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chap10odd - q Fš US U g h I t h X gf I ƒS r g ` C Q g...

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Unformatted text preview: q Fš { US U g h I t h X gf I ƒS r § g ` C Q g ˜ E r X g “ „m‰¢•RFD8¢‚¤žVi8¢‡¤k„vi8iih ‚ q ¤ £o ¥sVsq Ž ³ ‡ ² ~ € ´ˆ4p d¢} „ ~ € o  Pn p (¢} | ‚ q ¤ £o ¥sVsq œ ˜ ‘ ”  ‰ š ”  ‰ ˜ ‘ ”  ‰ – ”  ‰ ‘ ™ ¶ ‘ ”  ‰ ‘” žFF•d›r¢Vd›$FF•d›r¢Vd—rx¤F•d—r’d ~ € }  …o n p (¢u| ‚ ¥q Vo q ¤ £ œ ˜ ‘ ”  ‰ š ˜” žFF•d—rR·d Ž ³ ‡ ~ € „ ‰ q µ“p d¢} ›&Fš Ž  † ‹ ~ € „ ‰ q ¦$…p d¢} 6&Fš ‚ q ¤ £o ¥sVsq Ž ³ ‡ ² € ~ ´ˆ4p } „ ‚ q ¤ £o ¥sVsq œ £ ”  ‰ š”  ‰ ˜ ”  ‰ ¶ ”  ‰ ‘ ™ š ”  ‰ ‘” R¢u•d›r’d›$u•d›r¢Vd—rxldF•d—r’d ‚ q ¤ £o ¥sVsq œ £ ”  R¢u•d—‰ ‘ ·d ˜” q Fš Ž ³ ‡ € ~ „ ‰ q µ“p } ›&Fš Ž  † ‹ € ~ „ ‰ q ¦$…p } 6&Fš ~ € o  Pn p (¢} | € ~ o  Pn p ™} | € ~ o  Pn p ™} | € ~ o  Pn p ™} | {„¤Ijt¢iXV¤Whi¤CDVSWhRPGDVSiW!`¤gy¢Vf¢utxXF‚WRFRP¤Wieii™„V¢iiP•uFBi¤k…¤r¤C p fufuVS U g S I ˜ U “ I U “ h C I g CS h I t I G C Q G g “ h ˆ ¤ £o q h r G h r C t X I qo p Q o n h r G X gu“WhsUWh—d¢guXiXFC—dzWRIPG‰u“ihw(šy€ ±e© iX¤všy€ ¬‰¨ ci(šy€ ±e© °b{„¢•RFD¤i™Vi„T‚„ViWs¤¯YWRPi¤„mW‚T—‰iih “ h g ˆ t I U g h I t ‘ U I “ hS r d QS d US “ h Q C` “ h I G f I dS hS Q d g “ q † C C ˜ h – g h g “ h ` C q i¤8•d—•euW‡¤D¡˜ p ’d„‰u‚‡a p c Ÿ uVWik¡˜ p ‘ˆ  ˆ tS t XS U r q ¡ ¢ š ‚ š ™ «©§u ‘ ‚ ™ e®‘  ‚ š ™ „­F§– ‘ ‚ ™ «vª‘ U g h I t h X gf I ƒS r § ¢•RFD8¢‚¤R‚i(¢g f I h C ¤W¤…h ‘ – ‘ U g h I t ` C Q g ˜ E r ¢•RF!¤k„li(X ¬ ‘ € $¨ c ¨ š ¬ y€ $¨ c ¨ ‘ ¬ y€ $¨ c ¨ h e¨ © g G yh g h I 8yl•RFt { US U g h I t h X gf I ƒS r § g ` C Q g ˜ E r X g “ „m‰¢•RFD8¢‚¤žVi8¢‡¤k„vi8iih ‚ ¥q Vo q ¤ £ Ž  † ‹ † € ~ } Œ$…p …„ ‚ q ¤ £o ¥sVsq œ ¡ ‘ ”  ‰ ˜ ”  ‰ ˜ š ”  ‰ ¡ ” R¤F•d›r2•d›‰FF•d6$F•d ‚ q ¤ £o ¥sVsq œ ¡ ‘ ”  ‰ ¡ ” R¤F•d6$¢Vd q F‘ Ž  † ‹ † ~ € }„ ‰ q ¦$…p (¢…6&Fš ~ € o  sq p d¢} | ~ € o  sq p d¢} | ~ € }  …o q p d¢d| € ~ o  sq p } | € ~ o  sq p } | ‚ q ¤ £o ¥sVsq Ž  † ‹ † ~ € Œ$…p d¢} „ € ~ }  …o q p d| ‚ ¥q Vo q ¤ £ œ £ ‘ ”  ‰ £ ”  ‰ ¡ ‘ ”  ‰ – ” R¤F•d›‰F•d›$¤F•d6$F•d ‚ q ¤ £o ¥sVsq œ £ ‘ ”  ‰ ¡ ” R¤F•d6$¢Vd q F‘ Ž  † ‹ † € ~ „ ‰ q ¦$…p ™} 6&Fš { y If g t g U I d h U Q C x I U I “ “ h I G US “ h ˆ U Q g t t I gf G GS Q y Q Q I d Q C ¡¢V¢il•¤„r•¢¤Hr¤ijWRPDVPiw„T„uP¤$‚fi‚TzWWR„r¤4` h X I h Q C G ES C Uf I US h r G h r C y Q Q I d g “ h C h h r G XS y Q Q I d g “ h t XS h d g X X C d “ h I G