,11809,11934],{"className":11607,"ariaHidden":1462},[1481],[1398,11609,11611,11614,11660,11663,11666],{"className":11610},[1485],[1398,11612],{"className":11613,"style":1858},[1489],[1398,11615,11617,11620],{"className":11616},[1494],[1398,11618,11520],{"className":11619,"style":2139},[1494,1495],[1398,11621,11623],{"className":11622},[1595],[1398,11624,11626,11652],{"className":11625},[1599,1600],[1398,11627,11629,11649],{"className":11628},[1604],[1398,11630,11632],{"className":11631,"style":3631},[1608],[1398,11633,11634,11637],{"style":4987},[1398,11635],{"className":11636,"style":1617},[1616],[1398,11638,11640],{"className":11639},[1621,1622,1623,1624],[1398,11641,11643,11646],{"className":11642},[1494,1624],[1398,11644,3539],{"className":11645},[1494,1495,1624],[1398,11647,3650],{"className":11648},[1494,1495,1624],[1398,11650,1632],{"className":11651},[1631],[1398,11653,11655],{"className":11654},[1604],[1398,11656,11658],{"className":11657,"style":1639},[1608],[1398,11659],{},[1398,11661],{"className":11662,"style":1501},[1500],[1398,11664,1423],{"className":11665},[1505],[1398,11667],{"className":11668,"style":1501},[1500],[1398,11670,11672,11675,11727,11730,11733],{"className":11671},[1485],[1398,11673],{"className":11674,"style":3875},[1489],[1398,11676,11678,11681],{"className":11677},[1494],[1398,11679,3534],{"className":11680},[1494,1495],[1398,11682,11684],{"className":11683},[1595],[1398,11685,11687,11719],{"className":11686},[1599,1600],[1398,11688,11690,11716],{"className":11689},[1604],[1398,11691,11693],{"className":11692,"style":8152},[1608],[1398,11694,11695,11698],{"style":3634},[1398,11696],{"className":11697,"style":1617},[1616],[1398,11699,11701],{"className":11700},[1621,1622,1623,1624],[1398,11702,11704,11707,11710,11713],{"className":11703},[1494,1624],[1398,11705,8167],{"className":11706},[1494,1495,1624],[1398,11708,3534],{"className":11709},[1494,1495,1624],[1398,11711,3596],{"className":11712},[1494,1495,1624],[1398,11714,1025],{"className":11715},[1494,1495,1624],[1398,11717,1632],{"className":11718},[1631],[1398,11720,11722],{"className":11721},[1604],[1398,11723,11725],{"className":11724,"style":3765},[1608],[1398,11726],{},[1398,11728],{"className":11729,"style":1530},[1500],[1398,11731,1435],{"className":11732},[1534],[1398,11734],{"className":11735,"style":1530},[1500],[1398,11737,11739,11742,11745,11800,11803,11806],{"className":11738},[1485],[1398,11740],{"className":11741,"style":8203},[1489],[1398,11743,7961],{"className":11744,"style":3688},[1494,1495],[1398,11746,11748,11751],{"className":11747},[1494],[1398,11749,3534],{"className":11750},[1494,1495],[1398,11752,11754],{"className":11753},[1595],[1398,11755,11757,11792],{"className":11756},[1599,1600],[1398,11758,11760,11789],{"className":11759},[1604],[1398,11761,11763],{"className":11762,"style":1688},[1608],[1398,11764,11765,11768],{"style":3634},[1398,11766],{"className":11767,"style":1617},[1616],[1398,11769,11771],{"className":11770},[1621,1622,1623,1624],[1398,11772,11774,11777,11780,11783,11786],{"className":11773},[1494,1624],[1398,11775,3573],{"className":11776},[1494,1495,1624],[1398,11778,3539],{"className":11779},[1494,1495,1624],[1398,11781,3550],{"className":11782,"style":3654},[1494,1495,1624],[1398,11784,3550],{"className":11785,"style":3654},[1494,1495,1624],[1398,11787,3582],{"className":11788,"style":3755},[1494,1495,1624],[1398,11790,1632],{"className":11791},[1631],[1398,11793,11795],{"className":11794},[1604],[1398,11796,11798],{"className":11797,"style":3765},[1608],[1398,11799],{},[1398,11801],{"className":11802,"style":1530},[1500],[1398,11804,1435],{"className":11805},[1534],[1398,11807],{"className":11808,"style":1530},[1500],[1398,11810,11812,11816,11878,11925,11928,11931],{"className":11811},[1485],[1398,11813],{"className":11814,"style":11815},[1489],"height:2.0463em;vertical-align:-0.686em;",[1398,11817,11819,11822,11875],{"className":11818},[1494],[1398,11820],{"className":11821},[1548,8296],[1398,11823,11825],{"className":11824},[7985],[1398,11826,11828,11867],{"className":11827},[1599,1600],[1398,11829,11831,11864],{"className":11830},[1604],[1398,11832,11834,11845,11853],{"className":11833,"style":8309},[1608],[1398,11835,11836,11839],{"style":8312},[1398,11837],{"className":11838,"style":1666},[1616],[1398,11840,11842],{"className":11841},[1494],[1398,11843,7961],{"className":11844,"style":3688},[1494,1495],[1398,11846,11847,11850],{"style":8324},[1398,11848],{"className":11849,"style":1666},[1616],[1398,11851],{"className":11852,"style":1721},[8331],[1398,11854,11855,11858],{"style":8334},[1398,11856],{"className":11857,"style":1666},[1616],[1398,11859,11861],{"className":11860},[1494],[1398,11862,3557],{"className":11863,"style":3688},[1494,1495],[1398,11865,1632],{"className":11866},[1631],[1398,11868,11870],{"className":11869},[1604],[1398,11871,11873],{"className":11872,"style":8353},[1608],[1398,11874],{},[1398,11876],{"className":11877},[1645,8296],[1398,11879,11881,11884],{"className":11880},[1494],[1398,11882,3534],{"className":11883},[1494,1495],[1398,11885,11887],{"className":11886},[1595],[1398,11888,11890,11917],{"className":11889},[1599,1600],[1398,11891,11893,11914],{"className":11892},[1604],[1398,11894,11896],{"className":11895,"style":1688},[1608],[1398,11897,11898,11901],{"style":3634},[1398,11899],{"className":11900,"style":1617},[1616],[1398,11902,11904],{"className":11903},[1621,1622,1623,1624],[1398,11905,11907,11910],{"className":11906},[1494,1624],[1398,11908,3599],{"className":11909},[1494,1495,1624],[1398,11911,11913],{"className":11912},[1494,1495,1624],"ux",[1398,11915,1632],{"className":11916},[1631],[1398,11918,11920],{"className":11919},[1604],[1398,11921,11923],{"className":11922,"style":1639},[1608],[1398,11924],{},[1398,11926],{"className":11927,"style":1530},[1500],[1398,11929,1435],{"className":11930},[1534],[1398,11932],{"className":11933,"style":1530},[1500],[1398,11935,11937,11940],{"className":11936},[1485],[1398,11938],{"className":11939,"style":3612},[1489],[1398,11941,11943,11946],{"className":11942},[1494],[1398,11944,3534],{"className":11945},[1494,1495],[1398,11947,11949],{"className":11948},[1595],[1398,11950,11952,11981],{"className":11951},[1599,1600],[1398,11953,11955,11978],{"className":11954},[1604],[1398,11956,11958],{"className":11957,"style":1688},[1608],[1398,11959,11960,11963],{"style":3634},[1398,11961],{"className":11962,"style":1617},[1616],[1398,11964,11966],{"className":11965},[1621,1622,1623,1624],[1398,11967,11969,11972,11975],{"className":11968},[1494,1624],[1398,11970,3593],{"className":11971},[1494,1495,1624],[1398,11973,3596],{"className":11974},[1494,1495,1624],[1398,11976,3599],{"className":11977},[1494,1495,1624],[1398,11979,1632],{"className":11980},[1631],[1398,11982,11984],{"className":11983},[1604],[1398,11985,11987],{"className":11986,"style":1639},[1608],[1398,11988],{},[1025,11990,11991],{},"其中：",[1007,11993,11994,12025,12056,12192,12295,12554],{},[990,11995,11996,12024],{},[1398,11997,11999,12012],{"className":11998},[1401],[1398,12000,12002],{"className":12001},[1405],[1407,12003,12004],{"xmlns":1409},[1411,12005,12006,12010],{},[1414,12007,12008],{},[1417,12009,3557],{},[1474,12011,3557],{"encoding":1476},[1398,12013,12015],{"className":12014,"ariaHidden":1462},[1481],[1398,12016,12018,12021],{"className":12017},[1485],[1398,12019],{"className":12020,"style":1490},[1489],[1398,12022,3557],{"className":12023,"style":3688},[1494,1495],"：总位数；",[990,12026,12027,12055],{},[1398,12028,12030,12043],{"className":12029},[1401],[1398,12031,12033],{"className":12032},[1405],[1407,12034,12035],{"xmlns":1409},[1411,12036,12037,12041],{},[1414,12038,12039],{},[1417,12040,7961],{},[1474,12042,7961],{"encoding":1476},[1398,12044,12046],{"className":12045,"ariaHidden":1462},[1481],[1398,12047,12049,12052],{"className":12048},[1485],[1398,12050],{"className":12051,"style":1490},[1489],[1398,12053,7961],{"className":12054,"style":3688},[1494,1495],"：每个 block 的位数；",[990,12057,12058,12149,12150,8901],{},[1398,12059,12061,12088],{"className":12060},[1401],[1398,12062,12064],{"className":12063},[1405],[1407,12065,12066],{"xmlns":1409},[1411,12067,12068,12086],{},[1414,12069,12070],{},[1449,12071,12072,12074],{},[1417,12073,3534],{},[1414,12075,12076,12078,12080,12082,12084],{},[1417,12077,3593],{},[1417,12079,3547],{},[1417,12081,3534],{},[1417,12083,3596],{},[1417,12085,1025],{},[1474,12087,8696],{"encoding":1476},[1398,12089,12091],{"className":12090,"ariaHidden":1462},[1481],[1398,12092,12094,12097],{"className":12093},[1485],[1398,12095],{"className":12096,"style":3875},[1489],[1398,12098,12100,12103],{"className":12099},[1494],[1398,12101,3534],{"className":12102},[1494,1495],[1398,12104,12106],{"className":12105},[1595],[1398,12107,12109,12141],{"className":12108},[1599,1600],[1398,12110,12112,12138],{"className":12111},[1604],[1398,12113,12115],{"className":12114,"style":8152},[1608],[1398,12116,12117,12120],{"style":3634},[1398,12118],{"className":12119,"style":1617},[1616],[1398,12121,12123],{"className":12122},[1621,1622,1623,1624],[1398,12124,12126,12129,12132,12135],{"className":12125},[1494,1624],[1398,12127,8167],{"className":12128},[1494,1495,1624],[1398,12130,3534],{"className":12131},[1494,1495,1624],[1398,12133,3596],{"className":12134},[1494,1495,1624],[1398,12136,1025],{"className":12137},[1494,1495,1624],[1398,12139,1632],{"className":12140},[1631],[1398,12142,12144],{"className":12143},[1604],[1398,12145,12147],{"className":12146,"style":3765},[1608],[1398,12148],{},"：计算 ",[1398,12151,12153,12171],{"className":12152},[1401],[1398,12154,12156],{"className":12155},[1405],[1407,12157,12158],{"xmlns":1409},[1411,12159,12160,12168],{},[1414,12161,12162,12164,12166],{},[1417,12163,2114],{},[1421,12165,1797],{"separator":1462},[1417,12167,1931],{},[1474,12169,12170],{"encoding":1476},"P,G",[1398,12172,12174],{"className":12173,"ariaHidden":1462},[1481],[1398,12175,12177,12180,12183,12186,12189],{"className":12176},[1485],[1398,12178],{"className":12179,"style":1812},[1489],[1398,12181,2114],{"className":12182,"style":2139},[1494,1495],[1398,12184,1797],{"className":12185},[1819],[1398,12187],{"className":12188,"style":1823},[1500],[1398,12190,1931],{"className":12191},[1494,1495],[990,12193,12194,12294],{},[1398,12195,12197,12227],{"className":12196},[1401],[1398,12198,12200],{"className":12199},[1405],[1407,12201,12202],{"xmlns":1409},[1411,12203,12204,12224],{},[1414,12205,12206,12208],{},[1417,12207,7961],{},[1449,12209,12210,12212],{},[1417,12211,3534],{},[1414,12213,12214,12216,12218,12220,12222],{},[1417,12215,3573],{},[1417,12217,3539],{},[1417,12219,3550],{},[1417,12221,3550],{},[1417,12223,3582],{},[1474,12225,12226],{"encoding":1476},"Mt_{carry}",[1398,12228,12230],{"className":12229,"ariaHidden":1462},[1481],[1398,12231,12233,12236,12239],{"className":12232},[1485],[1398,12234],{"className":12235,"style":8203},[1489],[1398,12237,7961],{"className":12238,"style":3688},[1494,1495],[1398,12240,12242,12245],{"className":12241},[1494],[1398,12243,3534],{"className":12244},[1494,1495],[1398,12246,12248],{"className":12247},[1595],[1398,12249,12251,12286],{"className":12250},[1599,1600],[1398,12252,12254,12283],{"className":12253},[1604],[1398,12255,12257],{"className":12256,"style":1688},[1608],[1398,12258,12259,12262],{"style":3634},[1398,12260],{"className":12261,"style":1617},[1616],[1398,12263,12265],{"className":12264},[1621,1622,1623,1624],[1398,12266,12268,12271,12274,12277,12280],{"className":12267},[1494,1624],[1398,12269,3573],{"className":12270},[1494,1495,1624],[1398,12272,3539],{"className":12273},[1494,1495,1624],[1398,12275,3550],{"className":12276,"style":3654},[1494,1495,1624],[1398,12278,3550],{"className":12279,"style":3654},[1494,1495,1624],[1398,12281,3582],{"className":12282,"style":3755},[1494,1495,1624],[1398,12284,1632],{"className":12285},[1631],[1398,12287,12289],{"className":12288},[1604],[1398,12290,12292],{"className":12291,"style":3765},[1608],[1398,12293],{},"：第一个 block 内部产生 carry 的时间；",[990,12296,12297,12454,12455,12553],{},[1398,12298,12300,12330],{"className":12299},[1401],[1398,12301,12303],{"className":12302},[1405],[1407,12304,12305],{"xmlns":1409},[1411,12306,12307,12327],{},[1414,12308,12309,12315],{},[7985,12310,12311,12313],{},[1417,12312,3557],{},[1417,12314,7961],{},[1449,12316,12317,12319],{},[1417,12318,3534],{},[1414,12320,12321,12323,12325],{},[1417,12322,3599],{},[1417,12324,3596],{},[1417,12326,11587],{},[1474,12328,12329],{"encoding":1476},"\\frac{N}{M}t_{mux}",[1398,12331,12333],{"className":12332,"ariaHidden":1462},[1481],[1398,12334,12336,12340,12408],{"className":12335},[1485],[1398,12337],{"className":12338,"style":12339},[1489],"height:1.2173em;vertical-align:-0.345em;",[1398,12341,12343,12346,12405],{"className":12342},[1494],[1398,12344],{"className":12345},[1548,8296],[1398,12347,12349],{"className":12348},[7985],[1398,12350,12352,12397],{"className":12351},[1599,1600],[1398,12353,12355,12394],{"className":12354},[1604],[1398,12356,12358,12372,12380],{"className":12357,"style":9786},[1608],[1398,12359,12360,12363],{"style":9789},[1398,12361],{"className":12362,"style":1666},[1616],[1398,12364,12366],{"className":12365},[1621,1622,1623,1624],[1398,12367,12369],{"className":12368},[1494,1624],[1398,12370,7961],{"className":12371,"style":3688},[1494,1495,1624],[1398,12373,12374,12377],{"style":8324},[1398,12375],{"className":12376,"style":1666},[1616],[1398,12378],{"className":12379,"style":1721},[8331],[1398,12381,12382,12385],{"style":9812},[1398,12383],{"className":12384,"style":1666},[1616],[1398,12386,12388],{"className":12387},[1621,1622,1623,1624],[1398,12389,12391],{"className":12390},[1494,1624],[1398,12392,3557],{"className":12393,"style":3688},[1494,1495,1624],[1398,12395,1632],{"className":12396},[1631],[1398,12398,12400],{"className":12399},[1604],[1398,12401,12403],{"className":12402,"style":9834},[1608],[1398,12404],{},[1398,12406],{"className":12407},[1645,8296],[1398,12409,12411,12414],{"className":12410},[1494],[1398,12412,3534],{"className":12413},[1494,1495],[1398,12415,12417],{"className":12416},[1595],[1398,12418,12420,12446],{"className":12419},[1599,1600],[1398,12421,12423,12443],{"className":12422},[1604],[1398,12424,12426],{"className":12425,"style":1688},[1608],[1398,12427,12428,12431],{"style":3634},[1398,12429],{"className":12430,"style":1617},[1616],[1398,12432,12434],{"className":12433},[1621,1622,1623,1624],[1398,12435,12437,12440],{"className":12436},[1494,1624],[1398,12438,3599],{"className":12439},[1494,1495,1624],[1398,12441,11913],{"className":12442},[1494,1495,1624],[1398,12444,1632],{"className":12445},[1631],[1398,12447,12449],{"className":12448},[1604],[1398,12450,12452],{"className":12451,"style":1639},[1608],[1398,12453],{},"：一共有 ",[1398,12456,12458,12476],{"className":12457},[1401],[1398,12459,12461],{"className":12460},[1405],[1407,12462,12463],{"xmlns":1409},[1411,12464,12465,12473],{},[1414,12466,12467],{},[7985,12468,12469,12471],{},[1417,12470,3557],{},[1417,12472,7961],{},[1474,12474,12475],{"encoding":1476},"\\frac{N}{M}",[1398,12477,12479],{"className":12478,"ariaHidden":1462},[1481],[1398,12480,12482,12485],{"className":12481},[1485],[1398,12483],{"className":12484,"style":12339},[1489],[1398,12486,12488,12491,12550],{"className":12487},[1494],[1398,12489],{"className":12490},[1548,8296],[1398,12492,12494],{"className":12493},[7985],[1398,12495,12497,12542],{"className":12496},[1599,1600],[1398,12498,12500,12539],{"className":12499},[1604],[1398,12501,12503,12517,12525],{"className":12502,"style":9786},[1608],[1398,12504,12505,12508],{"style":9789},[1398,12506],{"className":12507,"style":1666},[1616],[1398,12509,12511],{"className":12510},[1621,1622,1623,1624],[1398,12512,12514],{"className":12513},[1494,1624],[1398,12515,7961],{"className":12516,"style":3688},[1494,1495,1624],[1398,12518,12519,12522],{"style":8324},[1398,12520],{"className":12521,"style":1666},[1616],[1398,12523],{"className":12524,"style":1721},[8331],[1398,12526,12527,12530],{"style":9812},[1398,12528],{"className":12529,"style":1666},[1616],[1398,12531,12533],{"className":12532},[1621,1622,1623,1624],[1398,12534,12536],{"className":12535},[1494,1624],[1398,12537,3557],{"className":12538,"style":3688},[1494,1495,1624],[1398,12540,1632],{"className":12541},[1631],[1398,12543,12545],{"className":12544},[1604],[1398,12546,12548],{"className":12547,"style":9834},[1608],[1398,12549],{},[1398,12551],{"className":12552},[1645,8296]," 个 block，所以真实 carry 要经过这么多个 MUX；",[990,12555,12556,9185],{},[1398,12557,12559,12582],{"className":12558},[1401],[1398,12560,12562],{"className":12561},[1405],[1407,12563,12564],{"xmlns":1409},[1411,12565,12566,12580],{},[1414,12567,12568],{},[1449,12569,12570,12572],{},[1417,12571,3534],{},[1414,12573,12574,12576,12578],{},[1417,12575,3593],{},[1417,12577,3596],{},[1417,12579,3599],{},[1474,12581,3962],{"encoding":1476},[1398,12583,12585],{"className":12584,"ariaHidden":1462},[1481],[1398,12586,12588,12591],{"className":12587},[1485],[1398,12589],{"className":12590,"style":3612},[1489],[1398,12592,12594,12597],{"className":12593},[1494],[1398,12595,3534],{"className":12596},[1494,1495],[1398,12598,12600],{"className":12599},[1595],[1398,12601,12603,12632],{"className":12602},[1599,1600],[1398,12604,12606,12629],{"className":12605},[1604],[1398,12607,12609],{"className":12608,"style":1688},[1608],[1398,12610,12611,12614],{"style":3634},[1398,12612],{"className":12613,"style":1617},[1616],[1398,12615,12617],{"className":12616},[1621,1622,1623,1624],[1398,12618,12620,12623,12626],{"className":12619},[1494,1624],[1398,12621,3593],{"className":12622},[1494,1495,1624],[1398,12624,3596],{"className":12625},[1494,1495,1624],[1398,12627,3599],{"className":12628},[1494,1495,1624],[1398,12630,1632],{"className":12631},[1631],[1398,12633,12635],{"className":12634},[1604],[1398,12636,12638],{"className":12637,"style":1639},[1608],[1398,12639],{},[12641,12642,12643],"blockquote",{},[1025,12644,12645],{},"这次注意，实际上会经过N\u002FM个mux",[1025,12647,12648],{},"细节查看下图蓝线",[1025,12650,12651],{},[1028,12652],{"alt":1028,"src":12653},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-22.png",[1741,12655,12657],{"id":12656},"square-root-carry-select-adder-平方根进位选择加法器","Square Root Carry Select Adder ｜ 平方根进位选择加法器",[1025,12659,12660],{},[1028,12661],{"alt":1028,"src":12662},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-23.png",[1025,12664,12665],{},"前面提到的是等分的block，如果block不等分，而是呈等差数列 逐级递增+1的话，最终计算式子如下：",[1398,12667,12669],{"className":12668},[2737],[1398,12670,12672,12767],{"className":12671},[1401],[1398,12673,12675],{"className":12674},[1405],[1407,12676,12677],{"xmlns":1409,"display":2746},[1411,12678,12679,12764],{},[1414,12680,12681,12683,12685,12687,12689,12691,12693,12695,12697,12699,12701,12703,12705,12707,12709,12711,12713,12715,12717,12719,12721,12723,12725,12727,12729,12731,12733,12744,12746,12748],{},[1417,12682,3557],{},[1421,12684,1423],{},[1417,12686,7961],{},[1421,12688,1435],{},[1421,12690,1439],{"stretchy":1438},[1417,12692,7961],{},[1421,12694,1435],{},[2883,12696,2885],{},[1421,12698,1458],{"stretchy":1438},[1421,12700,1435],{},[1421,12702,1439],{"stretchy":1438},[1417,12704,7961],{},[1421,12706,1435],{},[2883,12708,6033],{},[1421,12710,1458],{"stretchy":1438},[1421,12712,1435],{},[1421,12714,3328],{},[1421,12716,1435],{},[1421,12718,1439],{"stretchy":1438},[1417,12720,7961],{},[1421,12722,1435],{},[1417,12724,2114],{},[1421,12726,3560],{},[2883,12728,2885],{},[1421,12730,1458],{"stretchy":1438},[1421,12732,1423],{},[7985,12734,12735,12742],{},[12736,12737,12738,12740],"msup",{},[1417,12739,2114],{},[2883,12741,6033],{},[2883,12743,6033],{},[1421,12745,1435],{},[1417,12747,2114],{},[1414,12749,12750,12752,12754,12756,12762],{},[1421,12751,1439],{"fence":1462},[1417,12753,7961],{},[1421,12755,3560],{},[7985,12757,12758,12760],{},[2883,12759,2885],{},[2883,12761,6033],{},[1421,12763,1458],{"fence":1462},[1474,12765,12766],{"encoding":1476},"N=M+(M+1)+(M+2)+\\cdots+(M+P-1) = \\frac{P^2}{2}+P\\left(M-\\frac{1}{2}\\right)",[1398,12768,12770,12788,12806,12827,12848,12869,12890,12908,12929,12947,12968,13075],{"className":12769,"ariaHidden":1462},[1481],[1398,12771,12773,12776,12779,12782,12785],{"className":12772},[1485],[1398,12774],{"className":12775,"style":1490},[1489],[1398,12777,3557],{"className":12778,"style":3688},[1494,1495],[1398,12780],{"className":12781,"style":1501},[1500],[1398,12783,1423],{"className":12784},[1505],[1398,12786],{"className":12787,"style":1501},[1500],[1398,12789,12791,12794,12797,12800,12803],{"className":12790},[1485],[1398,12792],{"className":12793,"style":1515},[1489],[1398,12795,7961],{"className":12796,"style":3688},[1494,1495],[1398,12798],{"className":12799,"style":1530},[1500],[1398,12801,1435],{"className":12802},[1534],[1398,12804],{"className":12805,"style":1530},[1500],[1398,12807,12809,12812,12815,12818,12821,12824],{"className":12808},[1485],[1398,12810],{"className":12811,"style":1544},[1489],[1398,12813,1439],{"className":12814},[1548],[1398,12816,7961],{"className":12817,"style":3688},[1494,1495],[1398,12819],{"className":12820,"style":1530},[1500],[1398,12822,1435],{"className":12823},[1534],[1398,12825],{"className":12826,"style":1530},[1500],[1398,12828,12830,12833,12836,12839,12842,12845],{"className":12829},[1485],[1398,12831],{"className":12832,"style":1544},[1489],[1398,12834,2885],{"className":12835},[1494],[1398,12837,1458],{"className":12838},[1645],[1398,12840],{"className":12841,"style":1530},[1500],[1398,12843,1435],{"className":12844},[1534],[1398,12846],{"className":12847,"style":1530},[1500],[1398,12849,12851,12854,12857,12860,12863,12866],{"className":12850},[1485],[1398,12852],{"className":12853,"style":1544},[1489],[1398,12855,1439],{"className":12856},[1548],[1398,12858,7961],{"className":12859,"style":3688},[1494,1495],[1398,12861],{"className":12862,"style":1530},[1500],[1398,12864,1435],{"className":12865},[1534],[1398,12867],{"className":12868,"style":1530},[1500],[1398,12870,12872,12875,12878,12881,12884,12887],{"className":12871},[1485],[1398,12873],{"className":12874,"style":1544},[1489],[1398,12876,6033],{"className":12877},[1494],[1398,12879,1458],{"className":12880},[1645],[1398,12882],{"className":12883,"style":1530},[1500],[1398,12885,1435],{"className":12886},[1534],[1398,12888],{"className":12889,"style":1530},[1500],[1398,12891,12893,12896,12899,12902,12905],{"className":12892},[1485],[1398,12894],{"className":12895,"style":4908},[1489],[1398,12897,3328],{"className":12898},[3510],[1398,12900],{"className":12901,"style":1530},[1500],[1398,12903,1435],{"className":12904},[1534],[1398,12906],{"className":12907,"style":1530},[1500],[1398,12909,12911,12914,12917,12920,12923,12926],{"className":12910},[1485],[1398,12912],{"className":12913,"style":1544},[1489],[1398,12915,1439],{"className":12916},[1548],[1398,12918,7961],{"className":12919,"style":3688},[1494,1495],[1398,12921],{"className":12922,"style":1530},[1500],[1398,12924,1435],{"className":12925},[1534],[1398,12927],{"className":12928,"style":1530},[1500],[1398,12930,12932,12935,12938,12941,12944],{"className":12931},[1485],[1398,12933],{"className":12934,"style":1515},[1489],[1398,12936,2114],{"className":12937,"style":2139},[1494,1495],[1398,12939],{"className":12940,"style":1530},[1500],[1398,12942,3560],{"className":12943},[1534],[1398,12945],{"className":12946,"style":1530},[1500],[1398,12948,12950,12953,12956,12959,12962,12965],{"className":12949},[1485],[1398,12951],{"className":12952,"style":1544},[1489],[1398,12954,2885],{"className":12955},[1494],[1398,12957,1458],{"className":12958},[1645],[1398,12960],{"className":12961,"style":1501},[1500],[1398,12963,1423],{"className":12964},[1505],[1398,12966],{"className":12967,"style":1501},[1500],[1398,12969,12971,12975,13066,13069,13072],{"className":12970},[1485],[1398,12972],{"className":12973,"style":12974},[1489],"height:2.1771em;vertical-align:-0.686em;",[1398,12976,12978,12981,13063],{"className":12977},[1494],[1398,12979],{"className":12980},[1548,8296],[1398,12982,12984],{"className":12983},[7985],[1398,12985,12987,13055],{"className":12986},[1599,1600],[1398,12988,12990,13052],{"className":12989},[1604],[1398,12991,12994,13005,13013],{"className":12992,"style":12993},[1608],"height:1.4911em;",[1398,12995,12996,12999],{"style":8312},[1398,12997],{"className":12998,"style":1666},[1616],[1398,13000,13002],{"className":13001},[1494],[1398,13003,6033],{"className":13004},[1494],[1398,13006,13007,13010],{"style":8324},[1398,13008],{"className":13009,"style":1666},[1616],[1398,13011],{"className":13012,"style":1721},[8331],[1398,13014,13015,13018],{"style":8334},[1398,13016],{"className":13017,"style":1666},[1616],[1398,13019,13021],{"className":13020},[1494],[1398,13022,13024,13027],{"className":13023},[1494],[1398,13025,2114],{"className":13026,"style":2139},[1494,1495],[1398,13028,13030],{"className":13029},[1595],[1398,13031,13033],{"className":13032},[1599],[1398,13034,13036],{"classN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\\frac{P^2}{2}",[1398,13213,13215,13233],{"className":13214,"ariaHidden":1462},[1481],[1398,13216,13218,13221,13224,13227,13230],{"className":13217},[1485],[1398,13219],{"className":13220,"style":1490},[1489],[1398,13222,3557],{"className":13223,"style":3688},[1494,1495],[1398,13225],{"className":13226,"style":1501},[1500],[1398,13228,1423],{"className":13229},[1505],[1398,13231],{"className":13232,"style":1501},[1500],[1398,13234,13236,13239],{"className":13235},[1485],[1398,13237],{"className":13238,"style":12974},[1489],[1398,13240,13242,13245,13324],{"className":13241},[1494],[1398,13243],{"className":13244},[1548,8296],[1398,13246,13248],{"className":13247},[7985],[1398,13249,13251,13316],{"className":13250},[1599,1600],[1398,13252,13254,13313],{"className":13253},[1604],[1398,13255,13257,13268,13276],{"className":13256,"style":12993},[1608],[1398,13258,13259,13262],{"style":8312},[1398,13260],{"className":13261,"style":1666},[1616],[1398,13263,13265],{"className":13264},[1494],[1398,13266,6033],{"className":13267},[1494],[1398,13269,13270,13273],{"style":8324},[1398,13271],{"className":13272,"style":1666},[1616],[1398,13274],{"className":13275,"style":1721},[8331],[1398,13277,13278,13281],{"style":8334},[1398,13279],{"className":13280,"style":1666},[1616],[1398,13282,13284],{"className":13283},[1494],[1398,13285,13287,13290],{"className":13286},[1494],[1398,13288,2114],{"className":13289,"style":2139},[1494,1495],[1398,13291,13293],{"className":13292},[1595],[1398,13294,13296],{"className":13295},[1599],[1398,13297,13299],{"className":13298},[1604],[1398,13300,13302],{"className":13301,"style":13039},[1608],[1398,13303,13304,13307],{"style":13042},[1398,13305],{"className":13306,"style":1617},[1616],[1398,13308,13310],{"className":13309},[1621,1622,1623,1624],[1398,13311,6033],{"className":13312},[1494,1624],[1398,13314,1632],{"className":13315},[1631],[1398,13317,13319],{"className":13318},[1604],[1398,13320,13322],{"className":13321,"style":8353},[1608],[1398,13323],{},[1398,13325],{"className":13326},[1645,8296],[1025,13328,13329],{},"延迟就变成了",[1398,13331,13333],{"className":13332},[2737],[1398,13334,13336,13428],{"className":13335},[1401],[1398,13337,13339],{"className":13338},[1405],[1407,13340,13341],{"xmlns":1409,"display":2746},[1411,13342,13343,13425],{},[1414,13344,13345,13357,13359,13375,13377,13379,13395,13397,13399,13411,13413],{},[1449,13346,13347,13349],{},[1417,13348,11520],{},[1414,13350,13351,13353,13355],{},[1417,13352,3539],{},[1417,13354,3542],{},[1417,13356,3542],{},[1421,13358,1423],{},[1449,13360,13361,13363],{},[1417,13362,3534],{},[1414,13364,13365,13367,13369,13371,13373],{},[1417,13366,3593],{},[1417,13368,3547],{},[1417,13370,3534],{},[1417,13372,3596],{},[1417,13374,1025],{},[1421,13376,1435],{},[1417,13378,7961],{},[1449,13380,13381,13383],{},[1417,13382,3534],{},[1414,13384,13385,13387,13389,13391,13393],{},[1417,13386,3573],{},[1417,13388,3539],{},[1417,13390,3550],{},[1417,13392,3550],{},[1417,13394,3582],{},[1421,13396,1435],{},[1417,13398,2114],{},[1449,13400,13401,13403],{},[1417,13402,3534],{},[1414,13404,13405,13407,13409],{},[1417,13406,3599],{},[1417,13408,3596],{},[1417,13410,11587],{},[1421,13412,1435],{},[1449,13414,13415,13417],{},[1417,13416,3534],{},[1414,13418,13419,13421,13423],{},[1417,13420,3593],{},[1417,13422,3596],{},[1417,13424,3599],{},[1474,13426,13427],{"encoding":1476},"T_{add}=t_{setup}+Mt_{carry}+Pt_{mux}+t_{sum}",[1398,13429,13431,13492,13559,13632,13696],{"className":13430,"ariaHidden":1462},[1481],[1398,13432,13434,13437,13483,13486,13489],{"className":13433},[1485],[1398,13435],{"className":13436,"style":1858},[1489],[1398,13438,13440,13443],{"className":13439},[1494],[1398,13441,11520],{"className":13442,"style":2139},[1494,1495],[1398,13444,13446],{"className":13445},[1595],[1398,13447,13449,13475],{"className":13448},[1599,1600],[1398,13450,13452,13472],{"className":13451},[1604],[1398,13453,13455],{"className":13454,"style":3631},[1608],[1398,13456,13457,13460],{"style":4987},[1398,13458],{"className":13459,"style":1617},[1616],[1398,13461,13463],{"className":13462},[1621,1622,1623,1624],[1398,13464,13466,13469],{"className":13465},[1494,1624],[1398,13467,3539],{"className":13468},[1494,1495,1624],[1398,13470,3650],{"className":13471},[1494,1495,1624],[1398,13473,1632],{"className":13474},[1631],[1398,13476,13478],{"className":13477},[1604],[1398,13479,13481],{"className":13480,"style":1639},[1608],[1398,13482],{},[1398,13484],{"className":13485,"style":1501},[1500],[1398,13487,1423],{"className":13488},[1505],[1398,13490],{"className":13491,"style":1501},[1500],[1398,13493,13495,13498,13550,13553,13556],{"className":13494},[1485],[1398,13496],{"className":13497,"style":3875},[1489],[1398,13499,13501,13504],{"className":13500},[1494],[1398,13502,3534],{"className":13503},[1494,1495],[1398,13505,13507],{"className":13506},[1595],[1398,13508,13510,13542],{"className":13509},[1599,1600],[1398,13511,13513,13539],{"className":13512},[1604]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",[1398,13755,13757,13770],{"className":13756},[1401],[1398,13758,13760],{"className":13759},[1405],[1407,13761,13762],{"xmlns":1409},[1411,13763,13764,13768],{},[1414,13765,13766],{},[1417,13767,2114],{},[1474,13769,2114],{"encoding":1476},[1398,13771,13773],{"className":13772,"ariaHidden":1462},[1481],[1398,13774,13776,13779],{"className":13775},[1485],[1398,13777],{"className":13778,"style":1490},[1489],[1398,13780,2114],{"className":13781,"style":2139},[1494,1495]," 