chap3odd - BA993 7 53 2""& $"      ¨...

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Unformatted text preview: BA993 7 53 2" ) ("& $"      ¨ ¦ ¤ [email protected]@68#64%10%'#%#!©§¥£ ¡ ¢ ­ † } € r w © ¨ ƒ § r ~x }t {  v “ } • € ¥ yx w vt } zx € r w } Œ ™ †³ ž j´s Ÿ ²¯ ž q t¡ 4¬a¢«uuu”u|ª'„G0±i1ia|¢4'š4'1a¢„i™4v £ Ÿ ž ¯ ž ­ † } € r w © ¨ § r ~x }t {  v “ } • € ¥ yx w vt } zx €x ~ v ¤ ™ † y°‡®š¡ 4¬a¢«ª’t¦|u'GG¢”i1ia%¢4'4'1'1¢b’4v £ … ‡ ‡ ‡ … ‡ ‡ ‡ … … … … ¡ ž yž Ÿ yx w v ‚ } zx € r w } |¢4œ4'1a¢„’ƒ ‡ … … … ‡ … … … ‡ ‡ ‡ ‡ ¡ ž yž Ÿ yx w v ‚ } zx €x ~ v |¢4œ4'1'1¢d ‹!¢‡ † ‰† ‰ ‰† ‰ Š† !¢‡ ¡ Š!† ‰ ‹!¢‡ † Š!† ‰ ‹† !¢‡ ž Š!† ‰ Š!† ‰ !¢‡ † † !¢‡ Ÿ yž › s ~t } z }t } w r €t v zq ™ vx z r • } ’ w Œx — vtt v– } • € ~ r • }t {  v “ s ’ 88%k4„'š4a1|¢4j4'0qGkbti|˜g'|¢ji1u4Gu'G„0”ujq  } Œ Ž }  Œ kiiGG{  } Œ Ž }  Œ kiiGG{ ‡ … yx w v ‚ } zx € r w } |¢4yt4'1a¢„’ƒ  } Œ Ž }  Œ kiiG„{  } Œ Ž }  Œ kiiG„{ … ‡ yx w v ‚ } zx €x ~ v |¢4y4|1'1¢d ‡† ˆa… ‘ ‡† ˆ0‹ Š !† ‰ ‡† ˆa… s  4a1'¢v  q } w r €t ~ } {t r z yx w vt s rq pn l d ih f e d ˜ kG|4Iu%¢4'[email protected]™— – • • ‘ ” “ ‘ f € ‰ ˆ € R … € E c U vS V € s H YR S vS s F R U FSR p P h F fR U e c H Y P U Y W V U FSR P H F a40bx¢’8igQ‡†„ƒ‚xw1g[email protected]ig6#dda¢ba`[email protected] D 4 † } ~x y ™ } Ï Î s  Á À ¿ ¾ q Œ vx € y Œ !01|„º„¢¼ ³ 0̓8¢6Ì¢'1„G{ £ a|0ºi¢'x £ › …† } ™ { w (b) using complex gate approach z V DD a b c d V DD (a) using AND and NOR circuits c b d a a z b c d V DD † …† } ™ { w a|01G¢'x £ |˘gi1~ Œx Œ — v • ~ r • y r v ™ ¤ ¤ r ~ } € r w ¼ }t ¤ “ v y v ~t r  Œ r ~ €x { y ™x y © ¨ ƒ  Œ r Ç ƒ Æ w Œx ~ {  } € Œ } “ }t ¤ “x ~x Œ vx € y Œ {– ~x • 