g “ h ` C y If g t g “ h Q g ƒ g x 2¤WT¤¡Vv•m¤wV™uf•uFHWWR„riWv•‡uPiVHWWR„‰iWluVW—¢iiF—©WRP‰uW¤H¢V¢iruWu¢„¤„sC Ÿ ‚ qo ƒ“¢u Ž  † ‹ † € ~ „ ‰ q Œ‰Œ…p } 6Š”| ˆ…p (¢} „ ‡ † ~ € ‚ qo ƒ“¢u œ ˜ ‘ ”  ‰  ”  ‰ ™ £ ‘ ”  ‰ £ ”  ‰ š ™ ¡ ‘ ”  ‰ š ” žFF•d—$„Vd›™’©¤F•d›‰F•d—rx¤F•d—‰F•d ‚ qo ƒ“¢u œ ˜ ‘ ”  ‰ – š ‘” žFF•d›”¤¤’d q ’Œ$…p (¢} 6&F‘ ‘ Ž  † ‹ † ~ € „ ‰ q ~ € o  fn p d¢} | ~ € o  fn p d¢} | ~ € o  fn p d¢} | ‚ ƒq o u Ž  † ‹ † ~ € }„ ‰ q Œ‰Œ…p d¢…6Š”| ˆ…p ™…„ ‡ † € ~ } € ~ o  fn p } | ‚ qo ƒ“¢u œ – ”  ‰ š ”  ‰ ™ ¡ ‘ ”  ‰ ˜ ”  ‰ š ™ ˜ ”  ‰ – ” „dF•d—‰¢Vd›™’©¤F•d›r2•d—rxHu•d—‰F•d € ~ }  &o n p u| ‚ ƒq o u œ – ”  ‰ š ‘” „dF•d›”¢d’d q ’Œ$…p ™…6&F‘ ‘ Ž  † ‹ † € ~ }„ ‰ q € ~ }  &o n p u| { U I t g XS I h ˜ C US “ h I ¢¤B¢uV¤Wi¤kmjWRPG [email protected]r¤!¤i¤C p PsuPumluWkW—¢uPF—jWRPeuis„¢•RFw‘ S “ ` y f g CS I I C Q g h o h G r t X I qo q Q C o p Q o n h r G XS g “ h U h d g X X C d “ h I G g “ h ˆ U g h I t U “ h r QS g h C “ I f I d hS d “ q C ˜ ¤Iis‚Si„dTV„d”i“WsQ¤4`gWhRPGf¤„VSW‚TQ—eguWh™i†¤8C•hd–—•”uW…¤s2I p ’d„‰u‚‡a p W¤s„u…¢¤„‚RywvuVTis2I p g h g “ h ` C q ‘ˆ  ˆ tS † Q C xh g X f g ƒ gf€ C x h I t XS U r q U X CS h I h X g E gf G ES c a ` C X C US Q I G E C A 59 7 5 % 31 ) ' % # iFVWRW2¢H¢VPHVedb¤YFWVTRPHFDB@&86¢420(&$" !©§¥      ¨ ¦ £ ¡ ¤¢ ˆ q ¢2I p •¤„x¤iWzWWR„iWr¤4YV¢ut g U I d X I “ h y Q Q I d g “ h Q C` y If g X CS h I t I G C Q G U U gf U I “ C Uf I hÝ ˆ U g h I t ` C Q g ˜ E r X h U I gf g “ h “ hS x g X C g “ h US X CS h I h X g E gf G ES h U If US “ F‚WRFRf¤WieW¢V¤ij•V¤vyz„¢•RFs¤e„¡vi(l•¤¢‚YuWˆW‚riFHuWeVÈF‚WRW8¢H¢‚fHV•¤Vemiih £ ‘ ‚ ™ e®‘ ¶ ‚ ‘ ™ «©§š U g h I t h X gf I ƒS r § ¢•RFD8¢‚¤R‚i(¢g f I h C ¤W¤…h ‘ š U g h I t ` C Q g ˜ E r ¢•RF!¤k„li(X š ¬ y€ $¨ c š ± y€ ”© ° g G yh g h I 8yl•RFt { US U g h I t h X gf I ƒS r § g ` C Q g ˜ E r X g “ „m‰¢•RFD8¢‚¤žVi8¢‡¤k„vi8iih ‚ q ¤ £o ¥sVsq Ž  † ‹ † ~ € Œ$…p d¢} „ € ~ o  sq p } | ‚ q ¤ £o ¥sVsq œ ˜ š ”  ‰ ¡ ”  ‰ ¡ ‘ ”  ‰ – ” žFF•d›‰F•d›$¤F•d6$F•d € ~ }  …o q p d| ‚ ¥q Vo q ¤ £ œ ˜ š ”  ‰ ˜ ” žFF•d6‰Vd q Fš Ž  † ‹ † € ~ „ ‰ q ¦$…p ™} 6&Fš ‚ q ¤ £o ¥sVsq Ž  † ‹ † € ~ Œ$…p } „ ‚ q ¤ £o ¥sVsq œ ™ ¡ ‘ ”  ‰ – ”  ‰ ˜ š ”  ‰ ¡ ” x©¤F•d›‰F•d›‰FF•d6$F•d ‚ q ¤ £o ¥sVsq œ ¡ ‘ ”  ‰ ¶ ” R¤F•d6$¢Vd q Fš Ž  † ‹ † ~ € „ ‰ q ¦$…p (¢} 6&Fš € ~ o  sq p } | ~ € o  sq p d¢} | ~ € o  sq p d¢} | ~ € o  sq p d¢} | { US y If g t X CS h I t I G C Q G h r G h r C y Q Q I