近似为 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时，延迟写成：",[1398,13885,13887],{"className":13886},[2737],[1398,13888,13890,13988],{"className":13889},[1401],[1398,13891,13893],{"className":13892},[1405],[1407,13894,13895],{"xmlns":1409,"display":2746},[1411,13896,13897,13985],{},[1414,13898,13899,13911,13913,13929,13931,13933,13949,13951,13959,13971,13973],{},[1449,13900,13901,13903],{},[1417,13902,11520],{},[1414,13904,13905,13907,13909],{},[1417,13906,3539],{},[1417,13908,3542],{},[1417,13910,3542],{},[1421,13912,1423],{},[1449,13914,13915,13917],{},[1417,13916,3534],{},[1414,13918,13919,13921,13923,13925,13927],{},[1417,13920,3593],{},[1417,13922,3547],{},[1417,13924,3534],{},[1417,13926,3596],{},[1417,13928,1025],{},[1421,13930,1435],{},[1417,13932,7961],{},[1449,13934,13935,13937],{},[1417,13936,3534],{},[1414,13938,13939,13941,13943,13945,13947],{},[1417,13940,3573],{},[1417,13942,3539],{},[1417,13944,3550],{},[1417,13946,3550],{},[1417,13948,3582],{},[1421,13950,1435],{},[13796,13952,13953],{},[1414,13954,13955,13957],{},[2883,13956,6033],{},[1417,13958,3557],{},[1449,13960,13961,13963],{},[1417,13962,3534],{},[1414,13964,13965,13967,13969],{},[1417,13966,3599],{},[1417,13968,3596],{},[1417,13970,11587],{},[1421,13972,1435],{},[1449,13974,13975,13977],{},[1417,13976,3534],{},[1414,13978,13979,13981,13983],{},[1417,13980,3593],{},[1417,13982,3596],{},[1417,13984,3599],{},[1474,13986,13987],{"encoding":1476},"T_{add}=t_{setup}+Mt_{carry}+\\sqrt{2N} t_{mux}+t_{sum}",[1398,13989,13991,14052,14119,14192,14307],{"className":13990,"ariaHidden":1462},[1481],[1398,13992,13994,13997,14043,14046,14049],{"className":13993},[1485],[1398,13995],{"className":13996,"style":1858},[1489],[1398,13998,14000,14003],{"className":13999},[1494],[1398,14001,11520],{"className":14002,"style":2139},[1494,1495],[1398,14004,14006],{"className":14005},[1595],[1398,14007,14009,14035],{"className":14008},[1599,1600],[1398,14010,14012,14032],{"className":14011},[1604],[1398,14013,14015],{"className":14014,"style":3631},[1608],[1398,14016,14017,14020],{"style":4987},[1398,14018],{"className":14019,"style":1617},[1616],[1398,14021,14023],{"className":14022},[1621,1622,1623,1624],[1398,14024,14026,14029],{"className":14025},[1494,1624],[1398,14027,3539],{"className":14028},[1494,1495,1624],[1398,14030,3650],{"className":14031},[1494,1495,1624],[1398,14033,1632],{"className":14034},[1631],[1398,14036,14038],{"className":14037},[1604],[1398,14039,14041],{"className":14040,"style":1639},[1608],[1398,14042],{},[1398,14044],{"className":14045,"style":1501},[1500],[1398,14047,1423],{"className":14048},[1505],[1398,14050],{"className":14051,"style":1501},[1500],[1398,14053,14055,14058,14110,14113,14116],{"className":14054},[1485],[1398,14056],{"className":14057,"style":3875},[1489],[1398,14059,14061,14064],{"className":14060},[1494],[1398,14062,3534],{"className":14063},[1494,1495],[1398,14065,14067],{"className":14066},[1595],[1398,14068,14070,14102],{"className":14069},[1599,1600],[1398,14071,14073,14099],{"className":14072},[1604],[1398,14074,14076],{"className":14075,"style":8152},[1608],[1398,14077,14078,14081],{"style":3634},[1398,14079],{"className":14080,"style":1617},[1616],[1398,14082,14084],{"className":14083},[1621,1622,1623,1624],[1398,14085,14087,14090,14093,14096],{"className":14086},[1494,1624],[1398,14088,8167],{"className":14089},[1494,1495,1624],[1398,14091,3534],{"className":14092},[1494,1495,1624],[1398,14094,3596],{"className":14095},[1494,1495,1624],[1398,14097,1025],{"className":14098},[1494,1495,1624],[1398,14100,1632],{"className":14101},[1631],[1398,14103,14105],{"className":14104},[1604],[1398,14106,14108],{"className":14107,"style":3765},[1608],[1398,14109],{},[1398,14111],{"className":14112,"style":1530},[1500],[1398,14114,1435],{"className":14115},[1534],[1398,14117],{"className":14118,"style":1530},[1500],[1398,14120,14122,14125,14128,14183,14186,14189],{"className":14121},[1485],[1398,14123],{"className":14124,"style":8203},[1489],[1398,14126,7961],{"className":14127,"style":3688},[1494,1495],[1398,14129,14131,14134],{"className":14130},[1494],[1398,14132,3534],{"className":14133},[1494,1495],[1398,14135,14137],{"className":14136},[1595],[1398,14138,14140,14175],{"className":14139},[1599,1600],[1398,14141,14143,14172],{"className":14142},[1604],[1398,14144,14146],{"className":14145,"style":1688},[1608],[1398,14147,14148,14151],{"style":3634},[1398,14149],{"className":14150,"style":1617},[1616],[1398,14152,14154],{"className":14153},[1621,1622,1623,1624],[1398,14155,14157,14160,14163,14166,14169],{"className":14156},[1494,1624],[1398,14158,3573],{"className":14159},[1494,1495,1624],[1398,14161,3539],{"className":14162},[1494,1495,1624],[1398,14164,3550],{"className":14165,"style":3654},[1494,1495,1624],[1398,14167,3550],{"className":14168,"style":3654},[1494,1495,1624],[1398,14170,3582],{"className":14171,"style":3755},[1494,1495,1624],[1398,14173,1632],{"className":14174},[1631],[1398,14176,14178],{"className":14177},[1604],[1398,14179,14181],{"className":14180,"style":3765},[1608],[1398,14182],{},[1398,14184],{"className":14185,"style":1530},[1500],[1398,14187,1435],{"className":14188},[1534],[1398,14190],{"className":14191,"style":1530},[1500],[1398,14193,14195,14199,14252,14298,14301,14304],{"className":14194},[1485],[1398,14196],{"className":14197,"style":14198},[1489],"height:1.1255em;vertical-align:-0.15em;",[1398,14200,14202],{"className":14201},[1494,13820],[1398,14203,14205,14243],{"className":14204},[1599,1600],[1398,14206,14208,14240],{"className":14207},[1604],[1398,14209,14212,14227],{"className":14210,"style":14211},[1608],"height:0.9755em;",[1398,14213,14215,14218],{"className":14214,"style":1662},[13834],[1398,14216],{"className":14217,"style":1666},[1616],[1398,14219,14221,14224],{"className":14220,"style":13841},[1494],[1398,14222,6033],{"className":14223},[1494],[1398,14225,3557],{"className":14226,"style":3688},[1494,1495],[1398,14228,14230,14233],{"style":14229},"top:-2.9355em;",[1398,14231],{"className":14232,"style":1666},[1616],[1398,14234,14236],{"className":14235,"style":13858},[13857],[13860,14237,14238],{"xmlns":13862,"width":13863,"height":13864,"viewBox":13865,"preserveAspectRatio":13866},[13868,14239],{"d":13870},[1398,14241,1632],{"className":14242},[1631],[1398,14244,14246],{"className":14245},[1604],[1398,14247,14250],{"className":14248,"style":14249},[1608],"height:0.0645em;",[1398,14251],{},[1398,14253,14255,14258],{"className":14254},[1494],[1398,14256,3534],{"className":14257},[1494,1495],[1398,14259,14261],{"className":14260},[1595],[1398,14262,14264,14290],{"className":14263},[1599,1600],[1398,14265,14267,14287],{"className":14266},[1604],[1398,14268,14270],{"className":14269,"style":1688},[1608],[1398,14271,14272,14275],{"style":3634},[1398,14273],{"className":14274,"style":1617},[1616],[1398,14276,14278],{"className":14277},[1621,1622,1623,1624],[1398,14279,14281,14284],{"className":14280},[1494,1624],[1398,14282,3599],{"className":14283},[1494,1495,1624],[1398,14285,11913],{"className":14286},[1494,1495,1624],[1398,14288,1632],{"className":14289},[1631],[1398,14291,14293],{"className":14292},[1604],[1398,14294,14296],{"className":14295,"style":1639},[1608],[1398,14297],{},[1398,14299],{"className":14300,"style":1530},[1500],[1398,14302,1435],{"className":14303},[1534],[1398,14305],{"className":14306,"style":1530},[1500],[1398,14308,14310,14313],{"className":14309},[1485],[1398,14311],{"className":14312,"style":3612},[1489],[1398,14314,14316,14319],{"className":14315},[1494],[1398,14317,3534],{"className":14318},[1494,1495],[1398,14320,14322],{"className":14321},[1595],[1398,14323,14325,14354],{"className":14324},[1599,1600],[1398,14326,14328,14351],{"className":14327},[1604],[1398,14329,14331],{"className":14330,"style":1688},[1608],[1398,14332,14333,14336],{"style":3634},[1398,14334],{"className":14335,"style":1617},[1616],[1398,14337,14339],{"className":14338},[1621,1622,1623,1624],[1398,14340,14342,14345,14348],{"className":14341},[1494,1624],[1398,14343,3593],{"className":14344},[1494,1495,1624],[1398,14346,3596],{"className":14347},[1494,1495,1624],[1398,14349,3599],{"className":14350},[1494,1495,1624],[1398,14352,1632],{"className":14353},[1631],[1398,14355,14357],{"className":14356},[1604],[1398,14358,14360],{"className":14359,"style":1639},[1608],[1398,14361],{},[1025,14363,14364],{},"因此叫做平方根进位选择加法器",[1741,14366,14367],{"id":14367},"对比关键路径",[1025,14369,14370],{},"这个就是把时间和N的关系画了一个图来对比一下，没啥好说的 后面这俩性能比较好",[1025,14372,14373],{},[1028,14374],{"alt":1028,"src":14375},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-24.png",[978,14377,14379],{"id":14378},"_1s-0s-detectors-全-1-全-0-检测器","1’s & 0’s Detectors ｜ 全 1 \u002F 全 0 检测器",[1025,14381,14382,14385],{},[994,14383,14384],{},"功能","：判断一个多 bit 信号是不是全 1 或全 0",[1025,14387,14388,14389,14784],{},"比如 8-bit 输入：",[1398,14390,14392,14455],{"className":14391},[1401],[1398,14393,14395],{"className":14394},[1405],[1407,14396,14397],{"xmlns":1409},[1411,14398,14399,14452],{},[1414,14400,14401,14408,14415,14422,14428,14434,14440,14446],{},[1449,14402,14403,14405],{},[1417,14404,1426],{},[2883,14406,14407],{},"7",[1449,14409,14410,14412],{},[1417,14411,1426],{},[2883,14413,14414],{},"6",[1449,14416,14417,14419],{},[1417,14418,1426],{},[2883,14420,14421],{},"5",[1449,14423,14424,14426],{},[1417,14425,1426],{},[2883,14427,11129],{},[1449,14429,14430,14432],{},[1417,14431,1426],{},[2883,14433,6046],{},[1449,14435,14436,14438],{},[1417,14437,1426],{},[2883,14439,6033],{},[1449,14441,14442,14444],{},[1417,14443,1426],{},[2883,14445,2885],{},[1449,14447,14448,14450],{},[1417,14449,1426],{},[2883,14451,3030],{},[1474,14453,14454],{"encoding":1476},"A_7A_6A_5A_4A_3A_2A_1A_0",[1398,14456,14458],{"className":14457,"ariaHidden":1462},[1481],[1398,14459,14461,14464,14504,14544,14584,14624,14664,14704,14744],{"className":14460},[1485],[1398,14462],{"className":14463,"style":1858},[1489],[1398,14465,14467,14470],{"className":14466},[1494],[1398,14468,1426],{"className":14469},[1494,1495],[1398,14471,14473],{"className":14472},[1595],[1398,14474,14476,14496],{"className":14475},[1599,1600],[1398,14477,14479,14493],{"className":14478},[1604],[1398,14480,14482],{"className":14481,"style":6203},[1608],[1398,14483,14484,14487],{"style":3634},[1398,14485],{"className":14486,"style":1617},[1616],[1398,14488,14490],{"className":14489},[1621,1622,1623,1624],[1398,14491,14407],{"className":14492},[1494,1624],[1398,14494,1632],{"className":14495},[1631],[1398,14497,14499],{"className":14498},[1604],[1398,14500,14502],{"className":14501,"style":1639},[1608],[1398,14503],{},[1398,14505,14507,14510],{"className":14506},[1494],[1398,14508,1426],{"className":14509},[1494,1495],[1398,14511,14513],{"className":14512},[1595],[1398,14514,14516,14536],{"className":14515},[1599,1600],[1398,14517,14519,14533],{"className":14518},[1604],[1398,14520,14522],{"className":14521,"style":6203},[1608],[1398,14523,14524,14527],{"style":3634},[1398,14525],{"className":14526,"style":1617},[1616],[1398,14528,14530],{"className":14529},[1621,1622,1623,1624],[1398,14531,14414],{"className":14532},[1494,1624],[1398,14534,1632],{"className":14535},[1631],[1398,14537,14539],{"className":14538},[1604],[1398,14540,14542],{"className":14541,"style":1639},[1608],[1398,14543],{},[1398,14545,14547,14550],{"className":14546},[1494],[1398,14548,1426],{"className":14549},[1494,1495],[1398,14551,14553],{"className":14552},[1595],[1398,14554,14556,14576],{"className":14555},[1599,1600],[1398,14557,14559,14573],{"className":14558},[1604],[1398,14560,14562],{"className":14561,"style":6203},[1608],[1398,14563,14564,14567],{"style":3634},[1398,14565],{"className":14566,"style":1617},[1616],[1398,14568,14570],{"className":14569},[1621,1622,1623,1624],[1398,14571,14421],{"className":14572},[1494,1624],[1398,14574,1632],{"className":14575},[1631],[1398,14577,14579],{"className":14578},[1604],[1398,14580,14582],{"className":14581,"style":1639},[1608],[1398,14583],{},[1398,14585,14587,14590],{"className":14586},[1494],[1398,14588,1426],{"className":14589},[1494,1495],[1398,14591,14593],{"className":14592},[1595],[1398,14594,14596,14616],{"className":14595},[1599,1600],[1398,14597,14599,14613],{"className":14598},[1604],[1398,14600,14602],{"className":14601,"style":6203},[1608],[1398,14603,14604,14607],{"style":3634},[1398,14605],{"className":14606,"style":1617},[1616],[1398,14608,14610],{"className":14609},[1621,1622,1623,1624],[1398,14611,11129],{"className":14612},[1494,1624],[1398,14614,1632],{"className":14615},[1631],[1398,14617,14619],{"className":14618},[1604],[1398,14620,14622],{"className":14621,"style":1639},[1608],[1398,14623],{},[1398,14625,14627,14630],{"className":14626},[1494],[1398,14628,1426],{"className":14629},[1494,1495],[1398,14631,14633],{"className":14632},[1595],[1398,14634,14636,14656],{"className":14635},[1599,1600],[1398,14637,14639,14653],{"className":14638},[1604],[1398,14640,14642],{"className":14641,"style":6203},[1608],[1398,14643,14644,14647],{"style":3634},[1398,14645],{"className":14646,"style":1617},[1616],[1398,14648,14650],{"className":14649},[1621,1622,1623,1624],[1398,14651,6046],{"className":14652},[1494,1624],[1398,14654,1632],{"className":14655},[1631],[1398,14657,14659],{"className":14658},[1604],[1398,14660,14662],{"className":14661,"style":1639},[1608],[1398,14663],{},[1398,14665,14667,14670],{"className":14666},[1494],[1398,14668,1426],{"className":14669},[1494,1495],[1398,14671,14673],{"className":14672},[1595],[1398,14674,14676,14696],{"className":14675},[1599,1600],[1398,14677,14679,14693],{"className":14678},[1604],[1398,14680,14682],{"className":14681,"style":6203},[1608],[1398,14683,14684,14687],{"style":3634},[1398,14685],{"className":14686,"style":1617},[1616],[1398,14688,14690],{"className":14689},[1621,1622,1623,1624],[1398,14691,6033],{"className":14692},[1494,1624],[1398,14694,1632],{"className":14695},[1631],[1398,14697,14699],{"className":14698},[1604],[1398,14700,14702],{"className":14701,"style":1639},[1608],[1398,14703],{},[1398,14705,14707,14710],{"className":14706},[1494],[1398,14708,1426],{"className":14709},[1494,1495],[1398,14711,14713],{"className":14712},[1595],[1398,14714,14716,14736],{"className":14715},[1599,1600],[1398,14717,14719,14733],{"className":14718},[1604],[1398,14720,14722],{"className":14721,"style":6203},[1608],[1398,14723,14724,14727],{"style":3634},[1398,14725],{"className":14726,"style":1617},[1616],[1398,14728,14730],{"className":14729},[1621,1622,1623,1624],[1398,14731,2885],{"className":14732},[1494,1624],[1398,14734,1632],{"className":14735},[1631],[1398,14737,14739],{"className":14738},[1604],[1398,14740,14742],{"className":14741,"style":1639},[1608],[1398,14743],{},[1398,14745,14747,14750],{"className":14746},[1494],[1398,14748,1426],{"className":14749},[1494,1495],[1398,14751,14753],{"className":14752},[1595],[1398,14754,14756,14776],{"className":14755},[1599,1600],[1398,14757,14759,14773],{"className":14758},[1604],[1398,14760,14762],{"className":14761,"style":6203},[1608],[1398,14763,14764,14767],{"style":3634},[1398,14765],{"className":14766,"style":1617},[1616],[1398,14768,14770],{"className":14769},[1621,1622,1623,1624],[1398,14771,3030],{"className":14772},[1494,1624],[1398,14774,1632],{"className":14775},[1631],[1398,14777,14779],{"className":14778},[1604],[1398,14780,14782],{"className":14781,"style":1639},[1608],[1398,14783],{},",只有当所有位都是 1 时，全 1 检测器输出才是 1：",[1025,14786,14787],{},[1028,14788],{"alt":1028,"src":14789},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-25.png",[1025,14791,14792],{},[3237,14793,14794],{},"大 fan-in 门不好做，直接做一个 8 输入 AND，晶体管串并联会很复杂，延迟和面积都不好。",[1025,14796,14797],{},"所以课件给了几种实现方式：",[987,14799,14800,14803,14806],{},[990,14801,14802],{},"balanced tree：平衡树结构，层数少，比较规整；",[990,14804,14805],{},"skewed chain：偏斜链式结构，适合某些输入更关键的情况；",[990,14807,14808],{},"transistor-level detector：直接用晶体管拉高\u002F拉低节点，比如全 0 检测常可以做成 NOR 型结构。",[978,14810,14812],{"id":14811},"equality-comparator-相等比较器","Equality Comparator ｜ 相等比较器",[1025,14814,14815],{},"顾名思义。",[1025,14817,14818],{},[1028,14819],{"alt":1028,"src":14820},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-26.png",[1025,14822,14823,14824,14827,14828,14831],{},"有意思的一个点是——",[994,14825,14826],{},"equality comparator 本质是bitwise XNOR +allones detector","，即先采用",[994,14829,14830],{},"异或非\u002F同或","逻辑，然后去判断这几个位是否全是1，如果不全是1，就说明不相等，那实际上就是全 1 检测器",[978,14833,14835],{"id":14834},"magnitude-comparator-大小比较器","Magnitude Comparator ｜ 大小比较器",[1025,14837,14838],{},[1028,14839],{"alt":1028,"src":14840},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-27.png",[1025,14842,14843],{},"实际上是计算B-A 然后再看符号位和sum值来判断",[978,14845,14847],{"id":14846},"counters-计数器","Counters ｜ 计数器",[1025,14849,14850],{},[1028,14851],{"alt":1028,"src":14852},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-28.png",[983,14854,14856],{"id":14855},"binary-counter二进制计数器","binary counter｜二进制计数器",[1025,14858,14859,14860],{},"N-bit binary counter 会按二进制顺序计数：",[1398,14861,14863,14897],{"className":14862},[1401],[1398,14864,14866],{"className":14865},[1405],[1407,14867,14868],{"xmlns":1409},[1411,14869,14870,14894],{},[1414,14871,14872,14875,14877,14880,14882,14885,14887,14890,14892],{},[2883,14873,14874],{},"0000",[1421,14876,3309],{},[2883,14878,14879],{},"0001",[1421,14881,3309],{},[2883,14883,14884],{},"0010",[1421,14886,3309],{},[2883,14888,14889],{},"0011",[1421,14891,3309],{},[1421,14893,3328],{},[1474,14895,14896],{"encoding":1476},"0000 \\rightarrow 0001 \\rightarrow 0010 \\rightarrow 0011 \\rightarrow \\cdots",[1398,14898,14900,14918,14936,14954,14972],{"className":14899,"ariaHidden":1462},[1481],[1398,14901,14903,14906,14909,14912,14915],{"className":14902},[1485],[1398,14904],{"className":14905,"style":2992},[1489],[1398,14907,14874],{"className":14908},[1494],[1398,14910],{"className":14911,"style":1501},[1500],[1398,14913,3309],{"className":14914},[1505],[1398,14916],{"className":14917,"style":1501},[1500],[1398,14919,14921,14924,14927,14930,14933],{"className":14920},[1485],[1398,14922],{"className":14923,"style":2992},[1489],[1398,14925,14879],{"className":14926},[1494],[1398,14928],{"className":14929,"style":1501},[1500],[1398,14931,3309],{"className":14932},[1505],[1398,14934],{"className":14935,"style":1501},[1500],[1398,14937,14939,14942,14945,14948,14951],{"className":14938},[1485],[1398,14940],{"className":14941,"style":2992},[1489],[1398,14943,14884],{"className":14944},[1494],[1398,14946],{"className":14947,"style":1501},[1500],[1398,14949,3309],{"className":14950},[1505],[1398,14952],{"className":14953,"style":1501},[1500],[1398,14955,14957,14960,14963,14966,14969],{"className":14956},[1485],[1398,14958],{"className":14959,"style":2992},[1489],[1398,14961,14889],{"className":14962},[1494],[1398,14964],{"className":14965,"style":1501},[1500],[1398,14967,3309],{"className":14968},[1505],[1398,14970],{"className":14971,"style":1501},[1500],[1398,14973,14975,14978],{"className":14974},[1485],[1398,14976],{"className":14977,"style":3506},[1489],[1398,14979,3328],{"className":14980},[3510],[1025,14982,14983,14984,15044],{},"一个 N-bit counter 有",[1398,14985,14987,15005],{"className":14986},[1401],[1398,14988,14990],{"className":14989},[1405],[1407,14991,14992],{"xmlns":1409},[1411,14993,14994,15002],{},[1414,14995,14996],{},[12736,14997,14998,15000],{},[2883,14999,6033],{},[1417,15001,3557],{},[1474,15003,15004],{"encoding":1476},"2^N",[1398,15006,15008],{"className":15007,"ariaHidden":1462},[1481],[1398,15009,15011,15015],{"className":15010},[1485],[1398,15012],{"className":15013,"style":15014},[1489],"height:0.8413em;",[1398,15016,15018,15021],{"className":15017},[1494],[1398,15019,6033],{"className":15020},[1494],[1398,15022,15024],{"className":15023},[1595],[1398,15025,15027],{"className":15026},[1599],[1398,15028,15030],{"className":15029},[1604],[1398,15031,15033],{"className":15032,"style":15014},[1608],[1398,15034,15035,15038],{"style":13042},[1398,15036],{"className":15037,"style":1617},[1616],[1398,15039,15041],{"className":15040},[1621,1622,1623,1624],[1398,15042,3557],{"className":15043,"style":3688},[1494,1495,1624],"个状态（使用有限状态机来实现——数电内容，时序逻辑电路）",[1025,15046,15047],{},[1028,15048],{"alt":1028,"src":15049},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-29.png",[1025,15051,15052],{},"图里的 synchronous counter 是同步计数器，所有寄存器都由同一个 clock 触发，不是一位一位异步翻转。",[1025,15054,15055,15056],{},"TC 是 terminal count，终端计数信号；",[3237,15057,15058],{},"比如向上计数时：Q=1111，再加 1 就溢出回到 0000，这时可以产生 TC。",[1025,15060,15061],{},[1028,15062],{"alt":1028,"src":15063},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-30.png",[1025,15065,15066],{},"这张图是一个带功能选择的同步计数器：",[1007,15068,15069,15072,15075,15078,15081],{},[990,15070,15071],{},"up\u002Fdown：控制加 1 还是减 1；",[990,15073,15074],{},"load：允许直接装载外部数据 (D)；",[990,15076,15077],{},"reset：复位；",[990,15079,15080],{},"enable：允许计数；",[990,15082,15083],{},"TC：终端计数输出。",[983,15085,15087],{"id":15086},"lfsr-linear-feedback-shift-register-线性反馈移位寄存器",[994,15088,15089],{},"LFSR linear-feedback shift register ｜ 线性反馈移位寄存器",[1025,15091,15092,15095],{},[994,15093,15094],{},"LFSR，linear-feedback shift register，线性反馈移位寄存器"," 也是一个 N-bit 寄存器，但它不是简单加 1，而是：每个时钟把寄存器整体移位，然后把某几位 XOR 的结果反馈到最高位或最低位。",[1025,15097,15098,15099,15181,15182,5628],{},"N 位 LFSR 最多可以遍历除全 0 外的所有 ",[1398,15100,15102,15124],{"className":15101},[1401],[1398,15103,15105],{"className":15104},[1405],[1407,15106,15107],{"xmlns":1409},[1411,15108,15109,15121],{},[1414,15110,15111,15117,15119],{},[12736,15112,15113,15115],{},[2883,15114,6033],{},[1417,15116,3557],{},[1421,15118,3560],{},[2883,15120,2885],{},[1474,15122,15123],{"encoding":1476},"2^N-1",[1398,15125,15127,15172],{"className":15126,"ariaHidden":1462},[1481],[1398,15128,15130,15134,15163,15166,15169],{"className":15129},[1485],[1398,15131],{"className":15132,"style":15133},[1489],"height:0.9247em;vertical-align:-0.0833em;",[1398,15135,15137,15140],{"className":15136},[1494],[1398,15138,6033],{"className":15139},[1494],[1398,15141,15143],{"className":15142},[1595],[1398,15144,15146],{"className":15145},[1599],[1398,15147,15149],{"className":15148},[1604],[1398,15150,15152],{"className":15151,"style":15014},[1608],[1398,15153,15154,15157],{"style":13042},[1398,15155],{"className":15156,"style":1617},[1616],[1398,15158,15160],{"className":15159},[1621,1622,1623,1624],[1398,15161,3557],{"className":15162,"style":3688},[1494,1495,1624],[1398,15164],{"className":15165,"style":1530},[1500],[1398,15167,3560],{"className":15168},[1534],[1398,15170],{"className":15171,"style":1530},[1500],[1398,15173,15175,15178],{"className":15174},[1485],[1398,15176],{"className":15177,"style":2992},[1489],[1398,15179,2885],{"className":15180},[1494]," 个状态，但顺序不是正常二进制递增，而是看起来像",[3237,15183,15184],{},[994,15185,15186],{},"随机的伪随机顺序",[978,15188,15190],{"id":15189},"multiplier-乘法器设计","Multiplier ｜ 乘法器设计",[983,15192,15194],{"id":15193},"the-binary-multiplication-二进制乘法","The Binary Multiplication ｜ 二进制乘法",[987,15196,15197,15976],{},[990,15198,15199,15200,15228,15229,15257,15258,15228,15287,15315,15316,15319,9340,15551,5628,15774,15776,15777,15847,15848,15918,15919,15947,15948,5628],{},"二进制数的按位展开\n设 ",[1398,15201,15203,15216],{"className":15202},[1401],[1398,15204,15206],{"className":15205},[1405],[1407,15207,15208],{"xmlns":1409},[1411,15209,15210,15214],{},[1414,15211,15212],{},[1417,15213,11001],{},[1474,15215,11001],{"encoding":1476},[1398,15217,15219],{"className":15218,"ariaHidden":1462},[1481],[1398,15220,15222,15225],{"className":15221},[1485],[1398,15223],{"className":15224,"style":1490},[1489],[1398,15226,11001],{"className":15227,"style":11111},[1494,1495]," 是 ",[1398,15230,15232,15245],{"className":15231},[1401],[1398,15233,15235],{"className":15234},[1405],[1407,15236,15237],{"xmlns":1409},[1411,15238,15239,15243],{},[1414,15240,15241],{},[1417,15242,7961],{},[1474,15244,7961],{"encoding":1476},[1398,15246,15248],{"className":15247,"ariaHidden":1462},[1481],[1398,15249,15251,15254],{"className":15250},[1485],[1398,15252],{"className":15253,"style":1490},[1489],[1398,15255,7961],{"className":15256,"style":3688},[1494,1495]," 