4²º4¢1„Gak¬a¢r'”¢‚¬|4ÉG4ª1'G„8'„ʪuÉG4ș’Ãi|ºGÄk¬Åk”k'„”%|Ä¢'1„Gju%G¦· † ³ s  Á À ¿ ¾ q › Œ vx ~ ~ } ™ ¤ ¼ } } • € v € ~  Œ v ¤ ~ } ™ ™ v y ¹ v v ’ } • € – v … ‹† } ™ { w @´0Ãig¢6½o¢|11k1G¢¦i1¬»GG¢b¬k114t40˜i1b4¦¢!0˜1i¢|x £ ¢šº4©´„i¦i¦¸|o¶kjxg0y™— Œ v ¹ ™ v —€ } Œ } • · ln l d ih f e d ˜ µ 4 – • • ‘ ” “ ‘ f € ‰ ˆ € R … € E c U vS V € s H YR S vS s F R U FSR p P h F fR U e c H Y P U Y W V U FSR P H F a40bx¢’8igQ‡†„ƒ‚xw1g[email protected]ig6#dda¢ba`[email protected] ÒÛ ¾ Á ÒÛ ³ !„ͽ!g¿ ­ ¡ › ~x €x { y ™x y } • € ™ v– Œ vx ~ ~ } ™ ¤ ¼ } w Œx • y €x — ~ r ¥ v Ù † ~ Œ } ¤ ¤ r • } €x ~ v ¤ ¤ v } • € ¥ „%X|G„º'„G1¦4T¶¢|11k1G¢ti|G81'˜¬§„i0ڄGkbGaG¬'º¢„4i1G¢‡ ­ Øki• Ñ ƒ»ƒ”|x Ò Œ } † × × Ô ~ ¤ v € } • € € r } € r w Œ vx ~ ~x “ ~ Œ r ™ € } • €  Œ r Õ Ô ~x “ v € € v ’ } • € Œx } € r w Œ vx ~ ~x “ ~ Œ r ™ € } • € ¥ 4¬ši1ua±¬a¢Ã¢'1º|±1G48¬i1`G4փ|Ó¢¬¬4bG1‚|”¬a¢‚¢'11|§1G4º¬ši1ba… ­ rki• Ñ Ò Œ } † s ¹ v v ’ € ¼ } € } • € – v D† } ™ { w 8i40b¬0¬G14±!01i¢'x £ q } € r w Œ vx ~ ~x “ ~ Œ r ™ € r ™ v– }t ¤ “ r ¼ } Œ r ~ r  } € Œ } ~ } ™ ¤ } Œ v } • € v € ™ rtx “x ~ ~x €x { y ™x y } • · Ðn l d ih f e d ˜ ¬a¢§¢'11%±1G4º¬tu4ju'„”4i¶4u4Ãk¬xk1k1Gui¢ui1”¬ƒa%|±|1X|½'G„º|„uG¦¶%o`kjxg0y™— – • • ‘ ” “ ‘ f € ‰ ˆ € R … € E c U vS V € s H YR S vS s F R U FSR p P h F fR U e c H Y P U Y W V U FSR P H F a40bx¢’8igQ‡†„ƒ‚xw1g[email protected]ig6#dda¢ba`[email protected] ‡ ‰ Ò å ‡ œaˆÛ ‰ ­ ­ Ò å Š œI!Û ‰ suuu6q 0k6á © ¨ ƒ ã ä â s © ¨ ƒ ä ã â uuu6q ƒq6á › ~x } “x € Þ rt }  Œ vx € r w r ¤ v ™ ¤ } • € ¥ s € { ¤ € { v v € € { ¤ Œxq Œ vx €x ~ Œ r ™ € t } z }t } w r €t v z } • € – v ß ‡ Š Œ „%”|1k|kiØ¢'1a¢a„41„ªi1G88i„¬G¢±¬Xi„i|6r¢'1|1G4º¬œk4„'4a1'¢4ªG1d4àxa‚¢v  } ~ r ’  } ™ { ~ r } “ ~x Þ rt }  Œ vx € r w r ¤ v ™ ¤ } • € € r • € w Œx — v Œ ¹  Œ r ¥ } ™ { w Ž } • € Œ v  } ~ r Ý Ün l d ih f e d ˜ k¬4Ãk1i14k±u|Ãk|ki‚¢'1a¢a„41Gi1¦aG1”i%˜qi¢ÃG4G4ºi¢„ªi1Ë¢Ëk¬4XÃTyrkjxg0y™— … ‰ – • • ‘ ” “ ‘ f € ‰ ˆ € R … € E c U vS V € s H YR S vS s F R U FSR p P h F fR U e c H Y P U Y W V U FSR P H F a40bx¢’8igQ‡†„ƒ‚xw1g[email protected]ig6#dda¢ba`[email protected] † ~ € } ~ ‹ Þt Œ v Œx  } € { ’x ™ € ~x  } ’ t { v • ~  r v k1„¬”|G¢Ã|k¬i„'8¬¬|Gb|G¢iºË4¢'t ã ä ⠍ Œ } • €  Œ r ¥ ‹ ~x ~ ™ } ê { ’ – v ™ } ’ “ { Œ € ~ } ’ } • € ¥ v Ù † i1Ä40˜|u8„¢d4˜„G0¦¬kbi1Gi¢X0‹ ­ ’4T¦0q|ki¸¬Ëk1a„”¢ËkG˜04!0‹ ­ ¢k6á G4r å ™ v– ~ Þ rt }  v €  } ™ r ¤ “ v y Œ } • — ¥ µÛ ä ã â v € } ~ r } ™ y Œx ~ Þ rt }  } • € ¥ … ‰ 0‹ ­ ƒgjá ¬t¬4k1„|¢k|ki±G1y0 ­ ª4Tªa„1±„¬Ä4„±} Ñ ËG%G|±Ãª4Gr¢|1GG6šG¦· Û å ™ v– € r • € } }~ Œ r y † “ { “x Œx “ r ~ r • Œ vx € y Œ {– } • ó å ò ‡ ¡ ñ è ‹ ‡Û ‡ Á å ŠÛ ‡ Á Š µÛ [email protected]šu¢ˆ¢°I!¢Í’4!¢‡ ó å ò ‡ ¡ ñ è ‹ ‡Û ‡ Á å Û ‡ Á ‡Û [email protected]šu¢ˆ¢°I!¢Í’¢ˆa… ­ [email protected]šu¢ˆ¢°™!¢²I©u4!¢°™4!¢‡ ó å ò ‡ ¡ ñ è ‹ ‡Û ‡ Á ëÛ ‡ Á å ‹ è Š ‹Û ‡ Á Š Û ­ [email protected]šu¢ˆ¢°™!¢²I©uk|¢°™ ‰ ¢‡ ó å ò ‡ ¡ ñ è ‹ ‡Û ‡ Á ëÛ ‡ Á å ‹ è Š …Û ‡ Á Û ­ ­ s88„¢’ ‘ ªq¬a¢jq ¢kâ á ~ ™ } ê { Œ ì }€ r w ã ä s ~ ™ } ê { Œ ì }€ r w ä ã â 88„¢’ ‘ ªq¬a¢jq ©q6á › ~ ™ } ê { ’ – v ™ } ’ “ { Œ } • € ~ r å w Œx ™ } x ~ Œ v „º„b¢„d4u„b„ÅG1¦4rti|º„i%1G¢y ¥ Œ vx € r { ð } Þ rt }  } • € – v Œ vx € r ïxt r ™ } Œ } w } • € Þ ’  } Œx r € ’ v } ’ Œ r y ~ ™ } ê { ’ – v ™ } ’ “ { Œ “ { “x € ¤ ¨ s  o¢'1a„Åkmk%ki§i1½4Ä¢'1ak||4º„ik4”i1m0rki|41„4”Ì4„ªº„b¢„X4ª„bG0îGš|1G™6q ҜI4!0‹ å Š ëÛ Ò å Û œI4!0‹ ­ 4©u¢ˆ¢Í˜!¢°Á ‰ u4!¢°’4!