d g “ „Vg¢V¢ixF‚WRFRP¤TikuP•uFzWWR„iih ‚ qo ¥u Ž ³ ‡ ² ~ € ®eˆ4p (¢} „ ‚ qo ¥u q œ š ”  ‰ ‘”  ‰ ” š ™ ¶ ‘ ”  ‰ ‘”  Ü œ  š ”  ‰ – ”  ‰ ‘ ™ ¶ ‘ ”  ‰ ‘” s„dF•d›‰’d›V(xY¤F•d6e’dWi¤RF•d›$¢Vd›ixY¤F•d›r’d p 8jÚ n Û ‚ qo ¥u q œ š ”  ‰ ¶ – ˜ ¶”  Ü œ š ”  ‰ ¡ – –” D„dF•d›¤RF’dWiRF•d—‰¤¤’d p 8jÚ n Û ‚ qo ¥u œ š ”  ‰ ¡ ¶” „dF•d—‰¤’d q Fš Ž ³ ‡ ² € ~ „ ‰ q ´ˆ4p } 6&Fš ‚ qo ¥u Ž ³ ‡ ² ~ € ®eˆ4p (¢} „ ‚ ¥q o u q œ ¶ ‘ ”  ‰ ‘”  ‰ ” š ™ ¶ ‘ ”  ‰ ‘”  Ü œ ¶ ‘ ”  ‰ ¶ ”  ‰ ‘ ™ ¶ ‘ ”  ‰ ‘” sR¤F•d›‰’d›V(xY¤F•d6e’dWiR¤F•d›$¢Vd›ixY¤F•d›r’d p 8jÚ n Û ‚ qo ¥u q œ ¶ ‘ ”  ‰ ¶ – ˜ ¶”  Ü œ ¶ ‘ ”  ‰ ¡ ¶ –” DR¤F•d›¤RF’dWiR¤F•d—‰¤¤’d p 8jÚ n Û ‚ qo ¥u œ ¶ ‘ ”  ‰ ¡ ¶” R¤F•d—‰¤’d q Fš Ž ³ ‡ ² ~ € „ ‰ q ´ˆ4p d¢} 6&Fš € ~ o  Pn p } | € ~ o  Pn p } | € ~ o  Pn p } | € ~ o  Pn p } | ~ € o  Pn p d¢} | ~ € o  Pn p d¢} | ~ € }  …o n p d¢u| ~ € o  Pn p d¢} | { U I t g XS I h ˜ C US “ h I G US “ h ` C y If g t X CS h I t I G C Q G g “ „¤x¢uV¤Wi¤kmjWRPDViW!¤g¢V¢ijF‚WRFRP¤WPeuih ˆ g Q g tS X C d g h U r Št¢W„umWUiF—”¡˜s•iwEk¢•U¤„sdu(™Š¢—iP¢W™m•RFt ”© ziF—¢•”uW…¤©¢V¢ueuWu¤•RFt ”© ziF—¢•U U g I d C xh C Ù ˆ t g d r t g Q US g h I ° t X C d g U g “ h ` C y If g t g “ h g h I ° t X C d g ± ± g “ ` C Q h d I` t Cf Q “ t “ uWh‰¤¤C•—¤46¤IF‚H„guFVSi֓WVrlufuVBuWȕ—¢•—¢uPF—wmj•RFt ”© w•TPzuW6¢ur­RiWg¤W„WP˜ © hS x h r G XS g “ h C h t g h d g X X C d US g h I ° h U Q Ø g “ h X g “ x h I “ h g ƒ Q g U ± ˆ o u v¢whuP•uFC×i¤@o¤­¤C p PnurfGuVYiWvW—¢iiF—ÖWRf©uiˆ„¢•RFt ”© xzuWÖFuFWiWVlVi„T‚„vViWh r G h r t X I q p Q o h XS g “ h U h d g X X C d “ h I G g “ h ˆ U g h I ° š g “ h “ t r C Q “ h US hS r d QS d US “ ± Q¤4—WhRPD¤„VSWVT—xguWk „¢•RIFt ±”© —¤PWH(V¢u§F‚WRFRP¤WiH„VV¤Wx¤iz¢•RFt ‰¨ c ¨ uW$c C` “ I G f I d hS Q d “ h U g h ° X I “ h U y If g t X CS h I t I G C Q G Q gff I E U g ƒ I “ U g h I g “ h U ¬ q † C C ˜ h – g h g “ h ` C q ‘ˆ  ˆ tS i¤8•d—•euW‡¤kd p ’d„ruV!a p ¢•RFt $¨ c ¨ i¤I ”© wuVWiid p U g h I t X ° t XS U r q ¬ ± š ¢ š ‚ š ™ eFÕu ‚ š ™ ‘ FÕš ¶ ‚ ‘ ™ «©§š U g h I t h X gf I ƒS r § ¢•RFD8¢‚¤R‚i(¢g f I h C ¤W¤…h š š U g h I t ` C Q g ˜ E r ¢•RF!