位二进制数，",[1398,15259,15261,15275],{"className":15260},[1401],[1398,15262,15264],{"className":15263},[1405],[1407,15265,15266],{"xmlns":1409},[1411,15267,15268,15273],{},[1414,15269,15270],{},[1417,15271,15272],{},"Y",[1474,15274,15272],{"encoding":1476},[1398,15276,15278],{"className":15277,"ariaHidden":1462},[1481],[1398,15279,15281,15284],{"className":15280},[1485],[1398,15282],{"className":15283,"style":1490},[1489],[1398,15285,15272],{"className":15286,"style":1530},[1494,1495],[1398,15288,15290,15303],{"className":15289},[1401],[1398,15291,15293],{"className":15292},[1405],[1407,15294,15295],{"xmlns":1409},[1411,15296,15297,15301],{},[1414,15298,15299],{},[1417,15300,3557],{},[1474,15302,3557],{"encoding":1476},[1398,15304,15306],{"className":15305,"ariaHidden":1462},[1481],[1398,15307,15309,15312],{"className":15308},[1485],[1398,15310],{"className":15311,"style":1490},[1489],[1398,15313,3557],{"className":15314,"style":3688},[1494,1495]," 位二进制数，则：",[15317,15318],"br",{},[1398,15320,15322,15372],{"className":15321},[1401],[1398,15323,15325],{"className":15324},[1405],[1407,15326,15327],{"xmlns":1409},[1411,15328,15329,15369],{},[1414,15330,15331,15333,15335,15357,15363],{},[1417,15332,11001],{},[1421,15334,1423],{},[15336,15337,15338,15341,15349],"msubsup",{},[1421,15339,15340],{},"∑",[1414,15342,15343,15345,15347],{},[1417,15344,1455],{},[1421,15346,1423],{},[2883,15348,3030],{},[1414,15350,15351,15353,15355],{},[1417,15352,7961],{},[1421,15354,3560],{},[2883,15356,2885],{},[1449,15358,15359,15361],{},[1417,15360,11001],{},[1417,15362,1455],{},[12736,15364,15365,15367],{},[2883,15366,6033],{},[1417,15368,1455],{},[1474,15370,15371],{"encoding":1476},"X=\\sum_{i=0}^{M-1}X_i2^i",[1398,15373,15375,15393],{"className":15374,"ariaHidden":1462},[1481],[1398,15376,15378,15381,15384,15387,15390],{"className":15377},[1485],[1398,15379],{"className":15380,"style":1490},[1489],[1398,15382,11001],{"className":15383,"style":11111},[1494,1495],[1398,15385],{"className":15386,"style":1501},[1500],[1398,15388,1423],{"className":15389},[1505],[1398,15391],{"className":15392,"style":1501},[1500],[1398,15394,15396,15400,15477,15480,15521],{"className":15395},[1485],[1398,15397],{"className":15398,"style":15399},[1489],"height:1.2809em;vertical-align:-0.2997em;",[1398,15401,15404,15410],{"className":15402},[15403],"mop",[1398,15405,15340],{"className":15406,"style":15409},[15403,15407,15408],"op-symbol","small-op","position:relative;top:0em;",[1398,15411,15413],{"className":15412},[1595],[1398,15414,15416,15468],{"className":15415},[1599,1600],[1398,15417,15419,15465],{"className":15418},[1604],[1398,15420,15423,15444],{"className":15421,"style":15422},[1608],"height:0.9812em;",[1398,15424,15426,15429],{"style":15425},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1398,15427],{"className":15428,"style":1617},[1616],[1398,15430,15432],{"className":15431},[1621,1622,1623,1624],[1398,15433,15435,15438,15441],{"className":15434},[1494,1624],[1398,15436,1455],{"className":15437},[1494,1495,1624],[1398,15439,1423],{"className":15440},[1505,1624],[1398,15442,3030],{"className":15443},[1494,1624],[1398,15445,15447,15450],{"style":15446},"top:-3.2029em;margin-right:0.05em;",[1398,15448],{"className":15449,"style":1617},[1616],[1398,15451,15453],{"className":15452},[1621,1622,1623,1624],[1398,15454,15456,15459,15462],{"className":15455},[1494,1624],[1398,15457,7961],{"className":15458,"style":3688},[1494,1495,1624],[1398,15460,3560],{"className":15461},[1534,1624],[1398,15463,2885],{"className":15464},[1494,1624],[1398,15466,1632],{"className":15467},[1631],[1398,15469,15471],{"className":15470},[1604],[1398,15472,15475],{"className":15473,"style":15474},[1608],"height:0.2997em;",[1398,15476],{},[1398,15478],{"className":15479,"style":1823},[1500],[1398,15481,15483,15486],{"className":15482},[1494],[1398,15484,11001],{"className":15485,"style":11111},[1494,1495],[1398,15487,15489],{"className":15488},[1595],[1398,15490,15492,15513],{"className":15491},[1599,1600],[1398,15493,15495,15510],{"className":15494},[1604],[1398,15496,15498],{"className":15497,"style":1609},[1608],[1398,15499,15501,15504],{"style":15500},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1398,15502],{"className":15503,"style":1617},[1616],[1398,15505,15507],{"className":15506},[1621,1622,1623,1624],[1398,15508,1455],{"className":15509},[1494,1495,1624],[1398,15511,1632],{"className":15512},[1631],[1398,15514,15516],{"className":15515},[1604],[1398,15517,15519],{"className":15518,"style":1639},[1608],[1398,15520],{},[1398,15522,15524,15527],{"className":15523},[1494],[1398,15525,6033],{"className":15526},[1494],[1398,15528,15530],{"className":15529},[1595],[1398,15531,15533],{"className":15532},[1599],[1398,15534,15536],{"className":15535},[1604],[1398,15537,15540],{"className":15538,"style":15539},[1608],"height:0.8247em;",[1398,15541,15542,15545],{"style":13042},[1398,15543],{"className":15544,"style":1617},[1616],[1398,15546,15548],{"className":15547},[1621,1622,1623,1624],[1398,15549,1455],{"className":15550},[1494,1495,1624],[1398,15552,15554,15603],{"className":15553},[1401],[1398,15555,15557],{"className":15556},[1405],[1407,15558,15559],{"xmlns":1409},[1411,15560,15561,15600],{},[1414,15562,15563,15565,15567,15588,15594],{},[1417,15564,15272],{},[1421,15566,1423],{},[15336,15568,15569,15571,15580],{},[1421,15570,15340],{},[1414,15572,15573,15576,15578],{},[1417,15574,15575],{},"j",[1421,15577,1423],{},[2883,15579,3030],{},[1414,15581,15582,15584,15586],{},[1417,15583,3557],{},[1421,15585,3560],{},[2883,15587,2885],{},[1449,15589,15590,15592],{},[1417,15591,15272],{},[1417,15593,15575],{},[12736,15595,15596,15598],{},[2883,15597,6033],{},[1417,15599,15575],{},[1474,15601,15602],{"encoding":1476},"Y=\\sum_{j=0}^{N-1}Y_j2^j",[1398,15604,15606,15624],{"className":15605,"ariaHidden":1462},[1481],[1398,15607,15609,15612,15615,15618,15621],{"className":15608},[1485],[1398,15610],{"className":15611,"style":1490},[1489],[1398,15613,15272],{"className":15614,"style":1530},[1494,1495],[1398,15616],{"className":15617,"style":1501},[1500],[1398,15619,1423],{"className":15620},[1505],[1398,15622],{"className":15623,"style":1501},[1500],[1398,15625,15627,15631,15702,15705,15745],{"className":15626},[1485],[1398,15628],{"className":15629,"style":15630},[1489],"height:1.417em;vertical-align:-0.4358em;",[1398,15632,15634,15637],{"className":15633},[15403],[1398,15635,15340],{"className":15636,"style":15409},[15403,15407,15408],[1398,15638,15640],{"className":15639},[1595],[1398,15641,15643,15693],{"className":15642},[1599,1600],[1398,15644,15646,15690],{"className":15645},[1604],[1398,15647,15649,15670],{"className":15648,"style":15422},[1608],[1398,15650,15651,15654],{"style":15425},[1398,15652],{"className":15653,"style":1617},[1616],[1398,15655,15657],{"className":15656},[1621,1622,1623,1624],[1398,15658,15660,15664,15667],{"className":15659},[1494,1624],[1398,15661,15575],{"className":15662,"style":15663},[1494,1495,1624],"margin-right:0.0572em;",[1398,15665,1423],{"className":15666},[1505,1624],[1398,15668,3030],{"className":15669},[1494,1624],[1398,15671,15672,15675],{"style":15446},[1398,15673],{"className":15674,"style":1617},[1616],[1398,15676,15678],{"className":15677},[1621,1622,1623,1624],[1398,15679,15681,15684,15687],{"className":15680},[1494,1624],[1398,15682,3557],{"className":15683,"style":3688},[1494,1495,1624],[1398,15685,3560],{"className":15686},[1534,1624],[1398,15688,2885],{"className":15689},[1494,1624],[1398,15691,1632],{"className":15692},[1631],[1398,15694,15696],{"className":15695},[1604],[1398,15697,15700],{"className":15698,"style":15699},[1608],"height:0.4358em;",[1398,15701],{},[1398,15703],{"className":15704,"style":1823},[1500],[1398,15706,15708,15711],{"className":15707},[1494],[1398,15709,15272],{"className":15710,"style":1530},[1494,1495],[1398,15712,15714],{"className":15713},[1595],[1398,15715,15717,15737],{"className":15716},[1599,1600],[1398,15718,15720,15734],{"className":15719},[1604],[1398,15721,15723],{"className":15722,"style":1609},[1608],[1398,15724,15725,15728],{"style":5320},[1398,15726],{"className":15727,"style":1617},[1616],[1398,15729,15731],{"className":15730},[1621,1622,1623,1624],[1398,15732,15575],{"className":15733,"style":15663},[1494,1495,1624],[1398,15735,1632],{"className":15736},[1631],[1398,15738,15740],{"className":15739},[1604],[1398,15741,15743],{"className":15742,"style":3765},[1608],[1398,15744],{},[1398,15746,15748,15751],{"className":15747},[1494],[1398,15749,6033],{"className":15750},[1494],[1398,15752,15754],{"className":15753},[1595],[1398,15755,15757],{"className":15756},[1599],[1398,15758,15760],{"className":15759},[1604],[1398,15761,15763],{"className":15762,"style":15539},[1608],[1398,15764,15765,15768],{"style":13042},[1398,15766],{"className":15767,"style":1617},[1616],[1398,15769,15771],{"className":15770},[1621,1622,1623,1624],[1398,15772,15575],{"className":15773,"style":15663},[1494,1495,1624],[15317,15775],{},"其中，",[1398,15778,15780,15798],{"className":15779},[1401],[1398,15781,15783],{"className":15782},[1405],[1407,15784,15785],{"xmlns":1409},[1411,15786,15787,15795],{},[1414,15788,15789],{},[1449,15790,15791,15793],{},[1417,15792,11001],{},[1417,15794,1455],{},[1474,15796,15797],{"encoding":1476},"X_i",[1398,15799,15801],{"className":15800,"ariaHidden":1462},[1481],[1398,15802,15804,15807],{"className":15803},[1485],[1398,15805],{"className":15806,"style":1858},[1489],[1398,15808,15810,15813],{"className":15809},[1494],[1398,15811,11001],{"className":15812,"style":11111},[1494,1495],[1398,15814,15816],{"className":15815},[1595],[1398,15817,15819,15839],{"className":15818},[1599,1600],[1398,15820,15822,15836],{"className":15821},[1604],[1398,15823,15825],{"className":15824,"style":1609},[1608],[1398,15826,15827,15830],{"style":15500},[1398,15828],{"className":15829,"style":1617},[1616],[1398,15831,15833],{"className":15832},[1621,1622,1623,1624],[1398,15834,1455],{"className":15835},[1494,1495,1624],[1398,15837,1632],{"className":15838},[1631],[1398,15840,15842],{"className":15841},[1604],[1398,15843,15845],{"className":15844,"style":1639},[1608],[1398,15846],{}," 和 ",[1398,15849,15851,15869],{"className":15850},[1401],[1398,15852,15854],{"className":15853},[1405],[1407,15855,15856],{"xmlns":1409},[1411,15857,15858,15866],{},[1414,15859,15860],{},[1449,15861,15862,15864],{},[1417,15863,15272],{},[1417,15865,15575],{},[1474,15867,15868],{"encoding":1476},"Y_j",[1398,15870,15872],{"className":15871,"ariaHidden":1462},[1481],[1398,15873,15875,15878],{"className":15874},[1485],[1398,15876],{"className":15877,"style":8203},[1489],[1398,15879,15881,15884],{"className":15880},[1494],[1398,15882,15272],{"className":15883,"style":1530},[1494,1495],[1398,15885,15887],{"className":15886},[1595],[1398,15888,15890,15910],{"className":15889},[1599,1600],[1398,15891,15893,15907],{"className":15892},[1604],[1398,15894,15896],{"className":15895,"style":1609},[1608],[1398,15897,15898,15901],{"style":5320},[1398,15899],{"className":15900,"style":1617},[1616],[1398,15902,15904],{"className":15903},[1621,1622,1623,1624],[1398,15905,15575],{"className":15906,"style":15663},[1494,1495,1624],[1398,15908,1632],{"className":15909},[1631],[1398,15911,15913],{"className":15912},[1604],[1398,15914,15916],{"className":15915,"style":3765},[1608],[1398,15917],{}," 都是单个 bit，只能取 ",[1398,15920,15922,15935],{"className":15921},[1401],[1398,15923,15925],{"className":15924},[1405],[1407,15926,15927],{"xmlns":1409},[1411,15928,15929,15933],{},[1414,15930,15931],{},[2883,15932,3030],{},[1474,15934,3030],{"encoding":1476},[1398,15936,15938],{"className":15937,"ariaHidden":1462},[1481],[1398,15939,15941,15944],{"className":15940},[1485],[1398,15942],{"className":15943,"style":2992},[1489],[1398,15945,3030],{"className":15946},[1494]," 或 ",[1398,15949,15951,15964],{"className":15950},[1401],[1398,15952,15954],{"className":15953},[1405],[1407,15955,15956],{"xmlns":1409},[1411,15957,15958,15962],{},[1414,15959,15960],{},[2883,15961,2885],{},[1474,15963,2885],{"encoding":1476},[1398,15965,15967],{"className":15966,"ariaHidden":1462},[1481],[1398,15968,15970,15973],{"className":15969},[1485],[1398,15971],{"className":15972,"style":2992},[1489],[1398,15974,2885],{"className":15975},[1494],[990,15977,15978,15979,5628,16054,16056,16057,15847,16085,16113,16114],{},"乘法的数学展开\n乘积为 ",[1398,15980,15982,16006],{"className":15981},[1401],[1398,15983,15985],{"className":15984},[1405],[1407,15986,15987],{"xmlns":1409},[1411,15988,15989,16003],{},[1414,15990,15991,15994,15996,15998,16001],{},[1417,15992,15993],{},"Z",[1421,15995,1423],{},[1417,15997,11001],{},[1421,15999,16000],{},"×",[1417,16002,15272],{},[1474,16004,16005],{"encoding":1476},"Z=X\\times Y",[1398,16007,16009,16027,16045],{"className":16008,"ariaHidden":1462},[1481],[1398,16010,16012,16015,16018,16021,16024],{"className":16011},[1485],[1398,16013],{"className":16014,"style":1490},[1489],[1398,16016,15993],{"className":16017,"style":1526},[1494,1495],[1398,16019],{"className":16020,"style":1501},[1500],[1398,16022,1423],{"className":16023},[1505],[1398,16025],{"className":16026,"style":1501},[1500],[1398,16028,16030,16033,16036,16039,16042],{"className":16029},[1485],[1398,16031],{"className":16032,"style":1515},[1489],[1398,16034,11001],{"className":16035,"style":11111},[1494,1495],[1398,16037],{"className":16038,"style":1530},[1500],[1398,16040,16000],{"className":16041},[1534],[1398,16043],{"className":16044,"style":1530},[1500],[1398,16046,16048,16051],{"className":16047},[1485],[1398,16049],{"className":16050,"style":1490},[1489],[1398,16052,15272],{"className":16053,"style":1530},[1494,1495],[15317,16055],{},"把 ",[1398,16058,16060,16073],{"className":16059},[1401],[1398,16061,16063],{"className":16062},[1405],[1407,16064,16065],{"xmlns":1409},[1411,16066,16067,16071],{},[1414,16068,16069],{},[1417,16070,11001],{},[1474,16072,11001],{"encoding":1476},[1398,16074,16076],{"className":16075,"ariaHidden":1462},[1481],[1398,16077,16079,16082],{"className":16078},[1485],[1398,16080],{"className":16081,"style":1490},[1489],[1398,16083,11001],{"className":16084,"style":11111},[1494,1495],[1398,16086,16088,16101],{"className":16087},[1401],[1398,16089,16091],{"className":16090},[1405],[1407,16092,16093],{"xmlns":1409},[1411,16094,16095,16099],{},[1414,16096,16097],{},[1417,16098,15272],{},[1474,16100,15272],{"encoding":1476},[1398,16102,16104],{"className":16103,"ariaHidden":1462},[1481],[1398,16105,16107,16110],{"className":16106},[1485],[1398,16108],{"className":16109,"style":1490},[1489],[1398,16111,15272],{"className":16112,"style":1530},[1494,1495]," 的按位展开代入：",[1398,16115,16117],{"className":16116},[2737],[1398,16118,16120,16213],{"className":16119},[1401],[1398,16121,16123],{"className":16122},[1405],[1407,16124,16125],{"xmlns":1409,"display":2746},[1411,16126,16127,16210],{},[1414,16128,16129,16131,16133,16172],{},[1417,16130,15993],{},[1421,16132,1423],{},[1414,16134,16135,16137,16158,16164,16170],{},[1421,16136,1439],{"fence":1462},[16138,16139,16140,16142,16150],"munderover",{},[1421,16141,15340],{},[1414,16143,16144,16146,16148],{},[1417,16145,1455],{},[1421,16147,1423],{},[2883,16149,3030],{},[1414,16151,16152,16154,16156],{},[1417,16153,7961],{},[1421,16155,3560],{},[2883,16157,2885],{},[1449,16159,16160,16162],{},[1417,16161,11001],{},[1417,16163,1455],{},[12736,16165,16166,16168],{},[2883,16167,6033],{},[1417,16169,1455],{},[1421,16171,1458],{"fence":1462},[1414,16173,16174,16176,16196,16202,16208],{},[1421,16175,1439],{"fence":1462},[16138,16177,16178,16180,16188],{},[1421,16179,15340],{},[1414,16181,16182,16184,16186],{},[1417,16183,15575],{},[1421,16185,1423],{},[2883,16187,3030],{},[1414,16189,16190,16192,16194],{},[1417,16191,3557],{},[1421,16193,3560],{},[2883,16195,2885],{},[1449,16197,16198,16200],{},[1417,16199,15272],{},[1417,16201,15575],{},[12736,16203,16204,16206],{},[2883,16205,6033],{},[1417,16207,15575],{},[1421,16209,1458],{"fence":1462},[1474,16211,16212],{"encoding":1476},"Z=\\left(\\sum_{i=0}^{M-1}X_i2^i\\right)\\left(\\sum_{j=0}^{N-1}Y_j2^j\\right)",[1398,16214,16216,16234],{"className":16215,"ariaHidden":1462},[1481],[1398,16217,16219,16222,16225,16228,16231],{"className":16218},[1485],[1398,16220],{"className":16221,"style":1490},[1489],[1398,16223,15993],{"className":16224,"style":1526},[1494,1495],[1398,16226],{"className":16227,"style":1501},[1500],[1398,16229,1423],{"className":16230},[1505],[1398,16232],{"className":16233,"style":1501},[1500],[1398,16235,16237,16241,16412,16415],{"className":16236},[1485],[1398,16238],{"className":16239,"style":16240},[1489],"height:3.2421em;vertical-align:-1.4138em;",[1398,16242,16244,16251,16332,16335,16375,16406],{"className":16243},[3510],[1398,16245,16247],{"className":16246,"style":8285},[1548,8284],[1398,16248,1439],{"className":16249},[8289,16250],"size4",[1398,16252,16255],{"className":16253},[15403,16254],"op-limits",[1398,16256,16258,16323],{"className":16257},[1599,1600],[1398,16259,16261,16320],{"className":16260},[1604],[1398,16262,16265,16287,16299],{"className":16263,"style":16264},[1608],"height:1.8283em;",[1398,16266,16268,16272],{"style":16267},"top:-1.8723em;margin-left:0em;",[1398,16269],{"className":16270,"style":16271},[1616],"height:3.05em;",[1398,16273,16275],{"className":16274},[1621,1622,1623,1624],[1398,16276,16278,16281,16284],{"className":16277},[1494,1624],[1398,16279,1455],{"className":16280},[1494,1495,1624],[1398,16282,1423],{"className":16283},[1505,1624],[1398,16285,3030],{"className":16286},[1494,1624],[1398,16288,16290,16293],{"style":16289},"top:-3.05em;",[1398,16291],{"className":16292,"style":16271},[1616],[1398,16294,16295],{},[1398,16296,15340],{"className":16297},[15403,15407,16298],"large-op",[1398,16300,16302,16305],{"style":16301},"top:-4.3em;margin-left:0em;",[1398,16303],{"className":16304,"style":16271},[1616],[1398,16306,16308],{"className":16307},[1621,1622,1623,1624],[1398,16309,16311,16314,16317],{"className":16310},[1494,1624],[1398,16312,7961],{"className":16313,"style":3688},[1494,1495,1624],[1398,16315,3560],{"className":16316},[1534,1624],[1398,16318,2885],{"className":16319},[1494,1624],[1398,16321,1632],{"className":16322},[1631],[1398,16324,16326],{"className":16325},[1604],[1398,16327,16330],{"className":16328,"style":16329},[1608],"height:1.2777em;",[1398,16331],{},[1398,16333],{"className":16334,"style":1823},[1500],[1398,16336,16338,16341],{"className":16337},[1494],[1398,16339,11001],{"className":16340,"style":11111},[1494,1495],[1398,16342,16344],{"className":16343},[1595],[1398,16345,16347,16367],{"className":16346},[1599,1600],[1398,16348,16350,16364],{"className":16349},[1604],[1398,16351,16353],{"className":16352,"style":1609},[1608],[1398,16354,16355,16358],{"style":15500},[1398,16356],{"className":16357,"style":1617},[1616],[1398,16359,16361],{"className":16360},[1621,1622,1623,1624],[1398,16362,1455],{"className":16363},[1494,1495,1624],[1398,16365,1632],{"className":16366},[1631],[1398,16368,16370],{"className":16369},[1604],[1398,16371,16373],{"className":16372,"style":1639},[1608],[1398,16374],{},[1398,16376,16378,16381],{"className":16377},[1494],[1398,16379,6033],{"className":16380},[1494],[1398,16382,16384],{"className":16383},[1595],[1398,16385,16387],{"className":16386},[1599],[1398,16388,16390],{"className":16389},[1604],[1398,16391,16394],{"className":16392,"style":16393},[1608],"height:0.8747em;",[1398,16395,16397,16400],{"style":16396},"top:-3.113em;margin-right:0.05em;",[1398,16398],{"className":16399,"style":1617},[1616],[1398,16401,16403],{"className":16402},[1621,1622,1623,1624],[1398,16404,1455],{"className":16405},[1494,1495,1624],[1398,16407,16409],{"className":16408,"style":8285},[1645,8284],[1398,16410,1458],{"className":16411},[8289,16250],[1398,16413],{"className":16414,"style":1823},[1500],[1398,16416,16418,16424,16498,16501,16541,16570],{"className":16417},[3510],[1398,16419,16421],{"className":16420,"style":8285},[1548,8284],[1398,16422,1439],{"className":16423},[8289,16250],[1398,16425,16427],{"className":16426},[15403,16254],[1398,16428,16430,16489],{"className":16429},[1599,1600],[1398,16431,16433,16486],{"className":16432},[1604],[1398,16434,16436,16456,16466],{"className":16435,"style":16264},[1608],[1398,16437,16438,16441],{"style":16267},[1398,16439],{"className":16440,"style":16271},[1616],[1398,16442,16444],{"className":16443},[1621,1622,1623,1624],[1398,16445,16447,16450,16453],{"className":16446},[1494,1624],[1398,16448,15575],{"className":16449,"style":15663},[1494,1495,1624],[1398,16451,1423],{"className":16452},[1505,1624],[1398,16454,3030],{"className":16455},[1494,1624],[1398,16457,16458,16461],{"style":16289},[1398,16459],{"className":16460,"style":16271},[1616],[1398,16462,16463],{},[1398,16464,15340],{"className":16465},[15403,15407,16298],[1398,16467,16468,16471],{"style":16301},[1398,16469],{"className":16470,"style":16271},[1616],[1398,16472,16474],{"className":16473},[1621,1622,1623,1624],[1398,16475,16477,16480,16483],{"className":16476},[1494,1624],[1398,16478,3557],{"className":16479,"style":3688},[1494,1495,1624],[1398,16481,3560],{"className":16482},[1534,1624],[1398,16484,2885],{"className":16485},[1494,1624],[1398,16487,1632],{"className":16488},[1631],[1398,16490,16492],{"className":16491},[1604],[1398,16493,16496],{"className":16494,"style":16495},[1608],"height:1.4138em;",[1398,16497],{},[1398,16499],{"className":16500,"style":1823},[1500],[1398,16502,16504,16507],{"className":16503},[1494],[1398,16505,15272],{"className":16506,"style":1530},[1494,1495],[1398,16508,16510],{"className":16509},[1595],[1398,16511,16513,16533],{"className":16512},[1599,1600],[1398,16514,16516,16530],{"className":16515},[1604],[1398,16517,16519],{"className":16518,"style":1609},[1608],[1398,16520,16521,16524],{"style":5320},[1398,16522],{"className":16523,"style":1617},[1616],[1398,16525,16527],{"className":16526},[1621,1622,1623,1624],[1398,16528,15575],{"className":16529,"style":15663},[1494,1495,1624],[1398,16531,1632],{"className":16532},[1631],[1398,16534,16536],{"className":16535},[1604],[1398,16537,16539],{"className":16538,"style":3765},[1608],[1398,16540],{},[1398,16542,16544,16547],{"className":16543},[1494],[1398,16545,6033],{"className":16546},[1494],[1398,16548,16550],{"className":16549},[1595],[1398,16551,16553],{"className":16552},[1599],[1398,16554,16556],{"className":16555},[1604],[1398,16557,16559],{"className":16558,"style":16393},[1608],[1398,16560,16561,16564],{"style":16396},[1398,16562],{"className":16563,"style":1617},[1616],[1398,16565,16567],{"className":16566},[1621,1622,1623,1624],[1398,16568,15575],{"className":16569,"style":15663},[1494,1495,1624],[1398,16571,16573],{"className":16572,"style":8285},[1645,8284],[1398,16574,1458],{"className":16575},[8289,16250],[1025,16577,16578],{},"根据乘法分配律展开：",[1025,16580,16581,5628],{},[1398,16582,16584,16664],{"className":16583},[1401],[1398,16585,16587],{"className":16586},[1405],[1407,16588,16589],{"xmlns":1409},[1411,16590,16591,16661],{},[1414,16592,16593,16595,16597,16617,16637,16643,16649],{},[1417,16594,15993],{},[1421,16596,1423],{},[15336,16598,16599,16601,16609],{},[1421,16600,15340],{},[1414,16602,16603,16605,16607],{},[1417,16604,1455],{},[1421,16606,1423],{},[2883,16608,3030],{},[1414,16610,16611,16613,16615],{},[1417,16612,7961],{},[1421,16614,3560],{},[2883,16616,2885],{},[15336,16618,16619,16621,16629],{},[1421,16620,15340],{},[1414,16622,16623,16625,16627],{},[1417,16624,15575],{},[1421,16626,1423],{},[2883,16628,3030],{},[1414,16630,16631,16633,16635],{},[1417,16632,3557],{},[1421,16634,3560],{},[2883,16636,2885],{},[1449,16638,16639,16641],{},[1417,16640,11001],{},[1417,16642,1455],{},[1449,16644,16645,16647],{},[1417,16646,15272],{},[1417,16648,15575],{},[12736,16650,16651,16653],{},[2883,16652,6033],{},[1414,16654,16655,16657,16659],{},[1417,16656,1455],{},[1421,16658,1435],{},[1417,16660,15575],{},[1474,16662,16663],{"encoding":1476},"Z=\\sum_{i=0}^{M-1}\\sum_{j=0}^{N-1}X_iY_j2^{i+j}",[1398,16665,16667,16685],{"className":16666,"ariaHidden":1462},[1481],[1398,16668,16670,16673,16676,16679,16682],{"className":16669},[1485],[1398,16671],{"className":16672,"style":1490},[1489],[1398,16674,15993],{"className":16675,"style":1526},[1494,1495],[1398,16677],{"className":16678,"style":1501},[1500],[1398,16680,1423],{"className":16681},[1505],[1398,16683],{"className":16684,"style":1501},[1500],[1398,16686,16688,16691,16760,16763,16832,16835,16875,16915],{"className":16687},[1485],[1398,16689],{"className":16690,"style":15630},[1489],[1398,16692,16694,16697],{"className":16693},[15403],[1398,16695,15340],{"className":16696,"style":15409},[15403,15407,15408],[1398,16698,16700],{"className":16699},[1595],[1398,16701,16703,16752],{"className":16702},[1599,1600],[1398,16704,16706,16749],{"className":16705},[1604],[1398,16707,16709,16729],{"className":16708,"style":15422},[1608],[1398,16710,16711,16714],{"style":15425},[1398,16712],{"className":16713,"style":1617},[1616],[1398,16715,16717],{"className":16716},[1621,1622,1623,1624],[1398,16718,16720,16723,16726],{"className":16719},[1494,1624],[1398,16721,1455],{"className":16722},[1494,1495,1624],[1398,16724,1423],{"className":16725},[1505,1624],[1398,16727,3030],{"className":16728},[1494,1624],[1398,16730,16731,16734],{"style":15446},[1398,16732],{"className":16733,"style":1617},[1616],[1398,16735,16737],{"className":16736},[1621,1622,1623,1624],[1398,16738,16740,16743,16746],{"className":16739},[1494,1624],[1398,16741,7961],{"className":16742,"style":3688},[1494,1495,1624],[1398,16744,3560],{"className":16745},[1534,1624],[1398,16747,2885],{"className":16748},[1494,1624],[1398,16750,1632],{"className":16751},[1631],[1398,16753,16755],{"className":16754},[1604],[1398,16756,16758],{"className":16757,"style":15474},[1608],[1398,16759],{},[1398,16761],{"className":16762,"style":1823},[1500],[1398,16764,16766,16769],{"className":16765},[15403],[1398,16767,15340],{"className":16768,"style":15409},[15403,15407,15408],[1398,16770,16772],{"className":16771},[1595],[1398,16773,16775,16824],{"className":16774},[1599,1600],[1398,16776,16778,16821],{"className":16777},[1604],[1398,16779,16781,16801],{"className":16780,"style":15422},[1608],[1398,16782,16783,16786],{"style":15425},[1398,16784],{"className":16785,"style":1617},[1616],[1398,16787,16789],{"className":16788},[1621,1622,1623,1624],[1398,16790,16792,16795,16798],{"className":16791},[1494,1624],[1398,16793,15575],{"className":16794,"style":15663},[1494,1495,1624],[1398,16796,1423],{"className":16797},[1505,1624],[1398,16799,3030],{"className":16800},[1494,1624],[1398,16802,16803,16806],{"style":15446},[1398,16804],{"className":16805,"style":1617},[1616],[1398,16807,16809],{"className":16808},[1621,1622,1623,1624],[1398,16810,16812,16815,16818],{"className":16811},[1494,1624],[1398,16813,3557],{"className":16814,"style":3688},[1494,1495,1624],[1398,16816,3560],{"className":16817},[1534,1624],[1398,16819,2885],{"className":16820},[1494,1624],[1398,16822,1632],{"className":16823},[1631],[1398,16825,16827],{"className":16826},[1604],[1398,16828,16830],{"className":16829,"style":15699},[1608],[1398,16831],{},[1398,16833],{"className":16834,"style":1823},[1500],[1398,16836,16838,16841],{"className":16837},[1494],[1398,16839,11001],{"className":16840,"style":11111},[1494,1495],[1398,16842,16844],{"className":16843},[1595],[1398,16845,16847,16867],{"className":16846},[1599,1600],[1398,16848,16850,16864],{"className":16849},[1604],[1398,16851,16853],{"className":16852,"style":1609},[1608],[1398,16854,16855,16858],{"style":15500},[1398,16856],{"className":16857,"style":1617},[1616],[1398,16859,16861],{"className":16860},[1621,1622,1623,1624],[1398,16862,1455],{"className":16863},[1494,1495,1624],[1398,16865,1632],{"className":16866},[1631],[1398,16868,16870],{"className":16869},[1604],[1398,16871,16873],{"className":16872,"style":1639},[1608],[1398,16874],{},[1398,16876,16878,16881],{"className":16877},[1494],[1398,16879,15272],{"className":16880,"style":1530},[1494,1495],[1398,16882,16884],{"className":16883},[1595],[1398,16885,16887,16907],{"className":16886},[1599,1600],[1398,16888,16890,16904],{"className":16889},[1604],[1398,16891,16893],{"className":16892,"style":1609},[1608],[1398,16894,16895,16898],{"style":5320},[1398,16896],{"className":16897,"style":1617},[1616],[1398,16899,16901],{"className":16900},[1621,1622,1623,1624],[1398,16902,15575],{"className":16903,"style":15663},[1494,1495,1624],[1398,16905,1632],{"className":16906},[1631],[1398,16908,16910],{"className":16909},[1604],[1398,16911,16913],{"className":16912,"style":3765},[1608],[1398,16914],{},[1398,16916,16918,16921],{"className":16917},[1494],[1398,16919,6033],{"className":16920},[1494],[1398,16922,16924],{"className":16923},[1595],[1398,16925,16927],{"className":16926},[1599],[1398,16928,16930],{"className":16929},[1604],[1398,16931,16933],{"className":16932,"style":15539},[1608],[1398,16934,16935,16938],{"style":13042},[1398,16936],{"className":16937,"style":1617},[1616],[1398,16939,16941],{"className":16940},[1621,1622,1623,1624],[1398,16942,16944,16947,16950],{"className":16943},[1494,1624],[1398,16945,1455],{"className":16946},[1494,1495,1624],[1398,16948,1435],{"className":16949},[1534,1624],[1398,16951,15575],{"className":16952,"style":15663},[1494,1495,1624],[1025,16954,16955,16956,16959,16960,16959,17076],{},"这个式子说明：",[994,16957,16958],{},"二进制乘法可以分解成很多个"," ",[1398,16961,16963,16987],{"className":16962},[1401],[1398,16964,16966],{"className":16965},[1405],[1407,16967,16968],{"xmlns":1409},[1411,16969,16970,16984],{},[1414,16971,16972,16978],{},[1449,16973,16974,16976],{},[1417,16975,11001],{},[1417,16977,1455],{},[1449,16979,16980,16982],{},[1417,16981,15272],{},[1417,16983,15575],{},[1474,16985,16986],{"encoding":1476},"X_iY_j",[1398,16988,16990],{"className":16989,"ariaHidden":1462},[1481],[1398,16991,16993,16996,17036],{"className":16992},[1485],[1398,16994],{"className":16995,"style":8203},[1489],[1398,16997,16999,17002],{"className":16998},[1494],[1398,17000,11001],{"className":17001,"style":11111},[1494,1495],[1398,17003,17005],{"className":17004},[1595],[1398,17006,17008,17028],{"className":17007},[1599,1600],[1398,17009,17011,17025],{"className":17010},[1604],[1398,17012,17014],{"className":17013,"style":1609},[1608],[1398,17015,17016,17019],{"style":15500},[1398,17017],{"className":17018,"style":1617},[1616],[1398,17020,17022],{"className":17021},[1621,1622,1623,1624],[1398,17023,1455],{"className":17024},[1494,1495,1624],[1398,17026,1632],{"className":17027},[1631],[1398,17029,17031],{"className":17030},[1604],[1398,17032,17034],{"className":17033,"style":1639},[1608],[1398,17035],{},[1398,17037,17039,17042],{"className":17038},[1494],[1398,17040,15272],{"className":17041,"style":1530},[1494,1495],[1398,17043,17045],{"className":17044},[1595],[1398,17046,17048,17068],{"className":17047},[1599,1600],[1398,17049,17051,17065],{"className":17050},[1604],[1398,17052,17054],{"className":17053,"style":1609},[1608],[1398,17055,17056,17059],{"style":5320},[1398,17057],{"className":17058,"style":1617},[1616],[1398,17060,17062],{"className":17061},[1621,1622,1623,1624],[1398,17063,15575],{"className":17064,"style":15663},[1494,1495,1624],[1398,17066,1632],{"className":17067},[1631],[1398,17069,17071],{"className":17070},[1604],[1398,17072,17074],{"className":17073,"style":3765},[1608],[1398,17075],{},[994,17077,17078],{},"的部分积相加。",[1025,17080,17081],{},[1028,17082],{"alt":1028,"src":17083},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-31.png",[987,17085,17087],{"start":17086},3,[990,17088,17089,17090,17205,17206,5628,17209,17211,17212,15847,17281,17350,17351,17466,17467,17470,17471,17473,17474,17788,17790],{},"Partial