¤k„li(X š ± y€ ”© š ¬ y€ $¨ c š ± y€ ”© ° g G yh g h I 8yl•RFt Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected]  £ R¢ ‘ˆ  g US d Q g – à € Q g h Q g ƒ X C d ‘ € U U g d – à C ’d„•m„T„(w‰„•W„¤2F—yvW¢—ub©•h A ß { ˆ  g Q r tS ¬ iDRVd„HWuF‚‡a Excess-3 Code not used cout Binary Adder cin 0 0011 BCD code ˆ ˆ  g Q r tS a XS X x C “ U US Q g t t I y Q I XS ˜ hS ˜ RVd„”WuFV!wV­r0uW!Vb„ui¤WRimPVP“€ ‘ umWi™„•W„¤8F—$yvW¢—ub•h t XS U r Q g h Q g ƒ X C d ‘€ U U g d – à C £ d¢ A ß g “ h Þ9 7 5 % 31 ) ' % # 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PP@&86¢420(&$" Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] q ˜ h Q I ¡iWRPG p ‘ ˆ  g US d Q g – à € Q g t t I h X g E gf G E C d Ua g ¢Vd„•V„T„dbsk„ui¤i8¢H¢‚PF—i•£uX © ¤4kim¤iTgWWR„b¤e‚P¤dw(’d„WuFV!a Q C ` U XS I “ d y Q Q I d ` C gf G E I – à { šˆ  g Q r tS carry chain no active loop carry bit spureous carry! 0 c 011001010 100110101 0 111101111 carry chain active loop 1 = cin 011001010 100110101 + 1 111111110 011011010 100110101 ppppgpppp Some position with 00 or 11 cout All positions with 01 or 10 ˆ U g U I d “ h C ˜ ` C U gf G E I – g U x C “ U šˆ  g Q r tS „¢•¤„jW¤!¤k¢‚PH¤u—kr0uW©’d„WuF‚‡a ” ˆ G C Cf g ƒS h d I &¤(‚v¤VW—¤©C ¨ &F‚WRiVPvF—kViWz(B¢¤¤WikmS ˆ X CS h I XS ˜ E C d US “ h y ˜ X g † C Q ˜ U XS I “ d y Q Q I d g “ h g U I d h I “ h X Ý ˆ X CS hS U C G hS ˜ Q If r dS h Q I G g X C Q C` Q C   X CS h I XS ˜ E C d I US g Q g “ V¤PTjWWR„HuW­•¤„”RiWÄ‰ŠF‚W‚TF¡‰‚P‰RVi„VWWRfvuF”¤4l¤H¤z¤ŒF‚WRiVPvF—g‰mwW„iWh ” ˆ U h Q I h U X CS h I Q g G C g “ h g Q C` g „WWRW•jFVWRT„¤uWeW¤4„˜ CW„„–•r„•¢T©•w¤¢i‰¢‚TWR„&m¤r‚iW¢T‚PRW•Yw¤iYD&¤8Vw¤‚W—¤¤rVwW„uW¡¤•¤„‰RPWh Q g • C h h g U g Q g ˜ C h g ƒ I “ U gS Q Q I d ff I hf r U g Q gf ˜ I h U I g ƒ I “ C h ˆ G C Cf g ƒS h d I X I US g Q g “ h g U I d h I “ X Ý ˆ  X CS h I XS ˜ E C d g “ h g ƒ I “ U X CS hS U C G hS ˜ ff I U X I g E h I “ h Q C   X CS h I XS ˜ E C d C X US g Q g “ veRuŒFVWRiVPvF—wiWw¤i$iF‚W‚WF‰‚PV¤Š„i¤¢HeRiWŠR¤H¤z¤FVWRiVPvF—zi‰VHW„iWh { U g U I d t XS x Cff C` g “ h Q g tS U X C d g x f I X CS h I XS ˜ E C d U „¢•¤„Humr‚mF¯euWk„iVWiF—lsŠ¤iFVWRiVPvF—kVS XS€ y Q Q I d g “ h C h t g h d g X X C d h r G h r C y Q Q I d g “ h “ hS x Q g t t I g “ h ` C X CS h I Q g G C g “ h h I “ h y`S Q g ƒ C h q V8WWR„HuWg•ˆ¢•—¢uiF—”uP•iFjWWR„HuWW‚r”„ui¤­uW¤xF‚WR¢„¡¤­uW”RiWx¯‚¢„¤Y‰¡˜ p ˆ E g h U y U h X g E gf G E C d Ua g X C g “ h XS  ` C X CS h I h X g U g Q G g Q Q g “ h C X I US US “ h g d XS U h d g Q Q C d U j¢••(Wr2¢¢‚PHF—‰•£uFeuWgVb¤BFVWRW2¢•¢Ti„Wr„iW¤u¤kVkViWe—PVW‰—¢TW¤—kVS “ dS “ x q Ü ” ” ” Ü Ü Tmir¡¢¢ž„„„R¢R p ¤•—¢¤iViW¢W©i¢—iidWiiFš p W¤„‰RiWw•¤C ¨ RjiVii¤Œi¤kq YuVW—¤¢•iuWU p ks Q C h d g ƒ hf r U g Q I U g d r t C Q G q g U I d h I “ h g h ˆ t XS t t I t X I š t XS h d I Q h ˜ r è è t XS t Q I d US t t g XS I h ˜ C US hf r U g Q g “ h ‚ è s `S t X I g s C h f I r § g US hf r U g Q g “ h  ‚ è s `S yf h X g r § g U X C uViTR„TVij¢um¤Wi¤iViViW¢WiWHk$‚jP¤f™u“•&¤P8¢kmi‚iW¢WvuWPd®©kVP¤‚W8¢u8¢WiFsA ‚ è s t X I eHk‡i¤ ‰ è š Ž g s ‚ uˆªç Ž uˆªY(xu‡¢iWeç g s ‚ ç t C E g s X g “h ‰ g s ‰ ç š `Ý ˆ ’u‘FbÄi(‘  ‚ è s t X I  ‚ ç t C E g s X g “ µ­k‡P¤µ®YdHu‡¢uWh  ‚ è s t X I g s ‚ ç t C E g s X g “ µHk‡i¤Öuˆ®YdHu‡¢uWh ç ‚ g s ` Ý ˆ ®ŒuÄi(š ‚ g s `Ý ˆ †uÄiR ç { U g U I d ‘ t XS x Cff C „¢•¤„HuV‰‚VF4` g “ h Q g tS U X C d h U r E g F ˆ ç š ‚ g s ç ‚ g p Ü g n g d XS Ù ˆ g p t X uW„iVWiF—•Pvzȅ­Fƒu„­ƒC•™hH—iVuYwCˆi¤I wˆW‚rˆ¢HT¤4W„ŒF‚W‚iP¤”VP˜ Ž  g n “ hS x t g E Q C` Q g G X CS hS t t I hS g “ h ` C hS ˜ h r C y Q Q I d g “ h U uWb¤k‚fiuFBWWR„vuWkVS g €¤k‚Pk8¤„fËPF‚W‰WFHluiD¢q ô "Ü ¤ "„„„Ü ŠDè "Ü è 0e‚ g x¤•—¢¤uWh s ` C hS ˜ h X I d ØS X tS U h U C E g “ h ˆ s sÜ ” ” ” ¤ y s s å s Q Ch d g ƒ g “ y ˜ t g h X g U g Q G g Q X CS hS t t I g “ h ` C hf r U g Q g “ h US g p ‰ g 8B¢•8¢•¢WP„WdŠF‚W‚iP¤luW‡¤D‚iW¢WluWkV×C6zwn ÈuvW„uruH©(xutrqV¤Wi¤Y•i2¤Dx ‚ g s g Q g “ x ç t C E g s ‚ g p XS I h ˜ C C h h X I g F ˆ ÈiR Ž ä©W„u‰&­©dH­p ‚ Cˆi¤I Y(Y«‚ hx(È¢•8¢•¢Wi„Txˆi¤6‰¢„¡vi(xsh š ‚ ç g Q g “ x ç t C E g p t X ç t C E n g n y ˜ t gh X gU gQ G g Q p t X I n U Q g ˜ E r X C x è Q g tS U X C d U r h gf U G g h U C x h y ˜ t g E Q C ` Q g G g ˜ X I d h X g E gf G E C d Ua g X C XS X CS hS t t I g “ h h I “ h x C “ U C h q „uVTiF—bib„‚bP„••vyv(l¢T¤¯T„¡DH¤„w8¢H¢‚PF—b•£uF­VwF‚W‚ii¤iiWbRiW—uT•!2I p I Þ 59 7 5 % 31 ) ' % # f8@&86¢420(&$" Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] ¶ £ ¤¢ ˆ h US – g h C X U g C t h I “ h X CS hS t X C d x C e Q g ƒ C X I t XS h d g h g t  „•Vu—k¤ui¢(urRPWgF‚W‚iiF—ef"„¤B¤YuVW—¢•„uPd´‚ ŠCè q ¤ y t X I ‚ è q g h I Q g X g t ffS x g t I h U h U Q Ø g “ h q y Q Q I d€ t X r C Q I€ t X g C i¤eesl•RT„u¢¤fVV‰¤RW•k•TP$uWu¢iWWR„uiiFWRdP¢HuX p ¢¤RW•©sgmz¢T¤¯T„¡sVgF‚WVii¤I U g t I h U C xh XS t g E Q C` Q g G US X CS hS t t g “ h ` Ý ˆ q   ” ” ”   uWwÄ¢2¤—„„D¤„ t X I q ” ” ” U Q C h d g ƒ g “ h ` C X CS hS t t I g “ h C h U t X C G U g Q Q C d “ dS “ x q p i¤$¤ž„„‡¤¤ p T¤•—¢¤­uWw¤F‚W‚ii¤­uWB•‰iiF•¢WT¤—¢VirŠ¢ª‰ ŠDè š Äp Ž ¤ y ‰ q Ž t XS t t I ` C g U I d g “ h XS yf Q g G