Product：部分积\n每一个 ",[1398,17091,17093,17116],{"className":17092},[1401],[1398,17094,17096],{"className":17095},[1405],[1407,17097,17098],{"xmlns":1409},[1411,17099,17100,17114],{},[1414,17101,17102,17108],{},[1449,17103,17104,17106],{},[1417,17105,11001],{},[1417,17107,1455],{},[1449,17109,17110,17112],{},[1417,17111,15272],{},[1417,17113,15575],{},[1474,17115,16986],{"encoding":1476},[1398,17117,17119],{"className":17118,"ariaHidden":1462},[1481],[1398,17120,17122,17125,17165],{"className":17121},[1485],[1398,17123],{"className":17124,"style":8203},[1489],[1398,17126,17128,17131],{"className":17127},[1494],[1398,17129,11001],{"className":17130,"style":11111},[1494,1495],[1398,17132,17134],{"className":17133},[1595],[1398,17135,17137,17157],{"className":17136},[1599,1600],[1398,17138,17140,17154],{"className":17139},[1604],[1398,17141,17143],{"className":17142,"style":1609},[1608],[1398,17144,17145,17148],{"style":15500},[1398,17146],{"className":17147,"style":1617},[1616],[1398,17149,17151],{"className":17150},[1621,1622,1623,1624],[1398,17152,1455],{"className":17153},[1494,1495,1624],[1398,17155,1632],{"className":17156},[1631],[1398,17158,17160],{"className":17159},[1604],[1398,17161,17163],{"className":17162,"style":1639},[1608],[1398,17164],{},[1398,17166,17168,17171],{"className":17167},[1494],[1398,17169,15272],{"className":17170,"style":1530},[1494,1495],[1398,17172,17174],{"className":17173},[1595],[1398,17175,17177,17197],{"className":17176},[1599,1600],[1398,17178,17180,17194],{"className":17179},[1604],[1398,17181,17183],{"className":17182,"style":1609},[1608],[1398,17184,17185,17188],{"style":5320},[1398,17186],{"className":17187,"style":1617},[1616],[1398,17189,17191],{"className":17190},[1621,1622,1623,1624],[1398,17192,15575],{"className":17193,"style":15663},[1494,1495,1624],[1398,17195,1632],{"className":17196},[1631],[1398,17198,17200],{"className":17199},[1604],[1398,17201,17203],{"className":17202,"style":3765},[1608],[1398,17204],{}," 叫做一个 ",[994,17207,17208],{},"partial product，部分积",[15317,17210],{},"因为 ",[1398,17213,17215,17232],{"className":17214},[1401],[1398,17216,17218],{"className":17217},[1405],[1407,17219,17220],{"xmlns":1409},[1411,17221,17222,17230],{},[1414,17223,17224],{},[1449,17225,17226,17228],{},[1417,17227,11001],{},[1417,17229,1455],{},[1474,17231,15797],{"encoding":1476},[1398,17233,17235],{"className":17234,"ariaHidden":1462},[1481],[1398,17236,17238,17241],{"className":17237},[1485],[1398,17239],{"className":17240,"style":1858},[1489],[1398,17242,17244,17247],{"className":17243},[1494],[1398,17245,11001],{"className":17246,"style":11111},[1494,1495],[1398,17248,17250],{"className":17249},[1595],[1398,17251,17253,17273],{"className":17252},[1599,1600],[1398,17254,17256,17270],{"className":17255},[1604],[1398,17257,17259],{"className":17258,"style":1609},[1608],[1398,17260,17261,17264],{"style":15500},[1398,17262],{"className":17263,"style":1617},[1616],[1398,17265,17267],{"className":17266},[1621,1622,1623,1624],[1398,17268,1455],{"className":17269},[1494,1495,1624],[1398,17271,1632],{"className":17272},[1631],[1398,17274,17276],{"className":17275},[1604],[1398,17277,17279],{"className":17278,"style":1639},[1608],[1398,17280],{},[1398,17282,17284,17301],{"className":17283},[1401],[1398,17285,17287],{"className":17286},[1405],[1407,17288,17289],{"xmlns":1409},[1411,17290,17291,17299],{},[1414,17292,17293],{},[1449,17294,17295,17297],{},[1417,17296,15272],{},[1417,17298,15575],{},[1474,17300,15868],{"encoding":1476},[1398,17302,17304],{"className":17303,"ariaHidden":1462},[1481],[1398,17305,17307,17310],{"className":17306},[1485],[1398,17308],{"className":17309,"style":8203},[1489],[1398,17311,17313,17316],{"className":17312},[1494],[1398,17314,15272],{"className":17315,"style":1530},[1494,1495],[1398,17317,17319],{"className":17318},[1595],[1398,17320,17322,17342],{"className":17321},[1599,1600],[1398,17323,17325,17339],{"className":17324},[1604],[1398,17326,17328],{"className":17327,"style":1609},[1608],[1398,17329,17330,17333],{"style":5320},[1398,17331],{"className":17332,"style":1617},[1616],[1398,17334,17336],{"className":17335},[1621,1622,1623,1624],[1398,17337,15575],{"className":17338,"style":15663},[1494,1495,1624],[1398,17340,1632],{"className":17341},[1631],[1398,17343,17345],{"className":17344},[1604],[1398,17346,17348],{"className":17347,"style":3765},[1608],[1398,17349],{}," 都是二进制位，所以 ",[1398,17352,17354,17377],{"className":17353},[1401],[1398,17355,17357],{"className":17356},[1405],[1407,17358,17359],{"xmlns":1409},[1411,17360,17361,17375],{},[1414,17362,17363,17369],{},[1449,17364,17365,17367],{},[1417,17366,11001],{},[1417,17368,1455],{},[1449,17370,17371,17373],{},[1417,17372,15272],{},[1417,17374,15575],{},[1474,17376,16986],{"encoding":1476},[1398,17378,17380],{"className":17379,"ariaHidden":1462},[1481],[1398,17381,17383,17386,17426],{"className":17382},[1485],[1398,17384],{"className":17385,"style":8203},[1489],[1398,17387,17389,17392],{"className":17388},[1494],[1398,17390,11001],{"className":17391,"style":11111},[1494,1495],[1398,17393,17395],{"className":17394},[1595],[1398,17396,17398,17418],{"className":17397},[1599,1600],[1398,17399,17401,17415],{"className":17400},[1604],[1398,17402,17404],{"className":17403,"style":1609},[1608],[1398,17405,17406,17409],{"style":15500},[1398,17407],{"className":17408,"style":1617},[1616],[1398,17410,17412],{"className":17411},[1621,1622,1623,1624],[1398,17413,1455],{"className":17414},[1494,1495,1624],[1398,17416,1632],{"className":17417},[1631],[1398,17419,17421],{"className":17420},[1604],[1398,17422,17424],{"className":17423,"style":1639},[1608],[1398,17425],{},[1398,17427,17429,17432],{"className":17428},[1494],[1398,17430,15272],{"className":17431,"style":1530},[1494,1495],[1398,17433,17435],{"className":17434},[1595],[1398,17436,17438,17458],{"className":17437},[1599,1600],[1398,17439,17441,17455],{"className":17440},[1604],[1398,17442,17444],{"className":17443,"style":1609},[1608],[1398,17445,17446,17449],{"style":5320},[1398,17447],{"className":17448,"style":1617},[1616],[1398,17450,17452],{"className":17451},[1621,1622,1623,1624],[1398,17453,15575],{"className":17454,"style":15663},[1494,1495,1624],[1398,17456,1632],{"className":17457},[1631],[1398,17459,17461],{"className":17460},[1604],[1398,17462,17464],{"className":17463,"style":3765},[1608],[1398,17465],{}," 在硬件中可以直接用 ",[994,17468,17469],{},"AND 门"," 生成。",[15317,17472],{},"也就是：",[1398,17475,17477,17530],{"className":17476},[1401],[1398,17478,17480],{"className":17479},[1405],[1407,17481,17482],{"xmlns":1409},[1411,17483,17484,17527],{},[1414,17485,17486,17496,17498,17504,17510,17512,17518,17521],{},[1449,17487,17488,17490],{},[1417,17489,2114],{},[1414,17491,17492,17494],{},[1417,17493,1455],{},[1417,17495,15575],{},[1421,17497,1423],{},[1449,17499,17500,17502],{},[1417,17501,11001],{},[1417,17503,1455],{},[1449,17505,17506,17508],{},[1417,17507,15272],{},[1417,17509,15575],{},[1421,17511,1423],{},[1449,17513,17514,17516],{},[1417,17515,11001],{},[1417,17517,1455],{},[1421,17519,17520],{},"∧",[1449,17522,17523,17525],{},[1417,17524,15272],{},[1417,17526,15575],{},[1474,17528,17529],{"encoding":1476},"P_{ij}=X_iY_j=X_i\\land Y_j",[1398,17531,17533,17592,17687,17742],{"className":17532,"ariaHidden":1462},[1481],[1398,17534,17536,17539,17583,17586,17589],{"className":17535},[1485],[1398,17537],{"className":17538,"style":8203},[1489],[1398,17540,17542,17545],{"className":17541},[1494],[1398,17543,2114],{"className":17544,"style":2139},[1494,1495],[1398,17546,17548],{"className":17547},[1595],[1398,17549,17551,17575],{"className":17550},[1599,1600],[1398,17552,17554,17572],{"className":17553},[1604],[1398,17555,17557],{"className":17556,"style":1609},[1608],[1398,17558,17559,17562],{"style":4987},[1398,17560],{"className":17561,"style":1617},[1616],[1398,17563,17565],{"className":17564},[1621,1622,1623,1624],[1398,17566,17568],{"className":17567},[1494,1624],[1398,17569,17571],{"className":17570,"style":15663},[1494,1495,1624],"ij",[1398,17573,1632],{"className":17574},[1631],[1398,17576,17578],{"className":17577},[1604],[1398,17579,17581],{"className":17580,"style":3765},[1608],[1398,17582],{},[1398,17584],{"className":17585,"style":1501},[1500],[1398,17587,1423],{"className":17588},[1505],[1398,17590],{"className":17591,"style":1501},[1500],[1398,17593,17595,17598,17638,17678,17681,17684],{"className":17594},[1485],[1398,17596],{"className":17597,"style":8203},[1489],[1398,17599,17601,17604],{"className":17600},[1494],[1398,17602,11001],{"className":17603,"style":11111},[1494,1495],[1398,17605,17607],{"className":17606},[1595],[1398,17608,17610,17630],{"className":17609},[1599,1600],[1398,17611,17613,17627],{"className":17612},[1604],[1398,17614,17616],{"className":17615,"style":1609},[1608],[1398,17617,17618,17621],{"style":15500},[1398,17619],{"className":17620,"style":1617},[1616],[1398,17622,17624],{"className":17623},[1621,1622,1623,1624],[1398,17625,1455],{"className":17626},[1494,1495,1624],[1398,17628,1632],{"className":17629},[1631],[1398,17631,17633],{"className":17632},[1604],[1398,17634,17636],{"className":17635,"style":1639},[1608],[1398,17637],{},[1398,17639,17641,17644],{"className":17640},[1494],[1398,17642,15272],{"className":17643,"style":1530},[1494,1495],[1398,17645,17647],{"className":17646},[1595],[1398,17648,17650,17670],{"className":17649},[1599,1600],[1398,17651,17653,17667],{"className":17652},[1604],[1398,17654,17656],{"className":17655,"style":1609},[1608],[1398,17657,17658,17661],{"style":5320},[1398,17659],{"className":17660,"style":1617},[1616],[1398,17662,17664],{"className":17663},[1621,1622,1623,1624],[1398,17665,15575],{"className":17666,"style":15663},[1494,1495,1624],[1398,17668,1632],{"className":17669},[1631],[1398,17671,17673],{"className":17672},[1604],[1398,17674,17676],{"className":17675,"style":3765},[1608],[1398,17677],{},[1398,17679],{"className":17680,"style":1501},[1500],[1398,17682,1423],{"className":17683},[1505],[1398,17685],{"className":17686,"style":1501},[1500],[1398,17688,17690,17693,17733,17736,17739],{"className":17689},[1485],[1398,17691],{"className":17692,"style":1858},[1489],[1398,17694,17696,17699],{"className":17695},[1494],[1398,17697,11001],{"className":17698,"style":11111},[1494,1495],[1398,17700,17702],{"className":17701},[1595],[1398,17703,17705,17725],{"className":17704},[1599,1600],[1398,17706,17708,17722],{"className":17707},[1604],[1398,17709,17711],{"className":17710,"style":1609},[1608],[1398,17712,17713,17716],{"style":15500},[1398,17714],{"className":17715,"style":1617},[1616],[1398,17717,17719],{"className":17718},[1621,1622,1623,1624],[1398,17720,1455],{"className":17721},[1494,1495,1624],[1398,17723,1632],{"className":17724},[1631],[1398,17726,17728],{"className":17727},[1604],[1398,17729,17731],{"className":17730,"style":1639},[1608],[1398,17732],{},[1398,17734],{"className":17735,"style":1530},[1500],[1398,17737,17520],{"className":17738},[1534],[1398,17740],{"className":17741,"style":1530},[1500],[1398,17743,17745,17748],{"className":17744},[1485],[1398,17746],{"className":17747,"style":8203},[1489],[1398,17749,17751,17754],{"className":17750},[1494],[1398,17752,15272],{"className":17753,"style":1530},[1494,1495],[1398,17755,17757],{"className":17756},[1595],[1398,17758,17760,17780],{"className":17759},[1599,1600],[1398,17761,17763,17777],{"className":17762},[1604],[1398,17764,17766],{"className":17765,"style":1609},[1608],[1398,17767,17768,17771],{"style":5320},[1398,17769],{"className":17770,"style":1617},[1616],[1398,17772,17774],{"className":17773},[1621,1622,1623,1624],[1398,17775,15575],{"className":17776,"style":15663},[1494,1495,1624],[1398,17778,1632],{"className":17779},[1631],[1398,17781,17783],{"className":17782},[1604],[1398,17784,17786],{"className":17785,"style":3765},[1608],[1398,17787],{},[15317,17789],{},[1028,17791],{"alt":1028,"src":17792},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-32.png",[1025,17794,17795,17796,17974,17975,18090,18091,18165,18166,18281,18282,18335],{},"由于 ",[1398,17797,17799,17839],{"className":17798},[1401],[1398,17800,17802],{"className":17801},[1405],[1407,17803,17804],{"xmlns":1409},[1411,17805,17806,17836],{},[1414,17807,17808,17814,17816,17822,17824],{},[12736,17809,17810,17812],{},[2883,17811,6033],{},[1417,17813,1455],{},[1421,17815,1938],{},[12736,17817,17818,17820],{},[2883,17819,6033],{},[1417,17821,15575],{},[1421,17823,1423],{},[12736,17825,17826,17828],{},[2883,17827,6033],{},[1414,17829,17830,17832,17834],{},[1417,17831,1455],{},[1421,17833,1435],{},[1417,17835,15575],{},[1474,17837,17838],{"encoding":1476},"2^i\\cdot2^j=2^{i+j}",[1398,17840,17842,17886,17930],{"className":17841,"ariaHidden":1462},[1481],[1398,17843,17845,17848,17877,17880,17883],{"className":17844},[1485],[1398,17846],{"className":17847,"style":15539},[1489],[1398,17849,17851,17854],{"className":17850},[1494],[1398,17852,6033],{"className":17853},[1494],[1398,17855,17857],{"className":17856},[1595],[1398,17858,17860],{"className":17859},[1599],[1398,17861,17863],{"className":17862},[1604],[1398,17864,17866],{"className":17865,"style":15539},[1608],[1398,17867,17868,17871],{"style":13042},[1398,17869],{"className":17870,"style":1617},[1616],[1398,17872,17874],{"className":17873},[1621,1622,1623,1624],[1398,17875,1455],{"className":17876},[1494,1495,1624],[1398,17878],{"className":17879,"style":1530},[1500],[1398,17881,1938],{"className":17882},[1534],[1398,17884],{"className":17885,"style":1530},[1500],[1398,17887,17889,17892,17921,17924,17927],{"className":17888},[1485],[1398,17890],{"className":17891,"style":15539},[1489],[1398,17893,17895,17898],{"className":17894},[1494],[1398,17896,6033],{"className":17897},[1494],[1398,17899,17901],{"className":17900},[1595],[1398,17902,17904],{"className":17903},[1599],[1398,17905,17907],{"className":17906},[1604],[1398,17908,17910],{"className":17909,"style":15539},[1608],[1398,17911,17912,17915],{"style":13042},[1398,17913],{"className":17914,"style":1617},[1616],[1398,17916,17918],{"className":17917},[1621,1622,1623,1624],[1398,17919,15575],{"className":17920,"style":15663},[1494,1495,1624],[1398,17922],{"className":17923,"style":1501},[1500],[1398,17925,1423],{"className":17926},[1505],[1398,17928],{"className":17929,"style":1501},[1500],[1398,17931,17933,17936],{"className":17932},[1485],[1398,17934],{"className":17935,"style":15539},[1489],[1398,17937,17939,17942],{"className":17938},[1494],[1398,17940,6033],{"className":17941},[1494],[1398,17943,17945],{"className":17944},[1595],[1398,17946,17948],{"className":17947},[1599],[1398,17949,17951],{"className":17950},[1604],[1398,17952,17954],{"className":17953,"style":15539},[1608],[1398,17955,17956,17959],{"style":13042},[1398,17957],{"className":17958,"style":1617},[1616],[1398,17960,17962],{"className":17961},[1621,1622,1623,1624],[1398,17963,17965,17968,17971],{"className":17964},[1494,1624],[1398,17966,1455],{"className":17967},[1494,1495,1624],[1398,17969,1435],{"className":17970},[1534,1624],[1398,17972,15575],{"className":17973,"style":15663},[1494,1495,1624],"，所以部分积 ",[1398,17976,17978,18001],{"className":17977},[1401],[1398,17979,17981],{"className":17980},[1405],[1407,17982,17983],{"xmlns":1409},[1411,17984,17985,17999],{},[1414,17986,17987,17993],{},[1449,17988,17989,17991],{},[1417,17990,11001],{},[1417,17992,1455],{},[1449,17994,17995,17997],{},[1417,17996,15272],{},[1417,17998,15575],{},[1474,18000,16986],{"encoding":1476},[1398,18002,18004],{"className":18003,"ariaHidden":1462},[1481],[1398,18005,18007,18010,18050],{"className":18006},[1485],[1398,18008],{"className":18009,"style":8203},[1489],[1398,18011,18013,18016],{"className":18012},[1494],[1398,18014,11001],{"className":18015,"style":11111},[1494,1495],[1398,18017,18019],{"className":18018},[1595],[1398,18020,18022,18042],{"className":18021},[1599,1600],[1398,18023,18025,18039],{"className":18024},[1604],[1398,18026,18028],{"className":18027,"style":1609},[1608],[1398,18029,18030,18033],{"style":15500},[1398,18031],{"className":18032,"style":1617},[1616],[1398,18034,18036],{"className":18035},[1621,1622,1623,1624],[1398,18037,1455],{"className":18038},[1494,1495,1624],[1398,18040,1632],{"className":18041},[1631],[1398,18043,18045],{"className":18044},[1604],[1398,18046,18048],{"className":18047,"style":1639},[1608],[1398,18049],{},[1398,18051,18053,18056],{"className":18052},[1494],[1398,18054,15272],{"className":18055,"style":1530},[1494,1495],[1398,18057,18059],{"className":18058},[1595],[1398,18060,18062,18082],{"className":18061},[1599,1600],[1398,18063,18065,18079],{"className":18064},[1604],[1398,18066,18068],{"className":18067,"style":1609},[1608],[1398,18069,18070,18073],{"style":5320},[1398,18071],{"className":18072,"style":1617},[1616],[1398,18074,18076],{"className":18075},[1621,1622,1623,1624],[1398,18077,15575],{"className":18078,"style":15663},[1494,1495,1624],[1398,18080,1632],{"className":18081},[1631],[1398,18083,18085],{"className":18084},[1604],[1398,18086,18088],{"className":18087,"style":3765},[1608],[1398,18089],{}," 的权重是 ",[1398,18092,18094,18118],{"className":18093},[1401],[1398,18095,18097],{"className":18096},[1405],[1407,18098,18099],{"xmlns":1409},[1411,18100,18101,18115],{},[1414,18102,18103],{},[12736,18104,18105,18107],{},[2883,18106,6033],{},[1414,18108,18109,18111,18113],{},[1417,18110,1455],{},[1421,18112,1435],{},[1417,18114,15575],{},[1474,18116,18117],{"encoding":1476},"2^{i+j}",[1398,18119,18121],{"className":18120,"ariaHidden":1462},[1481],[1398,18122,18124,18127],{"className":18123},[1485],[1398,18125],{"className":18126,"style":15539},[1489],[1398,18128,18130,18133],{"className":18129},[1494],[1398,18131,6033],{"className":18132},[1494],[1398,18134,18136],{"className":18135},[1595],[1398,18137,18139],{"className":18138},[1599],[1398,18140,18142],{"className":18141},[1604],[1398,18143,18145],{"className":18144,"style":15539},[1608],[1398,18146,18147,18150],{"style":13042},[1398,18148],{"className":18149,"style":1617},[1616],[1398,18151,18153],{"className":18152},[1621,1622,1623,1624],[1398,18154,18156,18159,18162],{"className":18155},[1494,1624],[1398,18157,1455],{"className":18158},[1494,1495,1624],[1398,18160,1435],{"className":18161},[1534,1624],[1398,18163,15575],{"className":18164,"style":15663},[1494,1495,1624],"。因此，",[1398,18167,18169,18192],{"className":18168},[1401],[1398,18170,18172],{"className":18171},[1405],[1407,18173,18174],{"xmlns":1409},[1411,18175,18176,18190],{},[1414,18177,18178,18184],{},[1449,18179,18180,18182],{},[1417,18181,11001],{},[1417,18183,1455],{},[1449,18185,18186,18188],{},[1417,18187,15272],{},[1417,18189,15575],{},[1474,18191,16986],{"encoding":1476},[1398,18193,18195],{"className":18194,"ariaHidden":1462},[1481],[1398,18196,18198,18201,18241],{"className":18197},[1485],[1398,18199],{"className":18200,"style":8203},[1489],[1398,18202,18204,18207],{"className":18203},[1494],[1398,18205,11001],{"className":18206,"style":11111},[1494,1495],[1398,18208,18210],{"className":18209},[1595],[1398,18211,18213,18233],{"className":18212},[1599,1600],[1398,18214,18216,18230],{"className":18215},[1604],[1398,18217,18219],{"className":18218,"style":1609},[1608],[1398,18220,18221,18224],{"style":15500},[1398,18222],{"className":18223,"style":1617},[1616],[1398,18225,18227],{"className":18226},[1621,1622,1623,1624],[1398,18228,1455],{"className":18229},[1494,1495,1624],[1398,18231,1632],{"className":18232},[1631],[1398,18234,18236],{"className":18235},[1604],[1398,18237,18239],{"className":18238,"style":1639},[1608],[1398,18240],{},[1398,18242,18244,18247],{"className":18243},[1494],[1398,18245,15272],{"className":18246,"style":1530},[1494,1495],[1398,18248,18250],{"className":18249},[1595],[1398,18251,18253,18273],{"className":18252},[1599,1600],[1398,18254,18256,18270],{"className":18255},[1604],[1398,18257,18259],{"className":18258,"style":1609},[1608],[1398,18260,18261,18264],{"style":5320},[1398,18262],{"className":18263,"style":1617},[1616],[1398,18265,18267],{"className":18266},[1621,1622,1623,1624],[1398,18268,15575],{"className":18269,"style":15663},[1494,1495,1624],[1398,18271,1632],{"className":18272},[1631],[1398,18274,18276],{"className":18275},[1604],[1398,18277,18279],{"className":18278,"style":3765},[1608],[1398,18280],{}," 应该放在第 ",[1398,18283,18285,18303],{"className":18284},[1401],[1398,18286,18288],{"className":18287},[1405],[1407,18289,18290],{"xmlns":1409},[1411,18291,18292,18300],{},[1414,18293,18294,18296,18298],{},[1417,18295,1455],{},[1421,18297,1435],{},[1417,18299,15575],{},[1474,18301,18302],{"encoding":1476},"i+j",[1398,18304,18306,18325],{"className":18305,"ariaHidden":1462},[1481],[1398,18307,18309,18313,18316,18319,18322],{"className":18308},[1485],[1398,18310],{"className":18311,"style":18312},[1489],"height:0.7429em;vertical-align:-0.0833em;",[1398,18314,1455],{"className":18315},[1494,1495],[1398,18317],{"className":18318,"style":1530},[1500],[1398,18320,1435],{"className":18321},[1534],[1398,18323],{"className":18324,"style":1530},[1500],[1398,18326,18328,18332],{"className":18327},[1485],[1398,18329],{"className":18330,"style":18331},[1489],"height:0.854em;vertical-align:-0.1944em;",[1398,18333,15575],{"className":18334,"style":15663},[1494,1495]," 列",[1025,18337,18338,18339],{},"二进制乘法本质上就是：",[3237,18340,18341],{},[994,18342,18343],{},"根据乘数的每一位，决定是否加入一行被乘数，并把这一行左移对应位数。",[1025,18345,18346,18347,18439,18440,18468,18469,18497,18498,18590,18591],{},"如果某一位 ",[1398,18348,18350,18372],{"className":18349},[1401],[1398,18351,18353],{"className":18352},[1405],[1407,18354,18355],{"xmlns":1409},[1411,18356,18357,18369],{},[1414,18358,18359,18365,18367],{},[1449,18360,18361,18363],{},[1417,18362,15272],{},[1417,18364,15575],{},[1421,18366,1423],{},[2883,18368,2885],{},[1474,18370,18371],{"encoding":1476},"Y_j=1",[1398,18373,18375,18430],{"className":18374,"ariaHidden":1462},[1481],[1398,18376,18378,18381,18421,18424,18427],{"className":18377},[1485],[1398,18379],{"className":18380,"style":8203},[1489],[1398,18382,18384,18387],{"className":18383},[1494],[1398,18385,15272],{"className":18386,"style":1530},[1494,1495],[1398,18388,18390],{"className":18389},[1595],[1398,18391,18393,18413],{"className":18392},[1599,1600],[1398,18394,18396,18410],{"className":18395},[1604],[1398,18397,18399],{"className":18398,"style":1609},[1608],[1398,18400,18401,18404],{"style":5320},[1398,18402],{"className":18403,"style":1617},[1616],[1398,18405,18407],{"className":18406},[1621,1622,1623,1624],[1398,18408,15575],{"className":18409,"style":15663},[1494,1495,1624],[1398,18411,1632],{"className":18412},[1631],[1398,18414,18416],{"className":18415},[1604],[1398,18417,18419],{"className":18418,"style":3765},[1608],[1398,18420],{},[1398,18422],{"className":18423,"style":1501},[1500],[1398,18425,1423],{"className":18426},[1505],[1398,18428],{"className":18429,"style":1501},[1500],[1398,18431,18433,18436],{"className":18432},[1485],[1398,18434],{"className":18435,"style":2992},[1489],[1398,18437,2885],{"className":18438},[1494],"，就加入一行左移 ",[1398,18441,18443,18456],{"className":18442},[1401],[1398,18444,18446],{"className":18445},[1405],[1407,18447,18448],{"xmlns":1409},[1411,18449,18450,18454],{},[1414,18451,18452],{},[1417,18453,15575],{},[1474,18455,15575],{"encoding":1476},[1398,18457,18459],{"className":18458,"ariaHidden":1462},[1481],[1398,18460,18462,18465],{"className":18461},[1485],[1398,18463],{"className":18464,"style":18331},[1489],[1398,18466,15575],{"className":18467,"style":15663},[1494,1495]," 