C Q G † Q C x a X U g C t h U g h g “ 2 Äp uVPi¤™¤w•¤„wiWjVg‚T„¤WiBT¤‰h fW¢(ue•¢•luWh ¢••d•$2¢H¢VPHF—”•£uFwuW”¤ua E g h U y U h X g E gf G E C d Ua g X C g “ h Q C ˆ ‚ ¤ y è q f è q X g “ x U g U I d g “ h C h t g h If g Q g Q I U g U I d x C e Q g ƒ C g “ h h I “ h g g U X I d g X C gf ˜ I h g “ h E C Q ReŠDs’usg¢urD¢•¤„euWH•z¢•RV¢W”WRr¢•¤„ªf"„¤”uWDRiW”„•B¤„euF”‚PRW”uWäFTua C ¨ U g ¢wd C ¨ C ¨ C ¨ C ¨ U g ¢wd C ¨ ` 8ƒ ©     ¤ y è ŠDsq     è sq     ¤ y è ŠCp     ¤ y ŠDè ó     ¤ y è ŠC8Û {‚ˆ ó i¤gkii¤T„¤k8¢H¢‚PHF—$•bsD‚P“db¤gF‚WVii¤uWwuVTiiP„ŠC™‚PäiTluWBi¤iŠDè ó i¤I t X I Û U t X I Q g G C h X g E gf G E C d Ua C x h hS ˜ € X ` C X CS hS t t I g “ h t XS Q r t ¤ y è p hS ˜ E r U g “ h t X I ¤ y t X ¤ y è Û U t X I Q g G C g “ h ` C U hS ˜ h X I d ØS X tS U h U C E g “ h Q C` gf ˜ I h t XS x Cff C` g “ h Q g tS U X C A I — 59 7 5 % 31 ) ' % # ŠC8bii¤¢„¡¤ruWf¤‡WVP‡2¤„f‚iF‚W™WFHiuWw¤4k‚PRW”uV‰‚VF4kuW‡„uVTiFsiw˜@&8Œ¢420(&$" ˜ £ F¢ Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] c Q C ¬ $¨ c žj”¬ r¤4` ¨ i ¬ H c hS ˜ { ‘ˆ  g Q r tS E hi‚P“€ ‘ (’d„WuF‚‡a zi cout Mux ADD/NAND x3 y3 1 0 x2 y2 x1 y1 x0 y0 M cin xi yi M M M z3 z2 z1 z0 cout f=ADD/NAND cin M ˆ h r G h r C hS r d QS d U I t g h d gf g U US g h I „uf•uFD‚i„T‚„r¤x¢•—¢‚¢•rVv•RFt $¨ c ¨ ¬ guW”¤P„ui¤viWw¤ruf•uFluWP¢„(—VP‚W‚iw©¤l•iwuWjsiŠ¢•8¢H¢‚PV‰¤D$„ui¤‚PP‚T“8WWR„d “ h Q C Q g t t I g “ h ` C h r G h r C g “ h Q g – gf GS hf r E I ` C g U r g “ h y ß ˆ t g h X g E gf G ES U I x Q g t t I gf G GS Q€ y Q Q I c ˆ ‘ˆ  g Q r tS a XS X x C “ U US U X CS h I Q g G ×(’d„ŒTuF‚‡ÖmÖr0uWwV­iF‚WRT„¤C ‰¨ c ¨ P¤I ”¬ ­¤4` E g­‚P“€ ‘ ŒRi…&8ñ¢420(&$" t X c Q C H c hS ˜ c I á 59 7 5 % 31 ) ' % # ¬ ¬ Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] ¡ £ ¤¢ | | | | |  „ u  „ |  „ u u |  „ u  ¤ ç ¤ ô | o‡ ¢!| i‡ ç m m ¤¤¤  „¤¤  u„¤   ¤„¤  ¤u„   „u„   u¤„    ¤¤„ ¤¤u  „¤u  u„u   ¤„u  ¤u¤   „u¤   u¤¤    ¤¤¤ l ç l ç o ô † v¢¤ † v“o ó 8Û { gf ˜ I h X CS h d X r` t X ¤‚PRWgFVW—ii…HuVS € “ d hS x U t XS x Cff C` g “ h U I “ h I “ h hS r d QS d f I X CS h I XS ˜ E C d I U I g X C t US gf r t C E “ d I g ` C X CS h I h X g E gf G ES g “ d¢W‚r•”uVr0‚VF4kuWb¤iwRPW!Vi„T‚„u¤iFVWRiVPvF—ew¤iuFubms‚Pi(©T¤¢¡¤­F‚WRW8¢H¢‚PViuWh  „ u  ¤ g t C udsA à h c ± ib™à ± n à H H c z ± …GhŒ{Ù H hc E dà y X CS hS t X C F‚W‚iPFsA { t XS t C d X g t XS x Cff C` g “ h t XS Q g tS U X