位的 ",[1398,18470,18472,18485],{"className":18471},[1401],[1398,18473,18475],{"className":18474},[1405],[1407,18476,18477],{"xmlns":1409},[1411,18478,18479,18483],{},[1414,18480,18481],{},[1417,18482,11001],{},[1474,18484,11001],{"encoding":1476},[1398,18486,18488],{"className":18487,"ariaHidden":1462},[1481],[1398,18489,18491,18494],{"className":18490},[1485],[1398,18492],{"className":18493,"style":1490},[1489],[1398,18495,11001],{"className":18496,"style":11111},[1494,1495],"；如果 ",[1398,18499,18501,18523],{"className":18500},[1401],[1398,18502,18504],{"className":18503},[1405],[1407,18505,18506],{"xmlns":1409},[1411,18507,18508,18520],{},[1414,18509,18510,18516,18518],{},[1449,18511,18512,18514],{},[1417,18513,15272],{},[1417,18515,15575],{},[1421,18517,1423],{},[2883,18519,3030],{},[1474,18521,18522],{"encoding":1476},"Y_j=0",[1398,18524,18526,18581],{"className":18525,"ariaHidden":1462},[1481],[1398,18527,18529,18532,18572,18575,18578],{"className":18528},[1485],[1398,18530],{"className":18531,"style":8203},[1489],[1398,18533,18535,18538],{"className":18534},[1494],[1398,18536,15272],{"className":18537,"style":1530},[1494,1495],[1398,18539,18541],{"className":18540},[1595],[1398,18542,18544,18564],{"className":18543},[1599,1600],[1398,18545,18547,18561],{"className":18546},[1604],[1398,18548,18550],{"className":18549,"style":1609},[1608],[1398,18551,18552,18555],{"style":5320},[1398,18553],{"className":18554,"style":1617},[1616],[1398,18556,18558],{"className":18557},[1621,1622,1623,1624],[1398,18559,15575],{"className":18560,"style":15663},[1494,1495,1624],[1398,18562,1632],{"className":18563},[1631],[1398,18565,18567],{"className":18566},[1604],[1398,18568,18570],{"className":18569,"style":3765},[1608],[1398,18571],{},[1398,18573],{"className":18574,"style":1501},[1500],[1398,18576,1423],{"className":18577},[1505],[1398,18579],{"className":18580,"style":1501},[1500],[1398,18582,18584,18587],{"className":18583},[1485],[1398,18585],{"className":18586,"style":2992},[1489],[1398,18588,3030],{"className":18589},[1494],"，这一行就是全 ",[1398,18592,18594,18607],{"className":18593},[1401],[1398,18595,18597],{"className":18596},[1405],[1407,18598,18599],{"xmlns":1409},[1411,18600,18601,18605],{},[1414,18602,18603],{},[2883,18604,3030],{},[1474,18606,3030],{"encoding":1476},[1398,18608,18610],{"className":18609,"ariaHidden":1462},[1481],[1398,18611,18613,18616],{"className":18612},[1485],[1398,18614],{"className":18615,"style":2992},[1489],[1398,18617,3030],{"className":18618},[1494],[1025,18620,18621],{},"所以乘法可以看成很多行 partial product 的加法",[1025,18623,18624],{},[1028,18625],{"alt":1028,"src":18626},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-33.png",[1025,18628,18629],{},[3237,18630,18631],{},"实际上部分积的生成也是很简单——只需要做与运算就可以了",[983,18633,18635],{"id":18634},"the-array-multiplier-乘法器阵列","The Array Multiplier ｜ 乘法器阵列",[1025,18637,18638],{},[1028,18639],{"alt":1028,"src":18640},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-34.png",[1025,18642,18643],{},[1028,18644],{"alt":1028,"src":18645},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-35.png",[1366,18647,18648],{"id":18648},"全加器与半加器的应用",[1025,18650,18651],{},"实际上每一行的第一个都会用半加器HA，因为不需要进位；",[1366,18653,18655],{"id":18654},"critical-path-关键路径","Critical Path ｜ 关键路径",[1025,18657,18658],{},[1028,18659],{"alt":1028,"src":18660},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-36.png",[1025,18662,18663,18664,18667],{},"对于一个",[3237,18665,18666],{},"MxN","的阵列乘法器，关键路径（上图是4*4）",[1398,18669,18671],{"className":18670},[2737],[1398,18672,18674,18787],{"className":18673},[1401],[1398,18675,18677],{"className":18676},[1405],[1407,18678,18679],{"xmlns":1409,"display":2746},[1411,18680,18681,18784],{},[1414,18682,18683,18698,18700,18730,18746,18748,18750,18752,18754,18756,18758,18770,18772],{},[1449,18684,18685,18687],{},[1417,18686,3534],{},[1414,18688,18689,18691,18693,18696],{},[1417,18690,3599],{},[1417,18692,3596],{},[1417,18694,18695],{},"l",[1417,18697,3534],{},[1421,18699,1423],{},[1414,18701,18702,18705,18707,18709,18711,18713,18715,18717,18719,18721,18723,18725,18727],{},[1421,18703,18704],{"fence":1462},"[",[1421,18706,1439],{"stretchy":1438},[1417,18708,7961],{},[1421,18710,3560],{},[2883,18712,2885],{},[1421,18714,1458],{"stretchy":1438},[1421,18716,1435],{},[1421,18718,1439],{"stretchy":1438},[1417,18720,3557],{},[1421,18722,3560],{},[2883,18724,6033],{},[1421,18726,1458],{"stretchy":1438},[1421,18728,18729],{"fence":1462},"]",[1449,18731,18732,18734],{},[1417,18733,3534],{},[1414,18735,18736,18738,18740,18742,18744],{},[1417,18737,3573],{},[1417,18739,3539],{},[1417,18741,3550],{},[1417,18743,3550],{},[1417,18745,3582],{},[1421,18747,1435],{},[1421,18749,1439],{"stretchy":1438},[1417,18751,3557],{},[1421,18753,3560],{},[2883,18755,2885],{},[1421,18757,1458],{"stretchy":1438},[1449,18759,18760,18762],{},[1417,18761,3534],{},[1414,18763,18764,18766,18768],{},[1417,18765,3593],{},[1417,18767,3596],{},[1417,18769,3599],{},[1421,18771,1435],{},[1449,18773,18774,18776],{},[1417,18775,3534],{},[1414,18777,18778,18780,18782],{},[1417,18779,3539],{},[1417,18781,7833],{},[1417,18783,3542],{},[1474,18785,18786],{"encoding":1476},"t_{mult}=\\left[(M-1)+(N-2)\\right]t_{carry}+(N-1)t_{sum}+t_{and}",[1398,18788,18790,18858,18991,19012,19082],{"className":18789,"ariaHidden":1462},[1481],[1398,18791,18793,18796,18849,18852,18855],{"className":18792},[1485],[1398,18794],{"className":18795,"style":3612},[1489],[1398,18797,18799,18802],{"className":18798},[1494],[1398,18800,3534],{"className":18801},[1494,1495],[1398,18803,18805],{"className":18804},[1595],[1398,18806,18808,18841],{"className":18807},[1599,1600],[1398,18809,18811,18838],{"className":18810},[1604],[1398,18812,18814],{"className":18813,"style":3631},[1608],[1398,18815,18816,18819],{"style":3634},[1398,18817],{"className":18818,"style":1617},[1616],[1398,18820,18822],{"className":18821},[1621,1622,1623,1624],[1398,18823,18825,18828,18831,18835],{"className":18824},[1494,1624],[1398,18826,3599],{"className":18827},[1494,1495,1624],[1398,18829,3596],{"className":18830},[1494,1495,1624],[1398,18832,18695],{"className":18833,"style":18834},[1494,1495,1624],"margin-right:0.0197em;",[1398,18836,3534],{"className":18837},[1494,1495,1624],[1398,18839,1632],{"className":18840},[1631],[1398,18842,18844],{"className":18843},[1604],[1398,18845,18847],{"className":18846,"style":1639},[1608],[1398,18848],{},[1398,18850],{"className":18851,"style":1501},[1500],[1398,18853,1423],{"className":18854},[1505],[1398,18856],{"className":18857,"style":1501},[1500],[1398,18859,18861,18864,18924,18927,18982,18985,18988],{"className":18860},[1485],[1398,18862],{"className":18863,"style":3704},[1489],[1398,18865,18867,18870,18873,18876,18879,18882,18885,18888,18891,18894,18897,18900,18903,18906,18909,18912,18915,18918,18921],{"className":18866},[3510],[1398,18868,18704],{"className":18869,"style":8285},[1548,8284],[1398,18871,1439],{"className":18872},[1548],[1398,18874,7961],{"className":18875,"style":3688},[1494,1495],[1398,18877],{"className":18878,"style":1530},[1500],[1398,18880,3560],{"className":18881},[1534],[1398,18883],{"className":18884,"style":1530},[1500],[1398,18886,2885],{"className":18887},[1494],[1398,18889,1458],{"className":18890},[1645],[1398,18892],{"className":18893,"style":1530},[1500],[1398,18895,1435],{"className":18896},[1534],[1398,18898],{"className":18899,"style":1530},[1500],[1398,18901,1439],{"className":18902},[1548],[1398,18904,3557],{"className":18905,"style":3688},[1494,1495],[1398,18907],{"className":18908,"style":1530},[1500],[1398,18910,3560],{"className":18911},[1534],[1398,18913],{"className":18914,"style":1530},[1500],[1398,18916,6033],{"className":18917},[1494],[1398,18919,1458],{"className":18920},[1645],[1398,18922,18729],{"className":18923,"style":8285},[1645,8284],[1398,18925],{"className":18926,"style":1823},[1500],[1398,18928,18930,18933],{"className":18929},[1494],[1398,18931,3534],{"className":18932},[1494,1495],[1398,18934,18936],{"className":18935},[1595],[1398,18937,18939,18974],{"className":18938},[1599,1600],[1398,18940,18942,18971],{"className":18941},[1604],[1398,18943,18945],{"className":18944,"style":1688},[1608],[1398,18946,18947,18950],{"style":3634},[1398,18948],{"className":18949,"style":1617},[1616],[1398,18951,18953],{"className":18952},[1621,1622,1623,1624],[1398,18954,18956,18959,18962,18965,18968],{"className":18955},[1494,1624],[1398,18957,3573],{"className":18958},[1494,1495,1624],[1398,18960,3539],{"className":18961},[1494,1495,1624],[1398,18963,3550],{"className":18964,"style":3654},[1494,1495,1624],[1398,18966,3550],{"className":18967,"style":3654},[1494,1495,1624],[1398,18969,3582],{"className":18970,"style":3755},[1494,1495,1624],[1398,18972,1632],{"className":18973},[1631],[1398,18975,18977],{"className":18976},[1604],[1398,18978,18980],{"className":18979,"style":3765},[1608],[1398,18981],{},[1398,18983],{"className":18984,"style":1530},[1500],[1398,18986,1435],{"className":18987},[1534],[1398,18989],{"className":18990,"style":1530},[1500],[1398,18992,18994,18997,19000,19003,19006,19009],{"className":18993},[1485],[1398,18995],{"className":18996,"style":1544},[1489],[1398,18998,1439],{"className":18999},[1548],[1398,19001,3557],{"className":19002,"style":3688},[1494,1495],[1398,19004],{"className":19005,"style":1530},[1500],[1398,19007,3560],{"className":19008},[1534],[1398,19010],{"className":19011,"style":1530},[1500],[1398,19013,19015,19018,19021,19024,19073,19076,19079],{"className":19014},[1485],[1398,19016],{"className":19017,"style":1544},[1489],[1398,19019,2885],{"className":19020},[1494],[1398,19022,1458],{"className":19023},[1645],[1398,19025,19027,19030],{"className":19026},[1494],[1398,19028,3534],{"className":19029},[1494,1495],[1398,19031,19033],{"className":19032},[1595],[1398,19034,19036,19065],{"className":19035},[1599,1600],[1398,19037,19039,19062],{"className":19038},[1604],[1398,19040,19042],{"className":19041,"style":1688},[1608],[1398,19043,19044,19047],{"style":3634},[1398,19045],{"className":19046,"style":1617},[1616],[1398,19048,19050],{"className":19049},[1621,1622,1623,1624],[1398,19051,19053,19056,19059],{"className":19052},[1494,1624],[1398,19054,3593],{"className":19055},[1494,1495,1624],[1398,19057,3596],{"className":19058},[1494,1495,1624],[1398,19060,3599],{"className":19061},[1494,1495,1624],[1398,19063,1632],{"className":19064},[1631],[1398,19066,19068],{"className":19067},[1604],[1398,19069,19071],{"className":19070,"style":1639},[1608],[1398,19072],{},[1398,19074],{"className":19075,"style":1530},[1500],[1398,19077,1435],{"className":19078},[1534],[1398,19080],{"className":19081,"style":1530},[1500],[1398,19083,19085,19088],{"className":19084},[1485],[1398,19086],{"className":19087,"style":3612},[1489],[1398,19089,19091,19094],{"className":19090},[1494],[1398,19092,3534],{"className":19093},[1494,1495],[1398,19095,19097],{"className":19096},[1595],[1398,19098,19100,19127],{"className":19099},[1599,1600],[1398,19101,19103,19124],{"className":19102},[1604],[1398,19104,19106],{"className":19105,"style":3631},[1608],[1398,19107,19108,19111],{"style":3634},[1398,19109],{"className":19110,"style":1617},[1616],[1398,19112,19114],{"className":19113},[1621,1622,1623,1624],[1398,19115,19117,19121],{"className":19116},[1494,1624],[1398,19118,19120],{"className":19119},[1494,1495,1624],"an",[1398,19122,3542],{"className":19123},[1494,1495,1624],[1398,19125,1632],{"className":19126},[1631],[1398,19128,19130],{"className":19129},[1604],[1398,19131,19133],{"className":19132,"style":1639},[1608],[1398,19134],{},[1025,19136,11991],{},[1007,19138,19139,19340,19442,19534,19565],{},[990,19140,19141,19223,19224,19339],{},[1398,19142,19144,19168],{"className":19143},[1401],[1398,19145,19147],{"className":19146},[1405],[1407,19148,19149],{"xmlns":1409},[1411,19150,19151,19165],{},[1414,19152,19153],{},[1449,19154,19155,19157],{},[1417,19156,3534],{},[1414,19158,19159,19161,19163],{},[1417,19160,3539],{},[1417,19162,7833],{},[1417,19164,3542],{},[1474,19166,19167],{"encoding":1476},"t_{and}",[1398,19169,19171],{"className":19170,"ariaHidden":1462},[1481],[1398,19172,19174,19177],{"className":19173},[1485],[1398,19175],{"className":19176,"style":3612},[1489],[1398,19178,19180,19183],{"className":19179},[1494],[1398,19181,3534],{"className":19182},[1494,1495],[1398,19184,19186],{"className":19185},[1595],[1398,19187,19189,19215],{"className":19188},[1599,1600],[1398,19190,19192,19212],{"className":19191},[1604],[1398,19193,19195],{"className":19194,"style":3631},[1608],[1398,19196,19197,19200],{"style":3634},[1398,19198],{"className":19199,"style":1617},[1616],[1398,19201,19203],{"className":19202},[1621,1622,1623,1624],[1398,19204,19206,19209],{"className":19205},[1494,1624],[1398,19207,19120],{"className":19208},[1494,1495,1624],[1398,19210,3542],{"className":19211},[1494,1495,1624],[1398,19213,1632],{"className":19214},[1631],[1398,19216,19218],{"className":19217},[1604],[1398,19219,19221],{"className":19220,"style":1639},[1608],[1398,19222],{},"：生成部分积 ",[1398,19225,19227,19250],{"className":19226},[1401],[1398,19228,19230],{"className":19229},[1405],[1407,19231,19232],{"xmlns":1409},[1411,19233,19234,19248],{},[1414,19235,19236,19242],{},[1449,19237,19238,19240],{},[1417,19239,11001],{},[1417,19241,1455],{},[1449,19243,19244,19246],{},[1417,19245,15272],{},[1417,19247,15575],{},[1474,19249,16986],{"encoding":1476},[1398,19251,19253],{"className":19252,"ariaHidden":1462},[1481],[1398,19254,19256,19259,19299],{"className":19255},[1485],[1398,19257],{"className":19258,"style":8203},[1489],[1398,19260,19262,19265],{"className":19261},[1494],[1398,19263,11001],{"className":19264,"style":11111},[1494,1495],[1398,19266,19268],{"className":19267},[1595],[1398,19269,19271,19291],{"className":19270},[1599,1600],[1398,19272,19274,19288],{"className":19273},[1604],[1398,19275,19277],{"className":19276,"style":1609},[1608],[1398,19278,19279,19282],{"style":15500},[1398,19280],{"className":19281,"style":1617},[1616],[1398,19283,19285],{"className":19284},[1621,1622,1623,1624],[1398,19286,1455],{"className":19287},[1494,1495,1624],[1398,19289,1632],{"className":19290},[1631],[1398,19292,19294],{"className":19293},[1604],[1398,19295,19297],{"className":19296,"style":1639},[1608],[1398,19298],{},[1398,19300,19302,19305],{"className":19301},[1494],[1398,19303,15272],{"className":19304,"style":1530},[1494,1495],[1398,19306,19308],{"className":19307},[1595],[1398,19309,19311,19331],{"className":19310},[1599,1600],[1398,19312,19314,19328],{"className":19313},[1604],[1398,19315,19317],{"className":19316,"style":1609},[1608],[1398,19318,19319,19322],{"style":5320},[1398,19320],{"className":19321,"style":1617},[1616],[1398,19323,19325],{"className":19324},[1621,1622,1623,1624],[1398,19326,15575],{"className":19327,"style":15663},[1494,1495,1624],[1398,19329,1632],{"className":19330},[1631],[1398,19332,19334],{"className":19333},[1604],[1398,19335,19337],{"className":19336,"style":3765},[1608],[1398,19338],{}," 的 AND 门延迟；",[990,19341,19342,19436,19437],{},[1398,19343,19345,19372],{"className":19344},[1401],[1398,19346,19348],{"className":19347},[1405],[1407,19349,19350],{"xmlns":1409},[1411,19351,19352,19370],{},[1414,19353,19354],{},[1449,19355,19356,19358],{},[1417,19357,3534],{},[1414,19359,19360,19362,19364,19366,19368],{},[1417,19361,3573],{},[1417,19363,3539],{},[1417,19365,3550],{},[1417,19367,3550],{},[1417,19369,3582],{},[1474,19371,3865],{"encoding":1476},[1398,19373,19375],{"className":19374,"ariaHidden":1462},[1481],[1398,19376,19378,19381],{"className":19377},[1485],[1398,19379],{"className":19380,"style":3875},[1489],[1398,19382,19384,19387],{"className":19383},[1494],[1398,19385,3534],{"className":19386},[1494,1495],[1398,19388,19390],{"className":19389},[1595],[1398,19391,19393,19428],{"className":19392},[1599,1600],[1398,19394,19396,19425],{"className":19395},[1604],[1398,19397,19399],{"className":19398,"style":1688},[1608],[1398,19400,19401,19404],{"style":3634},[1398,19402],{"className":19403,"style":1617},[1616],[1398,19405,19407],{"className":19406},[1621,1622,1623,1624],[1398,19408,19410,19413,19416,19419,19422],{"className":19409},[1494,1624],[1398,19411,3573],{"className":19412},[1494,1495,1624],[1398,19414,3539],{"className":19415},[1494,1495,1624],[1398,19417,3550],{"className":19418,"style":3654},[1494,1495,1624],[1398,19420,3550],{"className":19421,"style":3654},[1494,1495,1624],[1398,19423,3582],{"className":19424,"style":3755},[1494,1495,1624],[1398,19426,1632],{"className":19427},[1631],[1398,19429,19431],{"className":19430},[1604],[1398,19432,19434],{"className":19433,"style":3765},[1608],[1398,19435],{},"：FA \u002F HA 的 carry 输出延迟\n",[1007,19438,19439],{},[990,19440,19441],{},"关键路径信号进入某个 HA \u002F FA 之后，从该输入传播到这个 HA \u002F FA 的 carry 输出的延迟；",[990,19443,19444,19528,19529],{},[1398,19445,19447,19470],{"className":19446},[1401],[1398,19448,19450],{"className":19449},[1405],[1407,19451,19452],{"xmlns":1409},[1411,19453,19454,19468],{},[1414,19455,19456],{},[1449,19457,19458,19460],{},[1417,19459,3534],{},[1414,19461,19462,19464,19466],{},[1417,19463,3593],{},[1417,19465,3596],{},[1417,19467,3599],{},[1474,19469,3962],{"encoding":1476},[1398,19471,19473],{"className":19472,"ariaHidden":1462},[1481],[1398,19474,19476,19479],{"className":19475},[1485],[1398,19477],{"className":19478,"style":3612},[1489],[1398,19480,19482,19485],{"className":19481},[1494],[1398,19483,3534],{"className":19484},[1494,1495],[1398,19486,19488],{"className":19487},[1595],[1398,19489,19491,19520],{"className":19490},[1599,1600],[1398,19492,19494,19517],{"className":19493},[1604],[1398,19495,19497],{"className":19496,"style":1688},[1608],[1398,19498,19499,19502],{"style":3634},[1398,19500],{"className":19501,"style":1617},[1616],[1398,19503,19505],{"className":19504},[1621,1622,1623,1624],[1398,19506,19508,19511,19514],{"className":19507},[1494,1624],[1398,19509,3593],{"className":19510},[1494,1495,1624],[1398,19512,3596],{"className":19513},[1494,1495,1624],[1398,19515,3599],{"className":19516},[1494,1495,1624],[1398,19518,1632],{"className":19519},[1631],[1398,19521,19523],{"className":19522},[1604],[1398,19524,19526],{"className":19525,"style":1639},[1608],[1398,19527],{},"：FA \u002F HA 的 sum 输出延迟；\n",[1007,19530,19531],{},[990,19532,19533],{},"关键路径信号进入某个 HA \u002F FA 之后，从该输入传播到这个 HA \u002F FA 的 sum 输出的延迟；",[990,19535,19536,19564],{},[1398,19537,19539,19552],{"className":19538},[1401],[1398,19540,19542],{"className":19541},[1405],[1407,19543,19544],{"xmlns":1409},[1411,19545,19546,19550],{},[1414,19547,19548],{},[1417,19549,7961],{},[1474,19551,7961],{"encoding":1476},[1398,19553,19555],{"className":19554,"ariaHidden":1462},[1481],[1398,19556,19558,19561],{"className":19557},[1485],[1398,19559],{"className":19560,"style":1490},[1489],[1398,19562,7961],{"className":19563,"style":3688},[1494,1495],"：被乘数位数；",[990,19566,19567,19595],{},[1398,19568,19570,19583],{"className":19569},[1401],[1398,19571,19573],{"className":19572},[1405],[1407,19574,19575],{"xmlns":1409},[1411,19576,19577,19581],{},[1414,19578,19579],{},[1417,19580,3557],{},[1474,19582,3557],{"encoding":1476},[1398,19584,19586],{"className":19585,"ariaHidden":1462},[1481],[1398,19587,19589,19592],{"className":19588},[1485],[1398,19590],{"className":19591,"style":1490},[1489],[1398,19593,3557],{"className":19594,"style":3688},[1494,1495],"：乘数位数。",[9187,19597,19598,19601,19866,20182,20344],{"type":9189},[1025,19599,19600],{},"关键路径分析",[1025,19602,19603,19604,19685,19686,19780,19781,19865],{},"关键路径从某个 partial product 开始，先经过一个 AND 门",[1398,19605,19607,19630],{"className":19606},[1401],[1398,19608,19610],{"className":19609},[1405],[1407,19611,19612],{"xmlns":1409},[1411,19613,19614,19628],{},[1414,19615,19616],{},[1449,19617,19618,19620],{},[1417,19619,3534],{},[1414,19621,19622,19624,19626],{},[1417,19623,3539],{},[1417,19625,7833],{},[1417,19627,3542],{},[1474,19629,19167],{"encoding":1476},[1398,19631,19633],{"className":19632,"ariaHidden":1462},[1481],[1398,19634,19636,19639],{"className":19635},[1485],[1398,19637],{"className":19638,"style":3612},[1489],[1398,19640,19642,19645],{"className":19641},[1494],[1398,19643,3534],{"className":19644},[1494,1495],[1398,19646,19648],{"className":19647},[1595],[1398,19649,19651,19677],{"className":19650},[1599,1600],[1398,19652,19654,19674],{"className":19653},[1604],[1398,19655,19657],{"className":19656,"style":3631},[1608],[1398,19658,19659,19662],{"style":3634},[1398,19660],{"className":19661,"style":1617},[1616],[1398,19663,19665],{"className":19664},[1621,1622,1623,1624],[1398,19666,19668,19671],{"className":19667},[1494,1624],[1398,19669,19120],{"className":19670},[1494,1495,1624],[1398,19672,3542],{"className":19673},[1494,1495,1624],[1398,19675,1632],{"className":19676},[1631],[1398,19678,19680],{"className":19679},[1604],[1398,19681,19683],{"className":19682,"style":1639},[1608],[1398,19684],{},"， 然后信号在阵列里传播，信号会经过很多 FA \u002F HA，\"横向\"走 是",[1398,19687,19689,19716],{"className":19688},[1401],[1398,19690,19692],{"className":19691},[1405],[1407,19693,19694],{"xmlns":1409},[1411,19695,19696,19714],{},[1414,19697,19698],{},[1449,19699,19700,19702],{},[1417,19701,3534],{},[1414,19703,19704,19706,19708,19710,19712],{},[1417,19705,3573],{},[1417,19707,3539],{},[1417,19709,3550],{},[1417,19711,3550],{},[1417,19713,3582],{},[1474,19715,3865],{"encoding":1476},[1398,19717,19719],{"className":19718,"ariaHidden":1462},[1481],[1398,19720,19722,19725],{"className":19721},[1485],[1398,19723],{"className":19724,"style":3875},[1489],[1398,19726,19728,19731],{"className":19727},[1494],[1398,19729,3534],{"className":19730},[1494,1495],[1398,19732,19734],{"className":19733},[1595],[1398,19735,19737,19772],{"className":19736},[1599,1600],[1398,19738,19740,19769],{"className":19739},[1604],[1398,19741,19743],{"className":19742,"style":1688},[1608],[1398,19744,19745,19748],{"style":3634},[1398,19746],{"className":19747,"style":1617},[1616],[1398,19749,19751],{"className":19750},[1621,1622,1623,1624],[1398,19752,19754,19757,19760,19763,19766],{"className":19753},[1494,1624],[1398,19755,3573],{"className":19756},[1494,1495,1624],[1398,19758,3539],{"className":19759},[1494,1495,1624],[1398,19761,3550],{"className":19762,"style":3654},[1494,1495,1624],[1398,19764,3550],{"className":19765,"style":3654},[1494,1495,1624],[1398,19767,3582],{"className":19768,"style":3755},[1494,1495,1624],[1398,19770,1632],{"className":19771},[1631],[1398,19773,19775],{"className":19774},[1604],[1398,19776,19778],{"className":19777,"style":3765},[1608],[1398,19779],{},", \"竖向\"走是",[1398,19782,19784,19807],{"className":19783},[1401],[1398,19785,19787],{"className":19786},[1405],[1407,19788,19789],{"xmlns":1409},[1411,19790,19791,19805],{},[1414,19792,19793],{},[1449,19794,19795,19797],{},[1417,19796,3534],{},[1414,19798,19799,19801,19803],{},[1417,19800,3593],{},[1417,19802,3596],{},[1417,19804,3599],{},[1474,19806,3962],{"encoding":1476},[1398,19808,19810],{"className":19809,"ariaHidden":1462},[1481],[1398,19811,19813,19816],{"className":19812},[1485],[1398,19814],{"className":19815,"style":3612},[1489],[1398,19817,19819,19822],{"className":19818},[1494],[1398,19820,3534],{"className":19821},[1494,1495],[1398,19823,19825],{"className":19824},[1595],[1398,19826,19828,19857],{"className":19827},[1599,1600],[1398,19829,19831,19854],{"className":19830},[1604],[1398,19832,19834],{"className":19833,"style":1688},[1608],[1398,19835,19836,19839],{"style":3634},[1398,19837],{"className":19838,"style":1617},[1616],[1398,19840,19842],{"className":19841},[1621,1622,1623,1624],[1398,19843,19845,19848,19851],{"className":19844},[1494,1624],[1398,19846,3593],{"className":19847},[1494,1495,1624],[1398,19849,3596],{"className":19850},[1494,1495,1624],[1398,19852,3599],{"className":19853},[1494,1495,1624],[1398,19855,1632],{"className":19856},[1631],[1398,19858,19860],{"className":19859},[1604],[1398,19861,19863],{"className":19862,"style":1639},[1608],[1398,19864],{},";",[1025,19867,19868,19869,19991,19992,19995,19996],{},"其实无论走哪一条路径，都是竖向走N-1个加法器，即",[1398,19870,19872,19906],{"className":19871},[1401],[1398,19873,19875],{"className":19874},[1405],[1407,19876,19877],{"xmlns":1409},[1411,19878,19879,19903],{},[1414,19880,19881,19883,19885,19887,19889,19891],{},[1421,19882,1439],{"stretchy":1438},[1417,19884,3557],{},[1421,19886,3560],{},[2883,19888,2885],{},[1421,19890,1458],{"stretchy":1438},[1449,19892,19893,19895],{},[1417,19894,3534],{},[1414,19896,19897,19899,19901],{},[1417,19898,3593],{},[1417,19900,3596],{},[1417,19902,3599],{},[1474,19904,19905],{"encoding":1476},"(N-1)t_{sum}",[1398,19907,19909,19930],{"className":19908,"ariaHidden":1462},[1481],[1398,19910,19912,19915,19918,19921,19924,19927],{"className":19911},[1485],[1398,19913],{"className":19914,"style":1544},[1489],[1398,19916,1439],{"className":19917},[1548],[1398,19919,3557],{"className":19920,"style":3688},[1494,1495],[1398,19922],{"className":19923,"style":1530},[1500],[1398,19925,3560],{"className":19926},[1534],[1398,19928],{"className":19929,"style":1530},[1500],[1398,19931,19933,19936,19939,19942],{"className":19932},[1485],[1398,19934],{"className":19935,"style":1544},[1489],[1398,19937,2885],{"className":19938},[1494],[1398,19940,1458],{"className":19941},[1645],[1398,19943,19945,19948],{"className":19944},[1494],[1398,19946,3534],{"className":19947},[1494,1495],[1398,19949,19951],{"className":19950},[1595],[1398,19952,19954,19983],{"className":19953},[1599,1600],[1398,19955,19957,19980],{"className":19956},[1604],[1398,19958,19960],{"className":19959,"style":1688},[1608],[1398,19961,19962,19965],{"style":3634},[1398,19963],{"className":19964,"style":1617},[1616],[1398,19966,19968],{"className":19967},[1621,1622,1623,1624],[1398,19969,19971,19974,19977],{"className":19970},[1494,1624],[1398,19972,3593],{"className":19973},[1494,1495,1624],[1398,19975,3596],{"className":19976},[1494,1495,1624],[1398,19978,3599],{"className":19979},[1494,1495,1624],[1398,19981,1632],{"className":19982},[1631],[1398,19984,19986],{"className":19985},[1604],[1398,19987,19989],{"className":19988,"style":1639},[1608],[1398,19990],{},"； ",[3237,19993,19994],{},"同时对于横向方向，都是走(M+N-1) -1 -1 = (M+N-3)个carry","，即",[1398,19997,19999,20055],{"className":19998},[1401],[1398,20000,20002],{"className":20001},[1405],[1407,20003,20004],{"xmlns":1409},[1411,20005,20006,20052],{},[1414,20007,20008,20036],{},[1414,20009,20010,20012,20014,20016,20018,20020,20022,20024,20026,20028,20030,20032,20034],{},[1421,20011,18704],{"fence":1462},[1421,20013,1439],{"stretchy":1438},[1417,20015,7961],{},[1421,20017,3560],{},[2883,20019,2885],{},[1421,20021,1458],{"stretchy":1438},[1421,20023,1435],{},[1421,20025,1439],{"stretchy":1438},[1417,20027,3557],{},[1421,20029,3560],{},[2883,20031,6033],{},[1421,20033,1458],{"stretchy":1438},[1421,20035,18729],{"fence":1462},[1449,20037,20038,20040],{},[1417,20039,3534],{},[1414,20041,20042,20044,20046,20048,20050],{},[1417,20043,3573],{},[1417,20045,3539],{},[1417,20047,3550],{},[1417,20049,3550],{},[1417,20051,3582],{},[1474,20053,20054],{"encoding":1476},"\\left[(M-1)+(N-2)\\right]t_{carry}",[1398,20056,20058],{"className":20057,"ariaHidden":1462},[1481],[1398,20059,20061,20064,20124,20127],{"className":20060},[1485],[1398,20062],{"className":20063,"style":3704},[1489],[1398,20065,20067,20070,20073,20076,20079,20082,20085,20088,20091,20094,20097,20100,20103,20106,20109,20112,20115,20118,20121],{"className":20066},[3510],[1398,20068,18704],{"className":20069,"style":8285},[1548,8284],[1398,20071,1439],{"className":20072},[1548],[1398,20074,7961],{"className":20075,"style":3688},[1494,1495],[1398,20077],{"className":20078,"style":1530},[1500],[1398,20080,3560],{"className":20081},[1534],[1398,20083],{"className":20084,"style":1530},[1500],[1398,20086,2885],{"className":20087},[1494],[1398,20089,1458],{"className":20090},[1645],[1398,20092],{"className":20093,"style":1530},[1500],[1398,20095,1435],{"className":20096},[1534],[1398,20098],{"className":20099,"style":1530},[1500],[1398,20101,1439],{"className":20102},[1548],[1398,20104,3557],{"className":20105,"style":3688},[1494,1495],[1398,20107],{"className":20108,"style":1530},[1500],[1398,20110,3560],{"className":20111},[1534],[1398,20113],{"className":20114,"style":1530},[1500],[1398,20116,6033],{"className":20117},[1494],[1398,20119,1458],{"className":20120},[1645],[1398,20122,18729],{"className":20123,"style":8285},[1645,8284],[1398,20125],{"className":20126,"style":1823},[1500],[1398,20128,20130,20133],{"className":20129},[1494],[1398,20131,3534],{"className":20132},[1494,1495],[1398,20134,20136],{"className":20135},[1595],[1398,20137,20139,20174],{"className":20138},[1599,1600],[1398,20140,20142,20171],{"className":20141},[1604],[1398,20143,20145],{"className":20144,"style":1688},[1608],[1398,20146,20147,20150],{"style":3634},[1398,20148],{"className":20149,"style":1617},[1616],[1398,20151,20153],{"className":20152},[1621,1622,1623,1624],[1398,20154,20156,20159,20162,20165,20168],{"className":20155},[1494,1624],[1398,20157,3573],{"className":20158},[1494,1495,1624],[1398,20160,3539],{"className":20161},[1494,1495,1624],[1398,20163,3550],{"className":20164,"style":3654},[1494,1495,1624],[1398,20166,3550],{"className":20167,"style":3654},[1494,1495,1624],[1398,20169,3582],{"className":20170,"style":3755},[1494,1495,1624],[1398,20172,1632],{"className":20173},[1631],[1398,20175,20177],{"className":20176},[1604],[1398,20178,20180],{"className":20179,"style":3765},[1608],[1398,20181],{},[12641,20183,20184,20187],{},[1025,20185,20186],{},"这里的解释是这样的：",[1025,20188,20189,20190],{},"对于横向方向，总长度实际上就是M+N-1，即输出位宽是M+N-1，那么横向之间的间隔就有(输出位宽-1)=N+M-2个宽度，然后实际上我们只关系最后一位的sum结果，因此最后一个加法器它的carry时间就不计算在内了，所以再减一，结果就是",[1398,20191,20193,20235],{"className":20192},[1401],[1398,20194,20196],{"className":20195},[1405],[1407,20197,20198],{"xmlns":1409},[1411,20199,20200,20232],{},[1414,20201,20202,20204,20206,20208,20210,20212,20214,20216],{},[1421,20203,1439],{"stretchy":1438},[1417,20205,7961],{},[1421,20207,1435],{},[1417,20209,3557],{},[1421,20211,3560],{},[2883,20213,6046],{},[1421,20215,1458],{"stretchy":1438},[1449,20217,20218,20220],{},[1417,20219,3534],{},[1414,20221,20222,20224,20226,20228,20230],{},[1417,20223,3573],{},[1417,20225,3539],{},[1417,20227,3550],{},[1417,20229,3550],{},[1417,20231,3582],{},[1474,20233,20234],{"encoding":1476},"(M + N - 3)t_{carry}",[1398,20236,20238,20259,20277],{"className":20237,"ariaHidden":1462},[1481],[1398,20239,20241,20244,20247,20250,20253,20256],{"className":20240},[1485],[1398,20242],{"className":20243,"style":1544},[1489],[1398,20245,1439],{"className":20246},[1548],[1398,20248,7961],{"className":20249,"style":3688},[1494,1495],[1398,20251],{"className":20252,"style":1530},[1500],[1398,20254,1435],{"className":20255},[1534],[1398,20257],{"className":20258,"style":1530},[1500],[1398,20260,20262,20265,20268,20271,20274],{"className":20261},[1485],[1398,20263],{"className":20264,"style":1515},[1489],[1398,20266,3557],{"className":20267,"style":3688},[1494,1495],[1398,20269],{"className":20270,"style":1530},[1500],[1398,20272,3560],{"className":20273},[1534],[1398,20275],{"className":20276,"style":1530},[1500],[1398,20278,20280,20283,20286,20289],{"className":20279},[1485],[1398,20281],{"className":20282,"style":3704},[1489],[1398,20284,6046],{"className":20285},[1494],[1398,20287,1458],{"className":20288},[1645],[1398,20290,20292,20295],{"className":20291},[1494],[1398,20293,3534],{"className":20294},[1494,1495],[1398,20296,20298],{"className":20297},[1595],[1398,20299,20301,20336],{"className":20300},[1599,1600],[1398,20302,20304,20333],{"className":20303},[1604],[1398,20305,20307],{"className":20306,"style":1688},[1608],[1398,20308,20309,20312],{"style":3634},[1398,20310],{"className":20311,"style":1617},[1616],[1398,20313,20315],{"className":20314},[1621,1622,1623,1624],[1398,20316,20318,20321,20324,20327,20330],{"className":20317},[1494,1624],[1398,20319,3573],{"className":20320},[1494,1495,1624],[1398,20322,3539],{"className":20323},[1494,1495,1624],[1398,20325,3550],{"className":20326,"style":3654},[1494,1495,1624],[1398,20328,3550],{"className":20329,"style":3654},[1494,1495,1624],[1398,20331,3582],{"className":20332,"style":3755},[1494,1495,1624],[1398,20334,1632],{"className":20335},[1631],[1398,20337,20339],{"className":20338},[1604],[1398,20340,20342],{"className":20341,"style":3765},[1608],[1398,20343],{},[1025,20345,20346,20347],{},"因此最终计算得出",[1398,20348,20350,20459],{"className":20349},[1401],[1398,20351,20353],{"className":20352},[1405],[1407,20354,20355],{"xmlns":1409},[1411,20356,20357,20457],{},[1414,20358,20359,20373,20375,20403,20419,20421,20423,20425,20427,20429,20431,20443,20445],{},[1449,20360,20361,20363],{},[1417,20362,3534],{},[1414,20364,20365,20367,20369,20371],{},[1417,20366,3599],{},[1417,20368,3596],{},[1417,20370,18695],{},[1417,20372,3534],{},[1421,20374,1423],{},[1414,20376,20377,20379,20381,20383,20385,20387,20389,20391,20393,20395,20397,20399,20401],{},[1421,20378,18704],{"fence":1462},[1421,20380,1439],{"stretchy":1438},[1417,20382,7961],{},[1421,20384,3560],{},[2883,20386,2885],{},[1421,20388,1458],{"stretchy":1438},[1421,20390,1435],{},[1421,20392,1439],{"stretchy":1438},[1417,20394,3557],{},[1421,20396,3560],{},[2883,20398,6033],{},[1421,20400,1458],{"stretchy":1438},[1421,20402,18729],{"fence":1462},[1449,20404,20405,20407],{},[1417,20406,3534],{},[1414,20408,20409,20411,20413,20415,20417],{},[1417,20410,3573],{},[1417,20412,3539],{},[1417,20414,3550],{},[1417,20416,3550],{},[1417,20418,3582],{},[1421,20420,1435],{},[1421,20422,1439],{"stretchy":1438},[1417,20424,3557],{},[1421,20426,3560],{},[2883,20428,2885],{},[1421,20430,1458],{"stretchy":1438},[1449,20432,20433,20435],{},[1417,20434,3534],{},[1414,20436,20437,20439,20441],{},[1417,20438,3593],{},[1417,20440,3596],{},[1417,20442,3599],{},[1421,20444,1435],{},[1449,20446,20447,20449],{},[1417,20448,3534],{},[1414,20450,20451,20453,20455],{},[1417,20452,3539],{},[1417,20454,7833],{},[1417,20456,3542],{},[1474,20458,18786],{"encoding":1476},[1398,20460,20462,20529,20662,20683,20753],{"className":20461,"ariaHidden":1462},[1481],[1398,20463,20465,20468,20520,20523,20526],{"className":20464},[1485],[1398,20466],{"className":20467,"style":3612},[1489],[1398,20469,20471,20474],{"className":20470},[1494],[1398,20472,3534],{"className":20473},[1494,1495],[1398,20475,20477],{"className":20476},[1595],[1398,20478,20480,20512],{"className":20479},[1599,1600],[1398,20481,20483,20509],{"className":20482},[1604],[1398,20484,20486],{"className":20485,"style":3631},[1608],[1398,20487,20488,20491],{"style":3634},[1398,20489],{"className":20490,"style":1617},[1616],[1398,20492,20494],{"className":20493},[1621,1622,1623,1624],[1398,20495,20497,20500,20503,20506],{"className":20496},[1494,1624],[1398,20498,3599],{"className":20499},[1494,1495,1624],[1398,20501,3596],{"className":20502},[1494,1495,1624],[1398,20504,18695],{"className":20505,"style":18834},[1494,1495,1624],[1398,20507,3534],{"className":20508},[1494,1495,1624],[1398,20510,1632],{"className":20511},[1631],[1398,20513,20515],{"className":20514},[1604],[1398,20516,20518],{"className":20517,"style":1639},[1608],[1398,20519],{},[1398,20521],{"className":20522,"style":1501},[1500],[1398,20524,1423],{"className":20525},[1505],[1398,20527],{"className":20528,"style":1501},[1500],[1398,20530,20532,20535,20595,20598,20653,20656,20659],{"className":20531},[1485],[1398,20533],{"className":20534,"style":3704},[1489],[1398,20536,20538,20541,20544,20547,20550,20553,20556,20559,20562,20565,20568,20571,20574,20577,20580,20583,20586,20589,20592],{"className":20537},[3510],[1398,20539,18704],{"className":20540,"style":8285},[1548,8284],[1398,20542,1439],{"className":20543},[1548],[1398,20545,7961],{"className":20546,"style":3688},[1494,1495],[1398,20548],{"className":20549,"style":1530},[1500],[1398,20551,3560],{"className":20552},[1534],[1398,20554],{"className":20555,"style":1530},[1500],[1398,20557,2885],{"className":20558},[1494],[1398,20560,1458],{"className":20561},[1645],[1398,20563],{"className":20564,"style":1530},[1500],[1398,20566,1435],{"className":20567},[1534],[1398,20569],{"className":20570,"style":1530},[1500],[1398,20572,1439],{"className":20573},[1548],[1398,20575,3557],{"className":20576,"style":3688},[1494,1495],[1398,20578],{"className":20579,"style":1530},[1500],[1398,20581,3560],{"className":20582},[1534],[1398,20584],{"className":20585,"style":1530},[1500],[1398,20587,6033],{"className":20588},[1494],[1398,20590,1458],{"className":20591},[1645],[1398,20593,18729],{"className":20594,"style":8285},[1645,8284],[1398,20596],{"className":20597,"style":1823},[1500],[1398,20599,20601,20604],{"className":20600},[1494],[1398,20602,3534],{"className":20603},[1494,1495],[1398,20605,20607],{"className":20606},[1595],[1398,20608,20610,20645],{"className":20609},[1599,1600],[1398,20611,20613,20642],{"className":20612},[1604],[1398,20614,20616],{"className":20615,"style":1688},[1608],[1398,20617,20618,20621],{"style":3634},[1398,20619],{"className":20620,"style":1617},[1616],[1398,20622,20624],{"className":20623},[1621,1622,1623,1624],[1398,20625,20627,20630,20633,20636,20639],{"className":20626},[1494,1624],[1398,20628,3573],{"className":20629},[1494,1495,1624],[1398,20631,3539],{"className":20632},[1494,1495,1624],[1398,20634,3550],{"className":20635,"style":3654},[1494,1495,1624],[1398,20637,3550],{"className":20638,"style":3654},[1494,1495,1624],[1398,20640,3582],{"className":20641,"style":3755},[1494,1495,1624],[1398,20643,1632],{"className":20644},[1631],[1398,20646,20648],{"className":20647},[1604],[1398,20649,20651],{"className":20650,"style":3765},[1608],[1398,20652],{},[1398,20654],{"className":20655,"style":1530},[1500],[1398,20657,1435],{"className":20658},[1534],[1398,20660],{"className":20661,"style":1530},[1500],[1398,20663,20665,20668,20671,20674,20677,20680],{"className":20664},[1485],[1398,20666],{"className":20667,"style":1544},[1489],[1398,20669,1439],{"className":20670},[1548],[1398,20672,3557],{"className":20673,"style":3688},[1494,1495],[1398,20675],{"className":20676,"style":1530},[1500],[1398,20678,3560],{"className":20679},[1534],[1398,20681],{"className":20682,"style":1530},[1500],[1398,20684,20686,20689,20692,20695,20744,20747,20750],{"className":20685},[1485],[1398,20687],{"className":20688,"style":1544},[1489],[1398,20690,2885],{"className":20691},[1494],[1398,20693,1458],{"className":20694},[1645],[1398,20696,20698,20701],{"className":20697},[1494],[1398,20699,3534],{"className":20700},[1494,1495],[1398,20702,20704],{"className":20703},[1595],[1398,20705,20707,20736],{"className":20706},[1599,1600],[1398,20708,20710,20733],{"className":20709},[1604],[1398,20711,20713],{"className":20712,"style":1688},[1608],[1398,20714,20715,20718],{"style":3634},[1398,20716],{"className":20717,"style":1617},[1616],[1398,20719,20721],{"className":20720},[1621,1622,1623,1624],[1398,20722,20724,20727,20730],{"className":20723},[1494,1624],[1398,20725,3593],{"className":20726},[1494,1495,1624],[1398,20728,3596],{"className":20729},[1494,1495,1624],[1398,20731,3599],{"className":20732},[1494,1495,1624],[1398,20734,1632],{"className":20735},[1631],[1398,20737,20739],{"className":20738},[1604],[1398,20740,20742],{"className":20741,"style":1639},[1608],[1398,20743],{},[1398,20745],{"className":20746,"style":1530},[1500],[1398,20748,1435],{"className":20749},[1534],[1398,20751],{"className":20752,"style":1530},[1500],[1398,20754,20756,20759],{"className":20755},[1485],[1398,20757],{"className":20758,"style":3612},[1489],[1398,20760,20762,20765],{"className":20761},[1494],[1398,20763,3534],{"className":20764},[1494,1495],[1398,20766,20768],{"className":20767},[1595],[1398,20769,20771,20797],{"className":20770},[1599,1600],[1398,20772,20774,20794],{"className":20773},[1604],[1398,20775,20777],{"className":20776,"style":3631},[1608],[1398,20778,20779,20782],{"style":3634},[1398,20780],{"className":20781,"style":1617},[1616],[1398,20783,20785],{"className":20784},[1621,1622,1623,1624],[1398,20786,20788,20791],{"className":20787},[1494,1624],[1398,20789,19120],{"className":20790},[1494,1495,1624],[1398,20792,3542],{"className":20793},[1494,1495,1624],[1398,20795,1632],{"className":20796},[1631],[1398,20798,20800],{"className":20799},[1604],[1398,20801,20803],{"className":20802,"style":1639},[1608],[1398,20804],{},[983,20806,20808],{"id":20807},"carry-save-multiplier-进位保存乘法器","Carry-Save Multiplier ｜ 进位保存乘法器",[1025,20810,20811,20812,20933],{},"普通 array multiplier 里，每一行加法器内部 carry 会横向 ripple：",[1398,20813,20815,20858],{"className":20814},[1401],[1398,20816,20818],{"className":20817},[1405],[1407,20819,20820],{"xmlns":1409},[1411,20821,20822,20855],{},[1414,20823,20824,20826,20828,20830,20832,20834,20836,20838,20840,20842,20844,20846,20848,20851,20853],{},[1417,20825,3573],{},[1417,20827,3539],{},[1417,20829,3550],{},[1417,20831,3550],{},[1417,20833,3582],{},[1421,20835,3309],{},[1417,20837,3573],{},[1417,20839,3539],{},[1417,20841,3550],{},[1417,20843,3550],{},[1417,20845,3582],{},[1421,20847,3309],{},[1417,20849,20850],{"mathvariant":2017},".",[1417,20852,20850],{"mathvariant":2017},[1417,20854,20850],{"mathvariant":2017},[1474,20856,20857],{"encoding":1476},"carry→carry→...",[1398,20859,20861,20892,20922],{"className":20860,"ariaHidden":1462},[1481],[1398,20862,20864,20868,20871,20874,20877,20880,20883,20886,20889],{"className":20863},[1485],[1398,20865],{"className":20866,"style":20867},[1489],"height:0.625em;vertical-align:-0.1944em;",[1398,20869,3573],{"className":20870},[1494,1495],[1398,20872,3539],{"className":20873},[1494,1495],[1398,20875,3550],{"className":20876,"style":3654},[1494,1495],[1398,20878,3550],{"className":20879,"style":3654},[1494,1495],[1398,20881,3582],{"className":20882,"style":3755},[1494,1495],[1398,20884],{"className":20885,"style":1501},[1500],[1398,20887,3309],{"className":20888},[1505],[1398,20890],{"className":20891,"style":1501},[1500],[1398,20893,20895,20898,20901,20904,20907,20910,20913,20916,20919],{"className":20894},[1485],[1398,20896],{"className":20897,"style":20867},[1489],[1398,20899,3573],{"className":20900},[1494,1495],[1398,20902,3539],{"className":20903},[1494,1495],[1398,20905,3550],{"className":20906,"style":3654},[1494,1495],[1398,20908,3550],{"className":20909,"style":3654},[1494,1495],[1398,20911,3582],{"className":20912,"style":3755},[1494,1495],[1398,20914],{"className":20915,"style":1501},[1500],[1398,20917,3309],{"className":20918},[1505],[1398,20920],{"className":20921,"style":1501},[1500],[1398,20923,20925,20929],{"className":20924},[1485],[1398,20926],{"className":20927,"style":20928},[1489],"height:0.1056em;",[1398,20930,20932],{"className":20931},[1494],"...",",所以延迟里会出现很多横向 carry delay 和竖向 sum delay;",[1025,20935,20936],{},"Carry-save multiplier 的核心思想是中间累加 partial products 时，不把 carry 立刻横向传播完，每个 FA 做好sum和carry的输出之后，作为一个“carry vector”的一部分保存下来，送到下一层\u002F下一列去处理进位",[1745,20938,20939],{"style":1747},[1749,20940,20941],{},[1752,20942,1755,20943,1755,20951],{"style":1754},[1757,20944,20946,1755],{"style":20945},"width: 42.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,20947,20948],{},[1028,20949],{"alt":1028,"src":20950},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-37.png",[1757,20952,20954,1755],{"style":20953},"width: 57.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,20955,20956],{},[1028,20957],{"alt":1028,"src":20958},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-38.png",[1025,20960,20961],{},"（左右对比）",[1366,20963,20965],{"id":20964},"csa-based-array-multiplier-基于保留进位加法器的乘法器","CSA-based Array Multiplier ｜ 基于保留进位加法器的乘法器",[12641,20967,20968,20971,20974,20979,20982,20994,20995,21017,21022,21026,21029,21208,21212,21215,21220,21224,21227,21249,21253,21256,21261,21265,21270,21276,21280,21285,21291,21297,21317,21321,21324,21328,21333,21336,21356,21362,21366,21496,21501,21507,21511,21666,21688,21691,21927,22036,22040,22127,22149,22153,22467,22477,22482,22486,22488,22513,22518,23016,23315,24000,24003,24007,24012,24270,24908,25052,25119,25124,25128],{},[1025,20969,20970],{},"这个小节是讲一种具体的实现方案，上面那个Carry-Save Multiplier是一个大类的乘法器结构",[1025,20972,20973],{},"CPA指的是进位传播加法器，实际上就是前面的串行加法器的大类",[1025,20975,20976],{},[1028,20977],{"alt":1028,"src":20978},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-39.png",[1025,20980,20981],{},"CSA指的是Carry-Save Adder，注意不是前面的进位选择加法器",[1025,20983,20984,20985,20988,16959,20991],{},"下图左就是CPA计算过程，每一次计算都会把进位考虑上；右就是CSA计算过程，每次先算出sum和进位 然后再把进位和sum加起来 ",[3237,20986,20987],{},"rnh is my",[3237,20989,20990],{},"(scy)",[3237,20992,20993],{},"good son","\n\n\n  \n> ",[1745,20996,20997],{"style":1747},[1749,20998,20999],{},[1752,21000,21001,1755,21009],{"style":1754},[1757,21002,21004,1755],{"style":21003},"width: 55.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,21005,21006],{},[1028,21007],{"alt":1028,"src":21008},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-40.png",[1757,21010,21012,1755],{"style":21011},"width: 44.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,21013,21014],{},[1028,21015],{"alt":1028,"src":21016},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-41.png",[1025,21018,21019],{},[1028,21020],{"alt":1028,"src":21021},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-42.png",[1741,21023,21025],{"id":21024},"critical-path","Critical Path",[1025,21027,21028],{},"关键路径这里就是 最多累加的地方 当然是x0y3 + x1y2 + x2y1 + x3y0这个累加是最长的路径\n然后再加上CPA计算的时间，就是关键路径延迟了",[12641,21030,21031],{},[1025,21032,21033,21034],{},"这里假设",[1398,21035,21037,21080],{"className":21036},[1401],[1398,21038,21040],{"className":21039},[1405],[1407,21041,21042],{"xmlns":1409},[1411,21043,21044,21077],{},[1414,21045,21046,21058,21061],{},[1449,21047,21048,21050],{},[1417,21049,3534],{},[1414,21051,21052,21054,21056],{},[1417,21053,3593],{},[1417,21055,3596],{},[1417,21057,3599],{},[1421,21059,21060],{},">",[1449,21062,21063,21065],{},[1417,21064,3534],{},[1414,21066,21067,21069,21071,21073,21075],{},[1417,21068,3573],{},[1417,21070,3539],{},[1417,21072,3550],{},[1417,21074,3550],{},[1417,21076,3582],{},[1474,21078,21079],{"encoding":1476},"t_{sum}>t_{carry}",[1398,21081,21083,21147],{"className":21082,"ariaHidden":1462},[1481],[1398,21084,21086,21089,21138,21141,21144],{"className":21085},[1485],[1398,21087],{"className":21088,"style":3612},[1489],[1398,21090,21092,21095],{"className":21091},[1494],[1398,21093,3534],{"className":21094},[1494,1495],[1398,21096,21098],{"className":21097},[1595],[1398,21099,21101,21130],{"className":21100},[1599,1600],[1398,21102,21104,21127],{"className":21103},[1604],[1398,21105,21107],{"className":21106,"style":1688},[1608],[1398,21108,21109,21112],{"style":3634},[1398,21110],{"className":21111,"style":1617},[1616],[1398,21113,21115],{"className":21114},[1621,1622,1623,1624],[1398,21116,21118,21121,21124],{"className":21117},[1494,1624],[1398,21119,3593],{"className":21120},[1494,1495,1624],[1398,21122,3596],{"className":21123},[1494,1495,1624],[1398,21125,3599],{"className":21126},[1494,1495,1624],[1398,21128,1632],{"className":21129},[1631],[1398,21131,21133],{"className":21132},[1604],[1398,21134,21136],{"className":21135,"style":1639},[1608],[1398,21137],{},[1398,21139],{"className":21140,"style":1501},[1500],[1398,21142,21060],{"className":21143},[1505],[1398,21145],{"className":21146,"style":1501},[1500],[1398,21148,21150,21153],{"className":21149},[1485],[1398,21151],{"className":21152,"style":3875},[1489],[1398,21154,21156,21159],{"className":21155},[1494],[1398,21157,3534],{"className":21158},[1494,1495],[1398,21160,21162],{"className":21161},[1595],[1398,21163,21165,21200],{"className":21164},[1599,1600],[1398,21166,21168,21197],{"className":21167},[1604],[1398,21169,21171],{"className":21170,"style":1688},[1608],[1398,21172,21173,21176],{"style":3634},[1398,21174],{"className":21175,"style":1617},[1616],[1398,21177,21179],{"className":21178},[1621,1622,1623,1624],[1398,21180,21182,21185,21188,21191,21194],{"className":21181},[1494,1624],[1398,21183,3573],{"className":21184},[1494,1495,1624],[1398,21186,3539],{"className":21187},[1494,1495,1624],[1398,21189,3550],{"className":21190,"style":3654},[1494,1495,1624],[1398,21192,3550],{"className":21193,"style":3654},[1494,1495,1624],[1398,21195,3582],{"className":21196,"style":3755},[1494,1495,1624],[1398,21198,1632],{"className":21199},[1631],[1398,21201,21203],{"className":21202},[1604],[1398,21204,21206],{"className":21205,"style":3765},[1608],[1398,21207],{},[1741,21209,21211],{"id":21210},"rectangular-array","Rectangular Array",[1025,21213,21214],{},"把斜着的CSA-based Array Multiplier阵列“压扁 \u002F 拉正”，排成一个规整的矩形，方便芯片版图实现",[1025,21216,21217],{},[1028,21218],{"alt":1028,"src":21219},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-43.png",[1366,21221,21223],{"id":21222},"wallace-tree-multiplier","Wallace-Tree Multiplier",[1025,21225,21226],{},"这个其实就是作业的那个题，对于4x4的乘法阵列，定制一个Wallace-Tree Multiplier ，如右图所示",[1745,21228,21229],{"style":1747},[1749,21230,21231],{},[1752,21232,1755,21233,1755,21241],{"style":1754},[1757,21234,21236,1755],{"style":21235},"width: 46.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,21237,21238],{},[1028,21239],{"alt":1028,"src":21240},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-44.png",[1757,21242,21244,1755],{"style":21243},"width: 53.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,21245,21246],{},[1028,21247],{"alt":1028,"src":21248},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-45.png",[1741,21250,21252],{"id":21251},"build-from-csa-based-multipler","Build From CSA-Based Multipler",[1025,21254,21255],{},"事实上Wallace-Tree Multiplier  就是一种CSA based 的阵列乘法器，因为全加器就是一种CSA加法器",[1025,21257,21258],{},[1028,21259],{"alt":1028,"src":21260},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-46.png",[1741,21262,21264],{"id":21263},"csa-vs-conventional-adder","CSA vs conventional Adder",[1025,21266,21267],{},[1028,21268],{"alt":1028,"src":21269},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-47.png",[1025,21271,21272,21273],{},"实际上也没什么区别 只是说全加器的进位在CSA这里也是作为输出，而不是作为",[3237,21274,21275],{},"下一级全加器的输入",[1741,21277,21279],{"id":21278},"wallace-tree-multiplier-的优势与劣势","Wallace-Tree Multiplier 的优势与劣势",[1025,21281,21282],{},[1028,21283],{"alt":1028,"src":21284},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-48.png",[1025,21286,21287,21288],{},"这张图说明了Wallace-Tree乘法器的速度为什么比普通的CSA链快，是因为普通CSA链也还是有很多的串行逻辑，但是Wallace-Tree节省了一些不必要的串行等待——能把串行CSA的O(N)复杂度压缩到O(logN)的复杂度。",[3237,21289,21290],{},"在乘法器中使用 Wallace Tree 的目的，是减少加法操作的数量，或者更准确地说，是减少 CSA 链的深度。",[1025,21292,21293,21294],{},"但是也有缺点，缺点是连线更复杂，但是也也可以构造 ",[3237,21295,21296],{},"Booth 编码的 Wallace Tree 乘法器。",[1745,21298,21299],{"style":1747},[1749,21300,21301],{},[1752,21302,1755,21303,1755,21310],{"style":1754},[1757,21304,21305,1755],{"style":21003},[1025,21306,21307],{},[1028,21308],{"alt":1028,"src":21309},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-49.png",[1757,21311,21312,1755],{"style":21011},[1025,21313,21314],{},[1028,21315],{"alt":1028,"src":21316},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-50.png",[978,21318,21320],{"id":21319},"shifter-移位器","Shifter ｜ 移位器",[1025,21322,21323],{},"移位器 shifter 的几种硬件实现方式",[983,21325,21327],{"id":21326},"the-binary-shifter","The Binary Shifter",[1025,21329,21330],{},[1028,21331],{"alt":1028,"src":21332},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-51.png",[1025,21334,21335],{},"有三个控制信号：",[1007,21337,21338,21344,21350],{},[990,21339,21340,21343],{},[994,21341,21342],{},"Right","：右移 1 位",[990,21345,21346,21349],{},[994,21347,21348],{},"nop","：no operation，不移位",[990,21351,21352,21355],{},[994,21353,21354],{},"Left","：左移 1 位",[1025,21357,21358,21359,5628],{},"可以把它理解成一个由传输门\u002F传输晶体管组成的 ",[994,21360,21361],{},"3 选 1 mux",[1366,21363,21365],{"id":21364},"a-programmable-binary-shifter","A programmable Binary Shifter",[1025,21367,21368,21369,21410,21411,21410,21449,21495],{},"表中 ",[1398,21370,21372,21391],{"className":21371},[1401],[1398,21373,21375],{"className":21374},[1405],[1407,21376,21377],{"xmlns":1409},[1411,21378,21379,21388],{},[1414,21380,21381,21383,21386],{},[1417,21382,3550],{},[1417,21384,21385],{},"g",[1417,21387,3534],{},[1474,21389,21390],{"encoding":1476},"rgt",[1398,21392,21394],{"className":21393,"ariaHidden":1462},[1481],[1398,21395,21397,21401,21404,21407],{"className":21396},[1485],[1398,21398],{"className":21399,"style":21400},[1489],"height:0.8095em;vertical-align:-0.1944em;",[1398,21402,3550],{"className":21403,"style":3654},[1494,1495],[1398,21405,21385],{"className":21406,"style":3755},[1494,1495],[1398,21408,3534],{"className":21409},[1494,1495],"、",[1398,21412,21414,21431],{"className":21413},[1401],[1398,21415,21417],{"className":21416},[1405],[1407,21418,21419],{"xmlns":1409},[1411,21420,21421,21429],{},[1414,21422,21423,21425,21427],{},[1417,21424,7833],{},[1417,21426,1469],{},[1417,21428,1025],{},[1474,21430,21348],{"encoding":1476},[1398,21432,21434],{"className":21433,"ariaHidden":1462},[1481],[1398,21435,21437,21440,21443,21446],{"className":21436},[1485],[1398,21438],{"className":21439,"style":20867},[1489],[1398,21441,7833],{"className":21442},[1494,1495],[1398,21444,1469],{"className":21445},[1494,1495],[1398,21447,1025],{"className":21448},[1494,1495],[1398,21450,21452,21473],{"className":21451},[1401],[1398,21453,21455],{"className":21454},[1405],[1407,21456,21457],{"xmlns":1409},[1411,21458,21459,21470],{},[1414,21460,21461,21463,21465,21468],{},[1417,21462,18695],{},[1417,21464,3547],{},[1417,21466,21467],{},"f",[1417,21469,3534],{},[1474,21471,21472],{"encoding":1476},"left",[1398,21474,21476],{"className":21475,"ariaHidden":1462},[1481],[1398,21477,21479,21482,21485,21488,21492],{"className":21478},[1485],[1398,21480],{"className":21481,"style":2033},[1489],[1398,21483,18695],{"className":21484,"style":18834},[1494,1495],[1398,21486,3547],{"className":21487},[1494,1495],[1398,21489,21467],{"className":21490,"style":21491},[1494,1495],"margin-right:0.1076em;",[1398,21493,3534],{"className":21494},[1494,1495]," 是控制信号，通常是 one-hot，也就是三者只能有一个为 1。",[1025,21497,21498],{},[1028,21499],{"alt":1028,"src":21500},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-52.png",[1025,21502,21503,21504],{},"注意这里",[994,21505,21506],{},"右移的时候高位补0",[983,21508,21510],{"id":21509},"the-barrel-shifter","The Barrel Shifter",[1025,21512,21513,21514,16959,21517,16959,21587,16959,21590,16959,21662,21665],{},"Barrel shifter 的思想是：",[3237,21515,21516],{},"每个输出",[1398,21518,21520,21538],{"className":21519},[1401],[1398,21521,21523],{"className":21522},[1405],[1407,21524,21525],{"xmlns":1409},[1411,21526,21527,21535],{},[1414,21528,21529],{},[1449,21530,21531,21533],{},[1417,21532,1429],{},[1417,21534,15575],{},[1474,21536,21537],{"encoding":1476},"B_j",[1398,21539,21541],{"className":21540,"ariaHidden":1462},[1481],[1398,21542,21544,21547],{"className":21543},[1485],[1398,21545],{"className":21546,"style":8203},[1489],[1398,21548,21550,21553],{"className":21549},[1494],[1398,21551,1429],{"className":21552,"style":1522},[1494,1495],[1398,21554,21556],{"className":21555},[1595],[1398,21557,21559,21579],{"className":21558},[1599,1600],[1398,21560,21562,21576],{"className":21561},[1604],[1398,21563,21565],{"className":21564,"style":1609},[1608],[1398,21566,21567,21570],{"style":7112},[1398,21568],{"className":21569,"style":1617},[1616],[1398,21571,21573],{"className":21572},[1621,1622,1623,1624],[1398,21574,15575],{"className":21575,"style":15663},[1494,1495,1624],[1398,21577,1632],{"className":21578},[1631],[1398,21580,21582],{"className":21581},[1604],[1398,21583,21585],{"className":21584,"style":3765},[1608],[1398,21586],{},[3237,21588,21589],{},"都可以从多个输入",[1398,21591,21593,21612],{"className":21592},[1401],[1398,21594,21596],{"className":21595},[1405],[1407,21597,21598],{"xmlns":1409},[1411,21599,21600,21609],{},[1414,21601,21602],{},[1449,21603,21604,21606],{},[1417,21605,1426],{},[1417,21607,21608],{},"k",[1474,21610,21611],{"encoding":1476},"A_k",[1398,21613,21615],{"className":21614,"ariaHidden":1462},[1481],[1398,21616,21618,21621],{"className":21617},[1485],[1398,21619],{"className":21620,"style":1858},[1489],[1398,21622,21624,21627],{"className":21623},[1494],[1398,21625,1426],{"className":21626},[1494,1495],[1398,21628,21630],{"className":21629},[1595],[1398,21631,21633,21654],{"className":21632},[1599,1600],[1398,21634,21636,21651],{"className":21635},[1604],[1398,21637,21639],{"className":21638,"style":3631},[1608],[1398,21640,21641,21644],{"style":3634},[1398,21642],{"className":21643,"style":1617},[1616],[1398,21645,21647],{"className":21646},[1621,1622,1623,1624],[1398,21648,21608],{"className":21649,"style":21650},[1494,1495,1624],"margin-right:0.0315em;",[1398,21652,1632],{"className":21653},[1631],[1398,21655,21657],{"className":21656},[1604],[1398,21658,21660],{"className":21659,"style":1639},[1608],[1398,21661],{},[3237,21663,21664],{},"中直接选择一个","。