C uumi(—P¢wiVrVVF¯eiWvumT„uVWPFsA £ ˆ  g US d Q g – à € U Q g ˜ E r X C xh g Q I G E C d C h † Q C xh g X g ƒS h I Q g h Ý ¢Vd„•V„T„dbssT„li(©sTRPHF—©•BW¤s„il¤‚WRT„•Ä™{ ‘ d„WiF‚‡a ˆ  g Q r tS carry-in carry-in Iterative Bit Comparator b 1 a 0 COMPARATOR OUTPUT b 0 ˆ qff g d h U C E h` gf g “ h C h t gSf G G ¢¯m¢—i•FHW4„‚luW•z¢‚mPiRI p q lu ™œ ‹ €w œ x ³ q lu | lv³ t ³ ‹ u l Q C q † vç p ¤ssœ $iou ‹ m v l Q C q † vç p ¤ssœ $iou ‹ m v ‚ ‚ œ ”oou ‹ m v l ç t X I † vŒi¤Dq o ó l ç t X I q † vŒi¤D“o ó ‚ ‚ o ó ‚ ‚ o Û •p ‚S p ` ‰o8Û •p ‚S p ` ‚ o Û ` Š8‡‚S carry-in a 1 carry-out Iterative Bit Comparator b n-1 carry-out Iterative Bit Comparator carry-out 0 0 a n-1 l ç X CS hS t X C d f IS hS XS g “ h “ hS † vxF‚W‚PiF—f¤mW‚iVliWgW‚rx x ³ vu œœ ‹ $w ³lu | ‹vv³ t u l † vç qs pq r ‚ µ| o‡ ç m { US ff g d g “ h ` C X CS h GS Q d U g t f g ƒ gf€ “ tS “ g “ h ˆff g d h U If g “ h ` C h r C€ y Q Q I d g “ ¢V&V¢—uW‡¤zF‚WiVT—W¢uŠ¢¤„‚uF‚iuiw“V¢—i•¤VliW¤iiF“2WTR„luWh E C Q` t g XS I h ˜ C US h r G h r C Q C h I Q I G E C d g “ h ˆ Q gff I E Ù t X I Q g h I g Q n f I r § à { U g rf I ƒ g g Q “ h g ƒ I “ U gS Q Q I FW4Œ¢uV¤Wi¤$V”uP•iF¤•RTRPHF—­uie¢„VV¤d’i¤…[email protected](™$„¢uV¤R­„WuWH¤¢P$¢VTWR„d g•¢ur©¢”| i‡ ç p uF“2TWR„©uFÈP¤!¢q † jç p V2TWR„YuF[email protected] ó i¤k2Û p iP¤T„¤uWD¤×¢¤¢D¤e‚P˜ U g “ h ˆ q h r C€ y Q Q I d g X C t X I l XS€ y Q Q I d g X C q t X I o U t X I Q g G C g “ h ` C “ d I g ` C hS m g X C U I “ ff g d “ d I à ˆ t g X tS U g t g ˜ C h g Q r h d r Q h U g ƒS h I Q g hS g “ h U x C “ uF”¤ibm¢—’T¤lŠ¢uF‚T¢uwB•­WuW—PT••¤‚WRT„•V­iW”ruTU ‘ d„BWuF‚‡­fD@&85 ¢420(&$" ˆ  g Q r tS a I k 59 7 % 31 ) ' % # £ £ ¤¢ Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] ˆ U † Q C xh g X g h I t y ˜ t g h X g E gf G ES yfS U I g g Q I U X CS U U g Q G – g g U g “ ¢(W¤s„iv•RFg8z¢•8¢H¢‚PVzVVW¤¢WRkPF‚WW¢WP(—e•¢iih B ¤ † [email protected] ó ‰ ô † vç l ç l B ô † jç o ›‰ ¤ † vç l Û l ¤ | o‡ ç m ‚ ô | o‡ ç m ‚ {„UiXFC‚SWUTU¢gWQiGd–—ggu“Whih„g¤tsx ô | o‡ i¤i| o‡ ˆ¢¤¢i¤¯iPR”jFx¢•¤Dß g ç t X I ¤ ç “ d I g Q C` U G I E€ ò X C t g U I m m ˆ X CS hS t X C d g Q I d a X C t I US g t C d g “ h h I “ h g ƒ Q g U ŠF‚W‚PiF—lWR„ih fFikV¤©i(—liWiRiWe¤W„•f˜ © Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected]   ¤Rš ˆ –ˆ  g Q r tS (’d„WuF‚‡a XS X x C “ U US Q gSf GS hf r E y I Q Q I g “ h XS gf r t C E “ d I g ` C U h r G h r C g “ h ` C U g rf I ƒ g “ h I Þ }9 7 5 % 31 ) ' % # VBr0uWkVD„‚Vf‚W‚iwB¢TWRiWgV$ViidH¢¤¢¤iWuP•uFeuW!