（任意移动多少个位置，算术移动）",[1745,21667,21668],{"style":1747},[1749,21669,21670],{},[1752,21671,1755,21672,1755,21680],{"style":1754},[1757,21673,21675,1755],{"style":21674},"width: 47.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,21676,21677],{},[1028,21678],{"alt":1028,"src":21679},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-53.png",[1757,21681,21683,1755],{"style":21682},"width: 52.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,21684,21685],{},[1028,21686],{"alt":1028,"src":21687},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-54.png",[1025,21689,21690],{},"本质上是一个很大的交叉开关阵列。",[1025,21692,21693,21694,21926],{},"例如 4-bit barrel shifter 中，每个输出都可能从 ",[1398,21695,21697,21739],{"className":21696},[1401],[1398,21698,21700],{"className":21699},[1405],[1407,21701,21702],{"xmlns":1409},[1411,21703,21704,21736],{},[1414,21705,21706,21712,21714,21720,21722,21728,21730],{},[1449,21707,21708,21710],{},[1417,21709,1426],{},[2883,21711,6046],{},[1421,21713,1797],{"separator":1462},[1449,21715,21716,21718],{},[1417,21717,1426],{},[2883,21719,6033],{},[1421,21721,1797],{"separator":1462},[1449,21723,21724,21726],{},[1417,21725,1426],{},[2883,21727,2885],{},[1421,21729,1797],{"separator":1462},[1449,21731,21732,21734],{},[1417,21733,1426],{},[2883,21735,3030],{},[1474,21737,21738],{"encoding":1476},"A_3,A_2,A_1,A_0",[1398,21740,21742],{"className":21741,"ariaHidden":1462},[1481],[1398,21743,21745,21748,21788,21791,21794,21834,21837,21840,21880,21883,21886],{"className":21744},[1485],[1398,21746],{"className":21747,"style":1812},[1489],[1398,21749,21751,21754],{"className":21750},[1494],[1398,21752,1426],{"className":21753},[1494,1495],[1398,21755,21757],{"className":21756},[1595],[1398,21758,21760,21780],{"className":21759},[1599,1600],[1398,21761,21763,21777],{"className":21762},[1604],[1398,21764,21766],{"className":21765,"style":6203},[1608],[1398,21767,21768,21771],{"style":3634},[1398,21769],{"className":21770,"style":1617},[1616],[1398,21772,21774],{"className":21773},[1621,1622,1623,1624],[1398,21775,6046],{"className":21776},[1494,1624],[1398,21778,1632],{"className":21779},[1631],[1398,21781,21783],{"className":21782},[1604],[1398,21784,21786],{"className":21785,"style":1639},[1608],[1398,21787],{},[1398,21789,1797],{"className":21790},[1819],[1398,21792],{"className":21793,"style":1823},[1500],[1398,21795,21797,21800],{"className":21796},[1494],[1398,21798,1426],{"className":21799},[1494,1495],[1398,21801,21803],{"className":21802},[1595],[1398,21804,21806,21826],{"className":21805},[1599,1600],[1398,21807,21809,21823],{"className":21808},[1604],[1398,21810,21812],{"className":21811,"style":6203},[1608],[1398,21813,21814,21817],{"style":3634},[1398,21815],{"className":21816,"style":1617},[1616],[1398,21818,21820],{"className":21819},[1621,1622,1623,1624],[1398,21821,6033],{"className":21822},[1494,1624],[1398,21824,1632],{"className":21825},[1631],[1398,21827,21829],{"className":21828},[1604],[1398,21830,21832],{"className":21831,"style":1639},[1608],[1398,21833],{},[1398,21835,1797],{"className":21836},[1819],[1398,21838],{"className":21839,"style":1823},[1500],[1398,21841,21843,21846],{"className":21842},[1494],[1398,21844,1426],{"className":21845},[1494,1495],[1398,21847,21849],{"className":21848},[1595],[1398,21850,21852,21872],{"className":21851},[1599,1600],[1398,21853,21855,21869],{"className":21854},[1604],[1398,21856,21858],{"className":21857,"style":6203},[1608],[1398,21859,21860,21863],{"style":3634},[1398,21861],{"className":21862,"style":1617},[1616],[1398,21864,21866],{"className":21865},[1621,1622,1623,1624],[1398,21867,2885],{"className":21868},[1494,1624],[1398,21870,1632],{"className":21871},[1631],[1398,21873,21875],{"className":21874},[1604],[1398,21876,21878],{"className":21877,"style":1639},[1608],[1398,21879],{},[1398,21881,1797],{"className":21882},[1819],[1398,21884],{"className":21885,"style":1823},[1500],[1398,21887,21889,21892],{"className":21888},[1494],[1398,21890,1426],{"className":21891},[1494,1495],[1398,21893,21895],{"className":21894},[1595],[1398,21896,21898,21918],{"className":21897},[1599,1600],[1398,21899,21901,21915],{"className":21900},[1604],[1398,21902,21904],{"className":21903,"style":6203},[1608],[1398,21905,21906,21909],{"style":3634},[1398,21907],{"className":21908,"style":1617},[1616],[1398,21910,21912],{"className":21911},[1621,1622,1623,1624],[1398,21913,3030],{"className":21914},[1494,1624],[1398,21916,1632],{"className":21917},[1631],[1398,21919,21921],{"className":21920},[1604],[1398,21922,21924],{"className":21923,"style":1639},[1608],[1398,21925],{}," 中选择，因此会有很多横向数据线、纵向控制线、交叉点开关。",[1025,21928,21929,21930,21958,21959,22035],{},"这个结构的面积主要不是被晶体管占掉的，而是被大量连线占掉的。对于 ",[1398,21931,21933,21946],{"className":21932},[1401],[1398,21934,21936],{"className":21935},[1405],[1407,21937,21938],{"xmlns":1409},[1411,21939,21940,21944],{},[1414,21941,21942],{},[1417,21943,3557],{},[1474,21945,3557],{"encoding":1476},[1398,21947,21949],{"className":21948,"ariaHidden":1462},[1481],[1398,21950,21952,21955],{"className":21951},[1485],[1398,21953],{"className":21954,"style":1490},[1489],[1398,21956,3557],{"className":21957,"style":3688},[1494,1495]," 位 barrel shifter，交叉连接规模大约是 ",[1398,21960,21962,21987],{"className":21961},[1401],[1398,21963,21965],{"className":21964},[1405],[1407,21966,21967],{"xmlns":1409},[1411,21968,21969,21984],{},[1414,21970,21971,21974,21976,21982],{},[1417,21972,21973],{},"O",[1421,21975,1439],{"stretchy":1438},[12736,21977,21978,21980],{},[1417,21979,3557],{},[2883,21981,6033],{},[1421,21983,1458],{"stretchy":1438},[1474,21985,21986],{"encoding":1476},"O(N^2)",[1398,21988,21990],{"className":21989,"ariaHidden":1462},[1481],[1398,21991,21993,21997,22000,22003,22032],{"className":21992},[1485],[1398,21994],{"className":21995,"style":21996},[1489],"height:1.0641em;vertical-align:-0.25em;",[1398,21998,21973],{"className":21999,"style":3654},[1494,1495],[1398,22001,1439],{"className":22002},[1548],[1398,22004,22006,22009],{"className":22005},[1494],[1398,22007,3557],{"className":22008,"style":3688},[1494,1495],[1398,22010,22012],{"className":22011},[1595],[1398,22013,22015],{"className":22014},[1599],[1398,22016,22018],{"className":22017},[1604],[1398,22019,22021],{"className":22020,"style":13039},[1608],[1398,22022,22023,22026],{"style":13042},[1398,22024],{"className":22025,"style":1617},[1616],[1398,22027,22029],{"className":22028},[1621,1622,1623,1624],[1398,22030,6033],{"className":22031},[1494,1624],[1398,22033,1458],{"className":22034},[1645],"，所以位宽变大以后，布线压力很明显。",[983,22037,22039],{"id":22038},"logarithmic-shifter","Logarithmic Shifter",[1025,22041,22042,22043,22126],{},"用多级小移位实现任意移位，不再用一个巨大的全交叉阵列，而是分成若干级，每一级只负责移 ",[1398,22044,22046,22077],{"className":22045},[1401],[1398,22047,22049],{"className":22048},[1405],[1407,22050,22051],{"xmlns":1409},[1411,22052,22053,22074],{},[1414,22054,22055,22057,22059,22061,22063,22065,22067,22069,22071],{},[2883,22056,2885],{},[1421,22058,1797],{"separator":1462},[2883,22060,6033],{},[1421,22062,1797],{"separator":1462},[2883,22064,11129],{},[1421,22066,1797],{"separator":1462},[2883,22068,11135],{},[1421,22070,1797],{"separator":1462},[1421,22072,22073],{},"…",[1474,22075,22076],{"encoding":1476},"1,2,4,8,\\dots",[1398,22078,22080],{"className":22079,"ariaHidden":1462},[1481],[1398,22081,22083,22087,22090,22093,22096,22099,22102,22105,22108,22111,22114,22117,22120,22123],{"className":22082},[1485],[1398,22084],{"className":22085,"style":22086},[1489],"height:0.8389em;vertical-align:-0.1944em;",[1398,22088,2885],{"className":22089},[1494],[1398,22091,1797],{"className":22092},[1819],[1398,22094],{"className":22095,"style":1823},[1500],[1398,22097,6033],{"className":22098},[1494],[1398,22100,1797],{"className":22101},[1819],[1398,22103],{"className":22104,"style":1823},[1500],[1398,22106,11129],{"className":22107},[1494],[1398,22109,1797],{"className":22110},[1819],[1398,22112],{"className":22113,"style":1823},[1500],[1398,22115,11135],{"className":22116},[1494],[1398,22118,1797],{"className":22119},[1819],[1398,22121],{"className":22122,"style":1823},[1500],[1398,22124,22073],{"className":22125},[3510]," 位。",[1745,22128,22129],{"style":1747},[1749,22130,22131],{},[1752,22132,1755,22133,1755,22141],{"style":1754},[1757,22134,22136,1755],{"style":22135},"width: 48.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,22137,22138],{},[1028,22139],{"alt":1028,"src":22140},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-55.png",[1757,22142,22144,1755],{"style":22143},"width: 51.0%; text-align: center; border: none; padding: 0.3em; margin: 0;",[1025,22145,22146],{},[1028,22147],{"alt":1028,"src":22148},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-56.png",[978,22150,22152],{"id":22151},"alu-arithmetic-logic-unit-运算器","ALU ｜ Arithmetic Logic Unit 运算器",[1025,22154,22155,22156,22159,22160,21410,22211,21410,22284,21410,22335,21410,22376,21410,22416],{},"ALU 需要根据 ",[994,22157,22158],{},"opcode"," 执行不同功能，比如：",[1398,22161,22163,22181],{"className":22162},[1401],[1398,22164,22166],{"className":22165},[1405],[1407,22167,22168],{"xmlns":1409},[1411,22169,22170,22178],{},[1414,22171,22172,22174,22176],{},[1417,22173,1426],{},[1421,22175,1435],{},[1417,22177,1429],{},[1474,22179,22180],{"encoding":1476},"A+B",[1398,22182,22184,22202],{"className":22183,"ariaHidden":1462},[1481],[1398,22185,22187,22190,22193,22196,22199],{"className":22186},[1485],[1398,22188],{"className":22189,"style":1515},[1489],[1398,22191,1426],{"className":22192},[1494,1495],[1398,22194],{"className":22195,"style":1530},[1500],[1398,22197,1435],{"className":22198},[1534],[1398,22200],{"className":22201,"style":1530},[1500],[1398,22203,22205,22208],{"className":22204},[1485],[1398,22206],{"className":22207,"style":1490},[1489],[1398,22209,1429],{"className":22210,"style":1522},[1494,1495],[1398,22212,22214,22236],{"className":22213},[1401],[1398,22215,22217],{"className":22216},[1405],[1407,22218,22219],{"xmlns":1409},[1411,22220,22221,22233],{},[1414,22222,22223,22225,22227,22229,22231],{},[1417,22224,1426],{},[1421,22226,1435],{},[1417,22228,1429],{},[1421,22230,1435],{},[2883,22232,2885],{},[1474,22234,22235],{"encoding":1476},"A+B+1",[1398,22237,22239,22257,22275],{"className":22238,"ariaHidden":1462},[1481],[1398,22240,22242,22245,22248,22251,22254],{"className":22241},[1485],[1398,22243],{"className":22244,"style":1515},[1489],[1398,22246,1426],{"className":22247},[1494,1495],[1398,22249],{"className":22250,"style":1530},[1500],[1398,22252,1435],{"className":22253},[1534],[1398,22255],{"className":22256,"style":1530},[1500],[1398,22258,22260,22263,22266,22269,22272],{"className":22259},[1485],[1398,22261],{"className":22262,"style":1515},[1489],[1398,22264,1429],{"className":22265,"style":1522},[1494,1495],[1398,22267],{"className":22268,"style":1530},[1500],[1398,22270,1435],{"className":22271},[1534],[1398,22273],{"className":22274,"style":1530},[1500],[1398,22276,22278,22281],{"className":22277},[1485],[1398,22279],{"className":22280,"style":2992},[1489],[1398,22282,2885],{"className":22283},[1494],[1398,22285,22287,22305],{"className":22286},[1401],[1398,22288,22290],{"className":22289},[1405],[1407,22291,22292],{"xmlns":1409},[1411,22293,22294,22302],{},[1414,22295,22296,22298,22300],{},[1417,22297,1426],{},[1421,22299,3560],{},[1417,22301,1429],{},[1474,22303,22304],{"encoding":1476},"A-B",[1398,22306,22308,22326],{"className":22307,"ariaHidden":1462},[1481],[1398,22309,22311,22314,22317,22320,22323],{"className":22310},[1485],[1398,22312],{"className":22313,"style":1515},[1489],[1398,22315,1426],{"className":22316},[1494,1495],[1398,22318],{"className":22319,"style":1530},[1500],[1398,22321,3560],{"className":22322},[1534],[1398,22324],{"className":22325,"style":1530},[1500],[1398,22327,22329,22332],{"className":22328},[1485],[1398,22330],{"className":22331,"style":1490},[1489],[1398,22333,1429],{"className":22334,"style":1522},[1494,1495],[1398,22336,22338,22357],{"className":22337},[1401],[1398,22339,22341],{"className":22340},[1405],[1407,22342,22343],{"xmlns":1409},[1411,22344,22345,22354],{},[1414,22346,22347,22349,22352],{},[1417,22348,1426],{},[1417,22350,22351],{"mathvariant":2017},"&",[1417,22353,1429],{},[1474,22355,22356],{"encoding":1476},"A\\&B",[1398,22358,22360],{"className":22359,"ariaHidden":1462},[1481],[1398,22361,22363,22367,22370,22373],{"className":22362},[1485],[1398,22364],{"className":22365,"style":22366},[1489],"height:0.6944em;",[1398,22368,1426],{"className":22369},[1494,1495],[1398,22371,22351],{"className":22372},[1494],[1398,22374,1429],{"className":22375,"style":1522},[1494,1495],[1398,22377,22379,22398],{"className":22378},[1401],[1398,22380,22382],{"className":22381},[1405],[1407,22383,22384],{"xmlns":1409},[1411,22385,22386,22395],{},[1414,22387,22388,22390,22393],{},[1417,22389,1426],{},[1417,22391,22392],{"mathvariant":2017},"∣",[1417,22394,1429],{},[1474,22396,22397],{"encoding":1476},"A|B",[1398,22399,22401],{"className":22400,"ariaHidden":1462},[1481],[1398,22402,22404,22407,22410,22413],{"className":22403},[1485],[1398,22405],{"className":22406,"style":1544},[1489],[1398,22408,1426],{"className":22409},[1494,1495],[1398,22411,22392],{"className":22412},[1494],[1398,22414,1429],{"className":22415,"style":1522},[1494,1495],[1398,22417,22419,22437],{"className":22418},[1401],[1398,22420,22422],{"className":22421},[1405],[1407,22423,22424],{"xmlns":1409},[1411,22425,22426,22434],{},[1414,22427,22428,22430,22432],{},[1417,22429,1426],{},[1421,22431,2121],{},[1417,22433,1429],{},[1474,22435,22436],{"encoding":1476},"A\\oplus B",[1398,22438,22440,22458],{"className":22439,"ariaHidden":1462},[1481],[1398,22441,22443,22446,22449,22452,22455],{"className":22442},[1485],[1398,22444],{"className":22445,"style":1515},[1489],[1398,22447,1426],{"className":22448},[1494,1495],[1398,22450],{"className":22451,"style":1530},[1500],[1398,22453,2121],{"className":22454},[1534],[1398,22456],{"className":22457,"style":1530},[1500],[1398,22459,22461,22464],{"className":22460},[1485],[1398,22462],{"className":22463,"style":1490},[1489],[1398,22465,1429],{"className":22466,"style":1522},[1494,1495],[1025,22468,22469,22470,22472,22473,22476],{},"其中 ",[994,22471,22158],{}," 决定当前做什么操作，",[994,22474,22475],{},"carry-in"," 也会参与决定具体算术功能",[1025,22478,22479],{},[1028,22480],{"alt":1028,"src":22481},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-57.png",[983,22483,22485],{"id":22484},"function-blocks-and-alus","Function blocks and ALUs",[1025,22487,1023],{},[1007,22489,22490,22497,22504,22507,22510],{},[990,22491,22492,22493,22496],{},"可以提供两个变量的",[994,22494,22495],{},"完整逻辑函数集合","，也可以只提供其中一个子集。",[990,22498,22499,22500,22503],{},"ALU 通常围绕加法器构建，因为加法是典型的算术运算，而且",[994,22501,22502],{},"进位链 carry chain"," 往往决定整体延迟。",[990,22505,22506],{},"Function block 可以用来计算全功能 ALU 所需的中间信号。",[990,22508,22509],{},"所需面积较小。",[990,22511,22512],{},"可以使用传输门实现，但传输门可能会引入额外延迟。",[1025,22514,22515],{},[1028,22516],{"alt":1028,"src":22517},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-58.png",[1398,22519,22521],{"className":22520},[2737],[1398,22522,22524,22620],{"className":22523},[1401],[1398,22525,22527],{"className":22526},[1405],[1407,22528,22529],{"xmlns":1409,"display":2746},[1411,22530,22531,22617],{},[1414,22532,22533,22535,22537,22539,22541,22543,22545,22547,22553,22559,22561,22567,22569,22571,22577,22579,22585,22587,22593,22595,22597,22603,22605,22607,22609,22611],{},[1417,22534,1469],{},[1417,22536,3596],{},[1417,22538,3534],{},[1417,22540,1025],{},[1417,22542,3596],{},[1417,22544,3534],{},[1421,22546,1423],{},[1460,22548,22549,22551],{"accent":1462},[1417,22550,3539],{},[1421,22552,1472],{"stretchy":1462},[1460,22554,22555,22557],{"accent":1462},[1417,22556,8005],{},[1421,22558,1472],{"stretchy":1462},[1417,22560,1469],{},[1449,22562,22563,22565],{},[1417,22564,1025],{},[2883,22566,3030],{},[1421,22568,1435],{},[1417,22570,3539],{},[1460,22572,22573,22575],{"accent":1462},[1417,22574,8005],{},[1421,22576,1472],{"stretchy":1462},[1417,22578,1469],{},[1449,22580,22581,22583],{},[1417,22582,1025],{},[2883,22584,2885],{},[1421,22586,1435],{},[1460,22588,22589,22591],{"accent":1462},[1417,22590,3539],{},[1421,22592,1472],{"stretchy":1462},[1417,22594,8005],{},[1417,22596,1469],{},[1449,22598,22599,22601],{},[1417,22600,1025],{},[2883,22602,6033],{},[1421,22604,1435],{},[1417,22606,3539],{},[1417,22608,8005],{},[1417,22610,1469],{},[1449,22612,22613,22615],{},[1417,22614,1025],{},[2883,22616,6046],{},[1474,22618,22619],{"encoding":1476},"output=\\overline{a}\\overline{b}op_0+a\\overline{b}op_1+\\overline{a}bop_2+abop_3",[1398,22621,22623,22654,22779,22871,22963],{"className":22622,"ariaHidden":1462},[1481],[1398,22624,22626,22629,22632,22635,22639,22642,22645,22648,22651],{"className":22625},[1485],[1398,22627],{"className":22628,"style":21400},[1489],[1398,22630,1469],{"className":22631},[1494,1495],[1398,22633,3596],{"className":22634},[1494,1495],[1398,22636,22638],{"className":22637},[1494,1495],"tp",[1398,22640,3596],{"className":22641},[1494,1495],[1398,22643,3534],{"className":22644},[1494,1495],[1398,22646],{"className":22647,"style":1501},[1500],[1398,22649,1423],{"className":22650},[1505],[1398,22652],{"className":22653,"style":1501},[1500],[1398,22655,22657,22661,22694,22727,22730,22770,22773,22776],{"className":22656},[1485],[1398,22658],{"className":22659,"style":22660},[1489],"height:1.0889em;vertical-align:-0.1944em;",[1398,22662,22664],{"className":22663},[1494,1649],[1398,22665,22667],{"className":22666},[1599],[1398,22668,22670],{"className":22669},[1604],[1398,22671,22674,22685],{"className":22672,"style":22673},[1608],"height:0.6306em;",[1398,22675,22676,22679],{"style":1662},[1398,22677],{"className":22678,"style":1666},[1616],[1398,22680,22682],{"className":22681},[1494],[1398,22683,3539],{"className":22684},[1494,1495],[1398,22686,22688,22691],{"style":22687},"top:-3.5506em;",[1398,22689],{"className":22690,"style":1666},[1616],[1398,22692],{"className":22693,"style":1721},[1720],[1398,22695,22697],{"className":22696},[1494,1649],[1398,22698,22700],{"className":22699},[1599],[1398,22701,22703],{"className":22702},[1604],[1398,22704,22707,22718],{"className":22705,"style":22706},[1608],"height:0.8944em;",[1398,22708,22709,22712],{"style":1662},[1398,22710],{"className":22711,"style":1666},[1616],[1398,22713,22715],{"className":22714},[1494],[1398,22716,8005],{"className":22717},[1494,1495],[1398,22719,22721,22724],{"style":22720},"top:-3.8144em;",[1398,22722],{"className":22723,"style":1666},[1616],[1398,22725],{"className":22726,"style":1721},[1720],[1398,22728,1469],{"className":22729},[1494,1495],[1398,22731,22733,22736],{"className":22732},[1494],[1398,22734,1025],{"className":22735},[1494,1495],[1398,22737,22739],{"className":22738},[1595],[1398,22740,22742,22762],{"className":22741},[1599,1600],[1398,22743,22745,22759],{"className":22744},[1604],[1398,22746,22748],{"className":22747,"style":6203},[1608],[1398,22749,22750,22753],{"style":3634},[1398,22751],{"className":22752,"style":1617},[1616],[1398,22754,22756],{"className":22755},[1621,1622,1623,1624],[1398,22757,3030],{"className":22758},[1494,1624],[1398,22760,1632],{"className":22761},[1631],[1398,22763,22765],{"className":22764},[1604],[1398,22766,22768],{"className":22767,"style":1639},[1608],[1398,22769],{},[1398,22771],{"className":22772,"style":1530},[1500],[1398,22774,1435],{"className":22775},[1534],[1398,22777],{"className":22778,"style":1530},[1500],[1398,22780,22782,22785,22788,22819,22822,22862,22865,22868],{"className":22781},[1485],[1398,22783],{"className":22784,"style":22660},[1489],[1398,22786,3539],{"className":22787},[1494,1495],[1398,22789,22791],{"className":22790},[1494,1649],[1398,22792,22794],{"className":22793},[1599],[1398,22795,22797],{"className":22796},[1604],[1398,22798,22800,22811],{"className":22799,"style":22706},[1608],[1398,22801,22802,22805],{"style":1662},[1398,22803],{"className":22804,"style":1666},[1616],[1398,22806,22808],{"className":22807},[1494],[1398,22809,8005],{"className":22810},[1494,1495],[1398,22812,22813,22816],{"style":22720},[1398,22814],{"className":22815,"style":1666},[1616],[1398,22817],{"className":22818,"style":1721},[1720],[1398,22820,1469],{"className":22821},[1494,1495],[1398,22823,22825,22828],{"className":22824},[1494],[1398,22826,1025],{"className":22827},[1494,1495],[1398,22829,22831],{"className":22830},[1595],[1398,22832,22834,22854],{"className":22833},[1599,1600],[1398,22835,22837,22851],{"className":22836},[1604],[1398,22838,22840],{"className":22839,"style":6203},[1608],[1398,22841,22842,22845],{"style":3634},[1398,22843],{"className":22844,"style":1617},[1616],[1398,22846,22848],{"className":22847},[1621,1622,1623,1624],[1398,22849,2885],{"className":22850},[1494,1624],[1398,22852,1632],{"className":22853},[1631],[1398,22855,22857],{"className":22856},[1604],[1398,22858,22860],{"className":22859,"style":1639},[1608],[1398,22861],{},[1398,22863],{"className":22864,"style":1530},[1500],[1398,22866,1435],{"className":22867},[1534],[1398,22869],{"className":22870,"style":1530},[1500],[1398,22872,22874,22877,22908,22911,22914,22954,22957,22960],{"className":22873},[1485],[1398,22875],{"className":22876,"style":2033},[1489],[1398,22878,22880],{"className":22879},[1494,1649],[1398,22881,22883],{"className":22882},[1599],[1398,22884,22886],{"className":22885},[1604],[1398,22887,22889,22900],{"className":22888,"style":22673},[1608],[1398,22890,22891,22894],{"style":1662},[1398,22892],{"className":22893,"style":1666},[1616],[1398,22895,22897],{"className":22896},[1494],[1398,22898,3539],{"className":22899},[1494,1495],[1398,22901,22902,22905],{"style":22687},[1398,22903],{"className":22904,"style":1666},[1616],[1398,22906],{"className":22907,"style":1721},[1720],[1398,22909,8005],{"className":22910},[1494,1495],[1398,22912,1469],{"className":22913},[1494,1495],[1398,22915,22917,22920],{"className":22916},[1494],[1398,22918,1025],{"className":22919},[1494,1495],[1398,22921,22923],{"className":22922},[1595],[1398,22924,22926,22946],{"className":22925},[1599,1600],[1398,22927,22929,22943],{"className":22928},[1604],[1398,22930,22932],{"className":22931,"style":6203},[1608],[1398,22933,22934,22937],{"style":3634},[1398,22935],{"className":22936,"style":1617},[1616],[1398,22938,22940],{"className":22939},[1621,1622,1623,1624],[1398,22941,6033],{"className":22942},[1494,1624],[1398,22944,1632],{"className":22945},[1631],[1398,22947,22949],{"className":22948},[1604],[1398,22950,22952],{"className":22951,"style":1639},[1608],[1398,22953],{},[1398,22955],{"className":22956,"style":1530},[1500],[1398,22958,1435],{"className":22959},[1534],[1398,22961],{"className":22962,"style":1530},[1500],[1398,22964,22966,22969,22973,22976],{"className":22965},[1485],[1398,22967],{"className":22968,"style":2033},[1489],[1398,22970,22972],{"className":22971},[1494,1495],"ab",[1398,22974,1469],{"className":22975},[1494,1495],[1398,22977,22979,22982],{"className":22978},[1494],[1398,22980,1025],{"className":22981},[1494,1495],[1398,22983,22985],{"className":22984},[1595],[1398,22986,22988,23008],{"className":22987},[1599,1600],[1398,22989,22991,23005],{"className":22990},[1604],[1398,22992,22994],{"className":22993,"style":6203},[1608],[1398,22995,22996,22999],{"style":3634},[1398,22997],{"className":22998,"style":1617},[1616],[1398,23000,23002],{"className":23001},[1621,1622,1623,1624],[1398,23003,6046],{"className":23004},[1494,1624],[1398,23006,1632],{"className":23007},[1631],[1398,23009,23011],{"className":23010},[1604],[1398,23012,23014],{"className":23013,"style":1639},[1608],[1398,23015],{},[1025,23017,23018,23019,23271,23272,23314],{},"这个公式的意思是：",[1398,23020,23022,23072],{"className":23021},[1401],[1398,23023,23025],{"className":23024},[1405],[1407,23026,23027],{"xmlns":1409},[1411,23028,23029,23069],{},[1414,23030,23031,23033,23039,23041,23043,23049,23051,23053,23059,23061,23063],{},[1417,23032,1469],{},[1449,23034,23035,23037],{},[1417,23036,1025],{},[2883,23038,3030],{},[1421,23040,1797],{"separator":1462},[1417,23042,1469],{},[1449,23044,23045,23047],{},[1417,23046,1025],{},[2883,23048,2885],{},[1421,23050,1797],{"separator":1462},[1417,23052,1469],{},[1449,23054,23055,23057],{},[1417,23056,1025],{},[2883,23058,6033],{},[1421,23060,1797],{"separator":1462},[1417,23062,1469],{},[1449,23064,23065,23067],{},[1417,23066,1025],{},[2883,23068,6046],{},[1474,23070,23071],{"encoding":1476},"op_0,op_1,op_2,op_3",[1398,23073,23075],{"className":23074,"ariaHidden":1462},[1481],[1398,23076,23078,23081,23084,23124,23127,23130,23133,23173,23176,23179,23182,23222,23225,23228,23231],{"className":23077},[1485],[1398,23079],{"className":23080,"style":20867},[1489],[1398,23082,1469],{"className":23083},[1494,1495],[1398,23085,23087,23090],{"className":23086},[1494],[1398,23088,1025],{"className":23089},[1494,1495],[1398,23091,23093],{"className":23092},[1595],[1398,23094,23096,23116],{"className":23095},[1599,1600],[1398,23097,23099,23113],{"className":23098},[1604],[1398,23100,23102],{"className":23101,"style":6203},[1608],[1398,23103,23104,23107],{"style":3634},[1398,23105],{"className":23106,"style":1617},[1616],[1398,23108,23110],{"className":23109},[1621,1622,1623,1624],[1398,23111,3030],{"className":23112},[1494,1624],[1398,23114,1632],{"className":23115},[1631],[1398,23117,23119],{"className":23118},[1604],[1398,23120,23122],{"className":23121,"style":1639},[1608],[1398,23123],{},[1398,23125,1797],{"className":23126},[1819],[1398,23128],{"className":23129,"style":1823},[1500],[1398,23131,1469],{"className":23132},[1494,1495],[1398,23134,23136,23139],{"className":23135},[1494],[1398,23137,1025],{"className":23138},[1494,1495],[1398,23140,23142],{"className":23141},[1595],[1398,23143,23145,23165],{"className":23144},[1599,1600],[1398,23146,23148,23162],{"className":23147},[1604],[1398,23149,23151],{"className":23150,"style":6203},[1608],[1398,23152,23153,23156],{"style":3634},[1398,23154],{"className":23155,"style":1617},[1616],[1398,23157,23159],{"className":23158},[1621,1622,1623,1624],[1398,23160,2885],{"className":23161},[1494,1624],[1398,23163,1632],{"className":23164},[1631],[1398,23166,23168],{"className":23167},[1604],[1398,23169,23171],{"className":23170,"style":1639},[1608],[1398,23172],{},[1398,23174,1797],{"className":23175},[1819],[1398,23177],{"className":23178,"style":1823},[1500],[1398,23180,1469],{"className":23181},[1494,1495],[1398,23183,23185,23188],{"className":23184},[1494],[1398,23186,1025],{"className":23187},[1494,1495],[1398,23189,23191],{"className":23190},[1595],[1398,23192,23194,23214],{"className":23193},[1599,1600],[1398,23195,23197,23211],{"className":23196},[1604],[1398,23198,23200],{"className":23199,"style":6203},[1608],[1398,23201,23202,23205],{"style":3634},[1398,23203],{"className":23204,"style":1617},[1616],[1398,23206,23208],{"className":23207},[1621,1622,1623,1624],[1398,23209,6033],{"className":23210},[1494,1624],[1398,23212,1632],{"className":23213},[1631],[1398,23215,23217],{"className":23216},[1604],[1398,23218,23220],{"className":23219,"style":1639},[1608],[1398,23221],{},[1398,23223,1797],{"className":23224},[1819],[1398,23226],{"className":23227,"style":1823},[1500],[1398,23229,1469],{"className":23230},[1494,1495],[1398,23232,23234,23237],{"className":23233},[1494],[1398,23235,1025],{"className":23236},[1494,1495],[1398,23238,23240],{"className":23239},[1595],[1398,23241,23243,23263],{"className":23242},[1599,1600],[1398,23244,23246,23260],{"className":23245},[1604],[1398,23247,23249],{"className":23248,"style":6203},[1608],[1398,23250,23251,23254],{"style":3634},[1398,23252],{"className":23253,"style":1617},[1616],[1398,23255,23257],{"className":23256},[1621,1622,1623,1624],[1398,23258,6046],{"className":23259},[1494,1624],[1398,23261,1632],{"className":23262},[1631],[1398,23264,23266],{"className":23265},[1604],[1398,23267,23269],{"className":23268,"style":1639},[1608],[1398,23270],{}," 