¤k¢um¤ž”ui‰fi~&86¢420(&$"  uRš Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] š  FRš x_bit y_bit x7 =1 x 2=0 x 3=0 x 4 =1 x5 =1 x 6 =0 y_bit x 0=1 x 1=1 c_out c_out Half Adder 1 Half Adder 0 1 0 c_in y0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 OR ‘ šˆ  g US d Q g – à { –ˆ  g Q r tS ¤’d„•V„T„dbs(’d„WuF‚‡a sum_out sum_out 1 x_bit y_bit sum_in MF 1 Full Adder sum_out MF 0 Module MF 1 1 0 0 1 MF 1 1 0 1 1 MF 0 MF MF 1 0 MF 1 1 0 0 MF 0 p 11 p10 1 1 0 MF 0 MF 0 1 p9 1 1 0 MF 1 p8 0 1 1 0 1 0 MF 1 0 1 0 1 1 1 MF 1 1 0 1 MF 0 1 1 1 MF 0 1 0 0 1 0 1 MF 0 1 0 MF 0 1 0 1 0 0 0 MH 1 y 2 =0 MH 0 1 y 3 =1 MH 1 y 4 =1 MH 1 y5 =1 MH 1 (b) 1 1 0 0 MF 1 0 1 0 p6 p7 0 1 1 MF 1 0 0 MF 0 1 1 MF 1 0 1 MF 0 0 MF 1 MF 0 MF 1 0 0 0 0 0 1 MF 0 MF 0 1 0 0 1 1 0 0 MF 1 MF 0 1 1 p 12 1 MF MF 0 MF 1 1 1 1 0 0 1 1 MF 1 1 0 MF 0 0 1 0 p13 0 1 c_in 0 0 0 0 (a) 0 c_out MH 0 Module MH p5 p4 p3 p2 p1 p0 y1 =0 =1 Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] x_bit sum_in a2 šˆ  g US d Q g – à € Q gSf GS hf r E hS ˜ ™ ¡ { ¶ˆ  g Q r tS ‘ ’d„WV„T„db„‚VPVW‚iwi‚P“€ ‘ D(’d„WuF‚‡a a3 cout a0 s2 s1 s0 z11 a1 s3 z10 4-bit Binary adder b3 b2 z9 z8 b0 cin a3 cout a2 a1 a0 s3 b1 s2 s1 s0 z7 z6 4-bit Binary adder b3 b2 z5 b1 z4 b0 cin z3 z2 z1 z0 0 x3 y7 y6 a2 y5 y4 a1 a0 s3 a3 cout s2 y3 s1 s0 4-bit Binary adder b3 b2 b1 b0 cin y2 a2 y1 y0 a1 a0 s3 a3 cout s2 s1 s0 4-bit Binary adder b3 b2 b1 b0 cin 0 x2 y7 y6 a2 y5 y4 a1 a0 s3 a3 cout s2 y3 s1 b3 y2 s0 4-bit Binary adder b2 b0 cin a3 cout a2 y1 y0 a1 a0 s3 b1 s2 s1 s0 4-bit Binary adder b3 b2 b1 b0 cin 0 0 x1 y7 y6 y5 y4 y3 y2 y1 y0 x0 y7 y6 y5 y4 y3 y2 y1 y0 ˆ ¶ˆ  g Q r tS a XS X x C “ U US Q gSf GS hf r E hS ˜ (’d„WuFV!BmBruTiVD„‚VP‚WViviVP“€ ‘ vuW!¤gF‚WRW8¢H¢‚PVuiˆb~&86¢420(&$" ™ ¡ g “ h ` C X CS h I h X g E gf G ES g “ h  }9 7 5 % 31 ) ' % # ‘  FRš Ô Ó Ó Ð Ò Ñ Ð Å Ì Ï Î Ì ¼ Í Ì ¸  ¾ ʽ ¿ Ì É º Á¼ ½ ʽ É ¹ ¼ ¾ ¹½¼ Ç » Æ ¹ ż ¾ à  º Á » ¾ Á À ¿ ¾ ¹½¼ » º ¹ R¤(2F‰¢uzsbvP™x2ËWs&R“2˔­Èž¯@(¡us…¡Ä!!RF[email protected] ...
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This note was uploaded on 02/18/2009 for the course EE 190048222 taught by Professor He during the Spring '09 term at UCLA.

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