分别对应 ",[1398,23273,23275,23293],{"className":23274},[1401],[1398,23276,23278],{"className":23277},[1405],[1407,23279,23280],{"xmlns":1409},[1411,23281,23282,23290],{},[1414,23283,23284,23286,23288],{},[1417,23285,3539],{},[1421,23287,1797],{"separator":1462},[1417,23289,8005],{},[1474,23291,23292],{"encoding":1476},"a,b",[1398,23294,23296],{"className":23295,"ariaHidden":1462},[1481],[1398,23297,23299,23302,23305,23308,23311],{"className":23298},[1485],[1398,23300],{"className":23301,"style":2033},[1489],[1398,23303,3539],{"className":23304},[1494,1495],[1398,23306,1797],{"className":23307},[1819],[1398,23309],{"className":23310,"style":1823},[1500],[1398,23312,8005],{"className":23313},[1494,1495]," 的四种输入情况。",[1745,23316,23317,23329],{},[23318,23319,23320],"thead",{},[1752,23321,23322,23326],{},[23323,23324,23325],"th",{},"输入",[23323,23327,23328],{},"输出由谁决定",[1749,23330,23331,23499,23666,23833],{},[1752,23332,23333,23422],{},[1757,23334,23335],{},[1398,23336,23338,23364],{"className":23337},[1401],[1398,23339,23341],{"className":23340},[1405],[1407,23342,23343],{"xmlns":1409},[1411,23344,23345,23361],{},[1414,23346,23347,23349,23351,23353,23355,23357,23359],{},[1417,23348,3539],{},[1421,23350,1423],{},[2883,23352,3030],{},[1421,23354,1797],{"separator":1462},[1417,23356,8005],{},[1421,23358,1423],{},[2883,23360,3030],{},[1474,23362,23363],{"encoding":1476},"a=0,b=0",[1398,23365,23367,23386,23413],{"className":23366,"ariaHidden":1462},[1481],[1398,23368,23370,23374,23377,23380,23383],{"className":23369},[1485],[1398,23371],{"className":23372,"style":23373},[1489],"height:0.4306em;",[1398,23375,3539],{"className":23376},[1494,1495],[1398,23378],{"className":23379,"style":1501},[1500],[1398,23381,1423],{"className":23382},[1505],[1398,23384],{"className":23385,"style":1501},[1500],[1398,23387,23389,23392,23395,23398,23401,23404,23407,23410],{"className":23388},[1485],[1398,23390],{"className":23391,"style":2033},[1489],[1398,23393,3030],{"className":23394},[1494],[1398,23396,1797],{"className":23397},[1819],[1398,23399],{"className":23400,"style":1823},[1500],[1398,23402,8005],{"className":23403},[1494,1495],[1398,23405],{"className":23406,"style":1501},[1500],[1398,23408,1423],{"className":23409},[1505],[1398,23411],{"className":23412,"style":1501},[1500],[1398,23414,23416,23419],{"className":23415},[1485],[1398,23417],{"className":23418,"style":2992},[1489],[1398,23420,3030],{"className":23421},[1494],[1757,23423,23424],{},[1398,23425,23427,23447],{"className":23426},[1401],[1398,23428,23430],{"className":23429},[1405],[1407,23431,23432],{"xmlns":1409},[1411,23433,23434,23444],{},[1414,23435,23436,23438],{},[1417,23437,1469],{},[1449,23439,23440,23442],{},[1417,23441,1025],{},[2883,23443,3030],{},[1474,23445,23446],{"encoding":1476},"op_0",[1398,23448,23450],{"className":23449,"ariaHidden":1462},[1481],[1398,23451,23453,23456,23459],{"className":23452},[1485],[1398,23454],{"className":23455,"style":20867},[1489],[1398,23457,1469],{"className":23458},[1494,1495],[1398,23460,23462,23465],{"className":23461},[1494],[1398,23463,1025],{"className":23464},[1494,1495],[1398,23466,23468],{"className":23467},[1595],[1398,23469,23471,23491],{"className":23470},[1599,1600],[1398,23472,23474,23488],{"className":23473},[1604],[1398,23475,23477],{"className":23476,"style":6203},[1608],[1398,23478,23479,23482],{"style":3634},[1398,23480],{"className":23481,"style":1617},[1616],[1398,23483,23485],{"className":23484},[1621,1622,1623,1624],[1398,23486,3030],{"className":23487},[1494,1624],[1398,23489,1632],{"className":23490},[1631],[1398,23492,23494],{"className":23493},[1604],[1398,23495,23497],{"className":23496,"style":1639},[1608],[1398,23498],{},[1752,23500,23501,23589],{},[1757,23502,23503],{},[1398,23504,23506,23532],{"className":23505},[1401],[1398,23507,23509],{"className":23508},[1405],[1407,23510,23511],{"xmlns":1409},[1411,23512,23513,23529],{},[1414,23514,23515,23517,23519,23521,23523,23525,23527],{},[1417,23516,3539],{},[1421,23518,1423],{},[2883,23520,2885],{},[1421,23522,1797],{"separator":1462},[1417,23524,8005],{},[1421,23526,1423],{},[2883,23528,3030],{},[1474,23530,23531],{"encoding":1476},"a=1,b=0",[1398,23533,23535,23553,23580],{"className":23534,"ariaHidden":1462},[1481],[1398,23536,23538,23541,23544,23547,23550],{"className":23537},[1485],[1398,23539],{"className":23540,"style":23373},[1489],[1398,23542,3539],{"className":23543},[1494,1495],[1398,23545],{"className":23546,"style":1501},[1500],[1398,23548,1423],{"className":23549},[1505],[1398,23551],{"className":23552,"style":1501},[1500],[1398,23554,23556,23559,23562,23565,23568,23571,23574,23577],{"className":23555},[1485],[1398,23557],{"className":23558,"style":2033},[1489],[1398,23560,2885],{"className":23561},[1494],[1398,23563,1797],{"className":23564},[1819],[1398,23566],{"className":23567,"style":1823},[1500],[1398,23569,8005],{"className":23570},[1494,1495],[1398,23572],{"className":23573,"style":1501},[1500],[1398,23575,1423],{"className":23576},[1505],[1398,23578],{"className":23579,"style":1501},[1500],[1398,23581,23583,23586],{"className":23582},[1485],[1398,23584],{"className":23585,"style":2992},[1489],[1398,23587,3030],{"className":23588},[1494],[1757,23590,23591],{},[1398,23592,23594,23614],{"className":23593},[1401],[1398,23595,23597],{"className":23596},[1405],[1407,23598,23599],{"xmlns":1409},[1411,23600,23601,23611],{},[1414,23602,23603,23605],{},[1417,23604,1469],{},[1449,23606,23607,23609],{},[1417,23608,1025],{},[2883,23610,2885],{},[1474,23612,23613],{"encoding":1476},"op_1",[1398,23615,23617],{"className":23616,"ariaHidden":1462},[1481],[1398,23618,23620,23623,23626],{"className":23619},[1485],[1398,23621],{"className":2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opcode 控制 function block，就可以灵活生成不同逻辑函数",[983,24004,24006],{"id":24005},"alu-structure","ALU Structure",[1025,24008,24009],{},[1028,24010],{"alt":1028,"src":24011},"\u002Fimg\u002FDigitalICDesign\u002FChapter12-Arithmetic-59.png",[1025,24013,24014,24015,21410,24072,21410,24128,21410,24204],{},"把 ALU 分成几个功能块：",[1398,24016,24018,24044],{"className":24017},[1401],[1398,24019,24021],{"className":24020},[1405],[1407,24022,24023],{"xmlns":1409},[1411,24024,24025,24041],{},[1414,24026,24027,24029,24031,24033,24035,24037,24039],{},[1417,24028,1931],{},[10980,24030,10982],{},[1417,24032,8005],{},[1417,24034,18695],{},[1417,24036,1469],{},[1417,24038,3573],{},[1417,24040,21608],{},[1474,24042,24043],{"encoding":1476},"G\\ block",[1398,24045,24047],{"className":24046,"ariaHidden":1462},[1481],[1398,24048,24050,24053,24056,24059,24062,24065,24069],{"className":24049},[1485],[1398,24051],{"className":24052,"style":22366},[1489],[1398,24054,1931],{"className":24055},[1494,1495],[1398,24057,10982],{"className":24058},[1500],[1398,24060,8005],{"className":24061},[1494,1495],[1398,24063,18695],{"className":24064,"style":18834},[1494,1495],[1398,24066,24068],{"className":24067},[1494,1495],"oc",[1398,24070,21608],{"className":24071,"style":21650},[1494,1495],[1398,24073,24075,24101],{"className":24074},[1401],[1398,24076,24078],{"className":24077},[1405],[1407,24079,24080],{"xmlns":1409},[1411,24081,24082,24098],{},[1414,24083,24084,24086,24088,24090,24092,24094,24096],{},[1417,24085,2114],{},[10980,24087,10982],{},[1417,24089,8005],{},[1417,24091,18695],{},[1417,24093,1469],{},[1417,24095,3573],{},[1417,24097,21608],{},[1474,24099,24100],{"encoding":1476},"P\\ block",[1398,24102,24104],{"className":24103,"ariaHidden":1462},[1481],[1398,24105,24107,24110,24113,24116,24119,24122,24125],{"className":24106},[1485],[1398,24108],{"className":24109,"style":22366},[1489],[1398,24111,2114],{"className":24112,"style":2139},[1494,1495],[1398,24114,10982],{"className":24115},[1500],[1398,24117,8005],{"className":24118},[1494,1495],[1398,24120,18695],{"className":24121,"style":18834},[1494,1495],[1398,24123,24068],{"className":24124},[1494,1495],[1398,24126,21608],{"className":24127,"style":21650},[1494,1495],[1398,24129,24131,24165],{"className":24130},[1401],[1398,24132,24134],{"className":24133},[1405],[1407,24135,24136],{"xmlns":1409},[1411,24137,24138,24162],{},[1414,24139,24140,24142,24144,24146,24148,24150,24152,24154,24156,24158,24160],{},[1417,24141,1432],{},[1417,24143,3539],{},[1417,24145,3550],{},[1417,24147,3550],{},[1417,24149,3582],{},[10980,24151,10982],{},[1417,24153,8005],{},[1417,24155,18695],{},[1417,24157,1469],{},[1417,24159,3573],{},[1417,24161,21608],{},[1474,24163,24164],{"encoding":1476},"Carry\\ block",[1398,24166,24168],{"className":24167,"ariaHidden":1462},[1481],[1398,24169,24171,24174,24177,24180,24183,24186,24189,24192,24195,24198,24201],{"className":24170},[1485],[1398,24172],{"className":24173,"style":2033},[1489],[1398,24175,1432],{"className":24176,"style":1526},[1494,1495],[1398,24178,3539],{"className":24179},[1494,1495],[1398,24181,3550],{"className":24182,"style":3654},[1494,1495],[1398,24184,3550],{"className":24185,"style":3654},[1494,1495],[1398,24187,3582],{"className":24188,"style":3755},[1494,1495],[1398,24190,10982],{"className":24191},[1500],[1398,24193,8005],{"className":24194},[1494,1495],[1398,24196,18695],{"className":24197,"style":18834},[1494,1495],[1398,24199,24068],{"className":24200},[1494,1495],[1398,24202,21608],{"className":24203,"style":21650},[1494,1495],[1398,24205,24207,24237],{"className":24206},[1401],[1398,24208,24210],{"className":24209},[1405],[1407,24211,24212],{"xmlns":1409},[1411,24213,24214,24234],{},[1414,24215,24216,24218,24220,24222,24224,24226,24228,24230,24232],{},[1417,24217,1419],{},[1417,24219,3596],{},[1417,24221,3599],{},[10980,24223,10982],{},[1417,24225,8005],{},[1417,24227,18695],{},[1417,24229,1469],{},[1417,24231,3573],{},[1417,24233,21608],{},[1474,24235,24236],{"encoding":1476},"Sum\\ block",[1398,24238,24240],{"className":24239,"ariaHidden":1462},[1481],[1398,24241,24243,24246,24249,24252,24255,24258,24261,24264,24267],{"className":24242},[1485],[1398,24244],{"className":24245,"style":22366},[1489],[1398,24247,1419],{"className":24248,"style":1496},[1494,1495],[1398,24250,3596],{"className":24251},[1494,1495],[1398,24253,3599],{"className":24254},[1494,1495],[1398,24256,10982],{"className":24257},[1500],[1398,24259,8005],{"className":24260},[1494,1495],[1398,24262,18695],{"className":24263,"style":18834},[1494,1495],[1398,24265,24068],{"className":24266},[1494,1495],[1398,24268,21608],{"className":24269,"style":21650},[1494,1495],[1025,24271,24272,24273,16959,24453,24650,24651],{},"在普通加法器中，常见定义是：",[1398,24274,24276,24308],{"className":24275},[1401],[1398,24277,24279],{"className":24278},[1405],[1407,24280,24281],{"xmlns":1409},[1411,24282,24283,24305],{},[1414,24284,24285,24291,24293,24299],{},[1449,24286,24287,24289],{},[1417,24288,1931],{},[1417,24290,1455],{},[1421,24292,1423],{},[1449,24294,24295,24297],{},[1417,24296,3539],{},[1417,24298,1455],{},[1449,24300,24301,24303],{},[1417,24302,8005],{},[1417,24304,1455],{},[1474,24306,24307],{"encoding":1476},"G_i=a_ib_i",[1398,24309,24311,24366],{"className":24310,"ariaHidden":1462},[1481],[1398,24312,24314,24317,24357,24360,24363],{"className":24313},[1485],[1398,24315],{"className":24316,"style":1858},[1489],[1398,24318,24320,24323],{"className":24319},[1494],[1398,24321,1931],{"className":24322},[1494,1495],[1398,24324,24326],{"className":24325},[1595],[1398,24327,24329,24349],{"className":24328},[1599,1600],[1398,24330,24332,24346],{"className":24331},[1604],[1398,24333,24335],{"className":24334,"style":1609},[1608],[1398,24336,24337,24340],{"style":3634},[1398,24338],{"className":24339,"style":1617},[1616],[1398,24341,24343],{"className":24342},[1621,1622,1623,1624],[1398,24344,1455],{"className":24345},[1494,1495,1624],[1398,24347,1632],{"className":24348},[1631],[1398,24350,24352],{"className":24351},[1604],[1398,24353,24355],{"className":24354,"style":1639},[1608],[1398,24356],{},[1398,24358],{"className":24359,"style":1501},[1500],[1398,24361,1423],{"className":24362},[1505],[1398,24364],{"className":24365,"style":1501},[1500],[1398,24367,24369,24373,24413],{"className":24368},[1485],[1398,24370],{"className":24371,"style":24372},[1489],"height:0.8444em;vertical-align:-0.15em;",[1398,24374,24376,24379],{"className":24375},[1494],[1398,24377,3539],{"className":24378},[1494,1495],[1398,24380,24382],{"className":24381},[1595],[1398,24383,24385,24405],{"className":24384},[1599,1600],[1398,24386,24388,24402],{"className":24387},[1604],[1398,24389,24391],{"className":24390,"style":1609},[1608],[1398,24392,24393,24396],{"style":3634},[1398,24394],{"className":24395,"style":1617},[1616],[1398,24397,24399],{"className":24398},[1621,1622,1623,1624],[1398,24400,1455],{"className":24401},[1494,1495,1624],[1398,24403,1632],{"className":24404},[1631],[1398,24406,24408],{"className":24407},[1604],[1398,24409,24411],{"className":24410,"style":1639},[1608],[1398,24412],{},[1398,24414,24416,24419],{"className":24415},[1494],[1398,24417,8005],{"className":24418},[1494,1495],[1398,24420,24422],{"className":24421},[1595],[1398,24423,24425,24445],{"className":24424},[1599,1600],[1398,24426,24428,24442],{"className":24427},[1604],[1398,24429,24431],{"className":24430,"style":1609},[1608],[1398,24432,24433,24436],{"style":3634},[1398,24434],{"className":24435,"style":1617},[1616],[1398,24437,24439],{"className":24438},[1621,1622,1623,1624],[1398,24440,1455],{"className":24441},[1494,1495,1624],[1398,24443,1632],{"className":24444},[1631],[1398,24446,24448],{"className":24447},[1604],[1398,24449,24451],{"className":24450,"style":1639},[1608],[1398,24452],{},[1398,24454,24456,24490],{"className":24455},[1401],[1398,24457,24459],{"className":24458},[1405],[1407,24460,24461],{"xmlns":1409},[1411,24462,24463,24487],{},[1414,24464,24465,24471,24473,24479,24481],{},[1449,24466,24467,24469],{},[1417,24468,2114],{},[1417,24470,1455],{},[1421,24472,1423],{},[1449,24474,24475,24477],{},[1417,24476,3539],{},[1417,24478,1455],{},[1421,24480,2121],{},[1449,24482,24483,24485],{},[1417,24484,8005],{},[1417,24486,1455],{},[1474,24488,24489],{"encoding":1476},"P_i=a_i\\oplus b_i",[1398,24491,24493,24548,24604],{"className":24492,"ariaHidden":1462},[1481],[1398,24494,24496,24499,24539,24542,24545],{"className":24495},[1485],[1398,24497],{"className":24498,"style":1858},[1489],[1398,24500,24502,24505],{"className":24501},[1494],[1398,24503,2114],{"className":24504,"style":2139},[1494,1495],[1398,24506,24508],{"className":24507},[1595],[1398,24509,24511,24531],{"className":24510},[1599,1600],[1398,24512,24514,24528],{"className":24513},[1604],[1398,24515,24517],{"className":24516,"style":1609},[1608],[1398,24518,24519,24522],{"style":4987},[1398,24520],{"className":24521,"style":1617},[1616],[1398,24523,24525],{"className":24524},[1621,1622,1623,1624],[1398,24526,1455],{"className":24527},[1494,1495,1624],[1398,24529,1632],{"className":24530},[1631],[1398,24532,24534],{"className":24533},[1604],[1398,24535,24537],{"className":24536,"style":1639},[1608],[1398,24538],{},[1398,24540],{"className":24541,"style":1501},[1500],[1398,24543,1423],{"className":24544},[1505],[1398,24546],{"className":24547,"style":1501},[1500],[1398,24549,24551,24555,24595,24598,24601],{"className":24550},[1485],[1398,24552],{"className":24553,"style":24554},[1489],"height:0.7333em;vertical-align:-0.15em;",[1398,24556,24558,24561],{"className":24557},[1494],[1398,24559,3539],{"className":24560},[1494,1495],[1398,24562,24564],{"className":24563},[1595],[1398,24565,24567,24587],{"className":24566},[1599,1600],[1398,24568,24570,24584],{"className":24569},[1604],[1398,24571,24573],{"className":24572,"style":1609},[1608],[1398,24574,24575,24578],{"style":3634},[1398,24576],{"className":24577,"style":1617},[1616],[1398,24579,24581],{"className":24580},[1621,1622,1623,1624],[1398,24582,1455],{"className":24583},[1494,1495,1624],[1398,24585,1632],{"className":24586},[1631],[1398,24588,24590],{"className":24589},[1604],[1398,24591,24593],{"className":24592,"style":1639},[1608],[1398,24594],{},[1398,24596],{"className":24597,"style":1530},[1500],[1398,24599,2121],{"className":24600},[1534],[1398,24602],{"className":24603,"style":1530},[1500],[1398,24605,24607,24610],{"className":24606},[1485],[1398,24608],{"className":24609,"style":24372},[1489],[1398,24611,24613,24616],{"className":24612},[1494],[1398,24614,8005],{"className":24615},[1494,1495],[1398,24617,24619],{"className":24618},[1595],[1398,24620,24622,24642],{"className":24621},[1599,1600],[1398,24623,24625,24639],{"className":24624},[1604],[1398,24626,24628],{"className":24627,"style":1609},[1608],[1398,24629,24630,24633],{"style":3634},[1398,24631],{"className":24632,"style":1617},[1616],[1398,24634,24636],{"className":24635},[1621,1622,1623,1624],[1398,24637,1455],{"className":24638},[1494,1495,1624],[1398,24640,1632],{"className":24641},[1631],[1398,24643,24645],{"className":24644},[1604],[1398,24646,24648],{"className":24647,"style":1639},[1608],[1398,24649],{},"进位关系为：",[1398,24652,24654,24700],{"className":24653},[1401],[1398,24655,24657],{"className":24656},[1405],[1407,24658,24659],{"xmlns":1409},[1411,24660,24661,24697],{},[1414,24662,24663,24675,24677,24683,24685,24691],{},[1449,24664,24665,24667],{},[1417,24666,1432],{},[1414,24668,24669,24671,24673],{},[1417,24670,1455],{},[1421,24672,1435],{},[2883,24674,2885],{},[1421,24676,1423],{},[1449,24678,24679,24681],{},[1417,24680,1931],{},[1417,24682,1455],{},[1421,24684,1435],{},[1449,24686,24687,24689],{},[1417,24688,2114],{},[1417,24690,1455],{},[1449,24692,24693,24695],{},[1417,24694,1432],{},[1417,24696,1455],{},[1474,24698,24699],{"encoding":1476},"C_{i+1}=G_i+P_iC_i",[1398,24701,24703,24767,24822],{"className":24702,"ariaHidden":1462},[1481],[1398,24704,24706,24709,24758,24761,24764],{"className":24705},[1485],[1398,24707],{"className":24708,"style":6713},[1489],[1398,24710,24712,24715],{"className":24711},[1494],[1398,24713,1432],{"className":24714,"style":1526},[1494,1495],[1398,24716,24718],{"className":24717},[1595],[1398,24719,24721,24750],{"className":24720},[1599,1600],[1398,24722,24724,24747],{"className":24723},[1604],[1398,24725,24727],{"className":24726,"style":1609},[1608],[1398,24728,24729,24732],{"style":1612},[1398,24730],{"className":24731,"style":1617},[1616],[1398,24733,24735],{"className":24734},[1621,1622,1623,1624],[1398,24736,24738,24741,24744],{"className":24737},[1494,1624],[1398,24739,1455],{"className":24740},[1494,1495,1624],[1398,24742,1435],{"className":24743},[1534,1624],[1398,24745,2885],{"className":24746},[1494,1624],[1398,24748,1632],{"className":24749},[1631],[1398,24751,24753],{"className":24752},[1604],[1398,24754,24756],{"className":24755,"style":6761},[1608],[1398,24757],{},[1398,24759],{"className":24760,"style":1501},[1500],[1398,24762,1423],{"className":24763},[1505],[1398,24765],{"className":24766,"style":1501},[1500],[1398,24768,24770,24773,24813,24816,24819],{"className":24769},[1485],[1398,24771],{"className":24772,"style":1858},[1489],[1398,24774,24776,24779],{"className":24775},[1494],[1398,24777,1931],{"className":24778},[1494,1495],[1398,24780,24782],{"className":24781},[1595],[1398,24783,24785,24805],{"className":24784},[1599,1600],[1398,24786,24788,24802],{"className":24787},[1604],[1398,24789,24791],{"className":24790,"style":1609},[1608],[1398,24792,24793,24796],{"style":3634},[1398,24794],{"className":24795,"style":1617},[1616],[1398,24797,24799],{"className":24798},[1621,1622,1623,1624],[1398,24800,1455],{"className":24801},[1494,1495,1624],[1398,24803,1632],{"className":24804},[1631],[1398,24806,24808],{"className":24807},[1604],[1398,24809,24811],{"className":24810,"style":1639},[1608],[1398,24812],{},[1398,24814],{"className":24815,"style":1530},[1500],[1398,24817,1435],{"className":24818},[1534],[1398,24820],{"className":24821,"style":1530},[1500],[1398,24823,24825,24828,24868],{"className":24824},[1485],[1398,24826],{"className":24827,"style":1858},[1489],[1398,24829,24831,24834],{"className":24830},[1494],[1398,24832,2114],{"className":24833,"style":2139},[1494,1495],[1398,24835,24837],{"className":24836},[1595],[1398,24838,24840,24860],{"className":24839},[1599,1600],[1398,24841,24843,24857],{"className":24842},[1604],[1398,24844,24846],{"className":24845,"style":1609},[1608],[1398,24847,24848,24851],{"style":4987},[1398,24849],{"className":24850,"style":1617},[1616],[1398,24852,24854],{"className":24853},[1621,1622,1623,1624],[1398,24855,1455],{"className":24856},[1494,1495,1624],[1398,24858,1632],{"className":24859},[1631],[1398,24861,24863],{"className":24862},[1604],[1398,24864,24866],{"className":24865,"style":1639},[1608],[1398,24867],{},[1398,24869,24871,24874],{"className":24870},[1494],[1398,24872,1432],{"className":24873,"style":1526},[1494,1495],[1398,24875,24877],{"className":24876},[1595],[1398,24878,24880,24900],{"className":24879},[1599,1600],[1398,24881,24883,24897],{"className":24882},[1604],[1398,24884,24886],{"className":24885,"style":1609},[1608],[1398,24887,24888,24891],{"style":1612},[1398,24889],{"className":24890,"style":1617},[1616],[1398,24892,24894],{"className":24893},[1621,1622,1623,1624],[1398,24895,1455],{"className":24896},[1494,1495,1624],[1398,24898,1632],{"className":24899},[1631],[1398,24901,24903],{"className":24902},[1604],[1398,24904,24906],{"className":24905,"style":1639},[1608],[1398,24907],{},[1025,24909,22469,24910,24980,24981,25051],{},[1398,24911,24913,24931],{"className":24912},[1401],[1398,24914,24916],{"className":24915},[1405],[1407,24917,24918],{"xmlns":1409},[1411,24919,24920,24928],{},[1414,24921,24922],{},[1449,24923,24924,24926],{},[1417,24925,1931],{},[1417,24927,1455],{},[1474,24929,24930],{"encoding":1476},"G_i",[1398,24932,24934],{"className":24933,"ariaHidden":1462},[1481],[1398,24935,24937,24940],{"className":24936},[1485],[1398,24938],{"className":24939,"style":1858},[1489],[1398,24941,24943,24946],{"className":24942},[1494],[1398,24944,1931],{"className":24945},[1494,1495],[1398,24947,24949],{"className":24948},[1595],[1398,24950,24952,24972],{"className":24951},[1599,1600],[1398,24953,24955,24969],{"className":24954},[1604],[1398,24956,24958],{"className":24957,"style":1609},[1608],[1398,24959,24960,24963],{"style":3634},[1398,24961],{"className":24962,"style":1617},[1616],[1398,24964,24966],{"className":24965},[1621,1622,1623,1624],[1398,24967,1455],{"className":24968},[1494,1495,1624],[1398,24970,1632],{"className":24971},[1631],[1398,24973,24975],{"className":24974},[1604],[1398,24976,24978],{"className":24977,"style":1639},[1608],[1398,24979],{}," 表示 generate，产生进位；",[1398,24982,24984,25002],{"className":24983},[1401],[1398,24985,24987],{"className":24986},[1405],[1407,24988,24989],{"xmlns":1409},[1411,24990,24991,24999],{},[1414,24992,24993],{},[1449,24994,24995,24997],{},[1417,24996,2114],{},[1417,24998,1455],{},[1474,25000,25001],{"encoding":1476},"P_i",[1398,25003,25005],{"className":25004,"ariaHidden":1462},[1481],[1398,25006,25008,25011],{"className":25007},[1485],[1398,25009],{"className":25010,"style":1858},[1489],[1398,25012,25014,25017],{"className":25013},[1494],[1398,25015,2114],{"className":25016,"style":2139},[1494,1495],[1398,25018,25020],{"className":25019},[1595],[1398,25021,25023,25043],{"className":25022},[1599,1600],[1398,25024,25026,25040],{"className":25025},[1604],[1398,25027,25029],{"className":25028,"style":1609},[1608],[1398,25030,25031,25034],{"style":4987},[1398,25032],{"className":25033,"style":1617},[1616],[1398,25035,25037],{"className":25036},[1621,1622,1623,1624],[1398,25038,1455],{"className":25039},[1494,1495,1624],[1398,25041,1632],{"className":25042},[1631],[1398,25044,25046],{"className":25045},[1604],[1398,25047,25049],{"className":25048,"style":1639},[1608],[1398,25050],{}," 表示 propagate，传播进位。",[1025,25053,25054,25057,16959,25085,16959,25088,16959,25116],{},[3237,25055,25056],{},"但是在 ALU 中，对于非加法操作，",[1398,25058,25060,25073],{"className":25059},[1401],[1398,25061,25063],{"className":25062},[1405],[1407,25064,25065],{"xmlns":1409},[1411,25066,25067,25071],{},[1414,25068,25069],{},[1417,25070,2114],{},[1474,25072,2114],{"encoding":1476},[1398,25074,25076],{"className":25075,"ariaHidden":1462},[1481],[1398,25077,25079,25082],{"className":25078},[1485],[1398,25080],{"className":25081,"style":1490},[1489],[1398,25083,2114],{"className":25084,"style":2139},[1494,1495],[3237,25086,25087],{},"和",[1398,25089,25091,25104],{"className":25090},[1401],[1398,25092,25094],{"className":25093},[1405],[1407,25095,25096],{"xmlns":1409},[1411,25097,25098,25102],{},[1414,25099,25100],{},[1417,25101,1931],{},[1474,25103,1931],{"encoding":1476},[1398,25105,25107],{"className":25106,"ariaHidden":1462},[1481],[1398,25108,25110,25113],{"className":25109},[1485],[1398,25111],{"className":25112,"style":1490},[1489],[1398,25114,1931],{"className":25115},[1494,1495],[3237,25117,25118],{},"不一定是真正的 carry-lookahead 中的 propagate 和 generate。它们可能只是由 opcode 控制生成的中间信号。",[1025,25120,25121],{},[994,25122,25123],{},"Carry unit 只负责进位逻辑，Sum unit 负责产生最终 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