¢‡ Š è ‹ ‡Û ‡ Á ëÛ ‡ è Š ‹Û ‡ Á Š Û ­ 4©u¢ˆ¢Í˜!¢°Á ‰ uk|¢°’ ‰ ¢‡ Š è ‹ ‡Û ‡ Á ëÛ ‡ è Š …Û ‡ Á Û ­ ­ s8º„b¢„’ ~ ™ } ê { s ~ ™ } ê { 8º„b¢„’ ‘ q¬a¢jq 0qâ á ‹ ì }€ r w ã ä ‘ q¬a¢jq ƒgjá ‹ ì }€ r w ä ã ⠛ € } w } — ~ ™ } ê { ’ v —€ w Œx ~ { s y „„4©X8„¢§½Qši|1G¦q6q ҜI4!0‹ å Š DÛ Ò å ¡Û œIaí0‹ ­ g„b¢„jq 0k6á s ™ } ê { ’ ã ä â ­ IXª¢ˆ¢°˜!¢°˜©ª4!¢°’4!¢‡ ‡ ¡ è ‹ ‡Û ‡ Á ëÛ ‡ Á ‹ è Š ‹Û ‡ Á Š Û ­ IXª¢ˆ¢°˜!¢°˜©ªk|¢°’ ‰ ¢‡ ‡ ¡ è ‹ ‡Û ‡ Á ëÛ ‡ Á ‹ è Š …Û ‡ Á Û ­ ­ sg„b¢„uq¬a¢jq 0k6á ™ } ê { ’ ì }€ r w ã ä â s ™ } ê { ’ ì }€ r w ä ã â g„b¢„uq¬a¢jq ƒq6á › Þ rt }  r ~ r • ™ } ê { ’ } • € Þ ’  } — vtt v – } € r w r – v w Œx € ~x ~ Œ v y ¹ ™ v — € } Œ } • € ¥ s Ò å q ç ‹ ‡Û ‡ Á ëÛ k%ki±¦4G’„¢ªi1¶ÅÃk½q||¢T¬a¢t‡4šG|1¬|1„¢¶º4©´„ii18Iœj™a¢ˆ¢°˜!¢‡ ­ g„b¢„jq ƒgjá Łk4'¢‡”|1ª¢|1a¢a„41Gª„4u¢44¬4j4¢'ª1'˜o„b¢„uui%1’ojq s ™ } ê { ’ ä ã â Þ ’ Œ } zx w } “x € Œ vx € r w r ¤ v ™ ¤  Œ r ‹ – v ™ v € y r–  r vt • €x — ™ } ê { ’ r w Œx ~ é s ’ Ò å Š DÛ ¡ œI4!Åq… Ò å µÛ ‡ œI4!¢„… ­ IX™4!¢°™4!¢‡ ‡ ¡ è Š ‹Û ‡ Á Š Û ­ IX™k|¢°™ ‰ ¢‡ ‡ ¡ è Š …Û ‡ Á Û › } ™ r ~ Þ rt }  Œ vx € r w r ¤ v ™ ¤ } • € ‡ 41a¦¢k|kG‚¢'1a¢a„4ºGªi1”I¡ ­ ã ä ¢kâ á ä ã â ©q6á ­ ­ ‡4˜4¬46Ã4¢'±™4v £ x6²|omkjxg0y™— ç – v ™ v € y r–  r vt r ™ s rq æn l d ih f e d ˜ – • • ‘ ” “ ‘ f € ‰ ˆ € R … € E c U vS V € s H YR S vS s F R U FSR p P h F fR U e c H Y P U Y W V U FSR P H F a40bx¢’8igQ‡†„ƒ‚xw1g[email protected]ig6#dda¢ba`[email protected] ‹ ‰ ‰   Ìû ­ rx6q ¡©Åä ô ª˜šCq ¡©Åä ô s þ ý ÿ õ û s ú ù ø ÿ õ  Œ G4r £ ¾ Ìû ­ rx6q wƒƒã ô ª˜šCq wƒƒã ô s þ ý ÷ö õ û s ú ù ø ÷ö õ › ~ Œx w ™ r “ } ~x v Œ } • € Œx r € ’ v } „G|¢ºa±¬|¢iG1Ã|41G4½—  ¤ rx6q ä s þ ý ô ¤ À ¨§¤ u’šCq ä ô  ¤ s ú ù ø ¨ ¿ ¤ srx6q ã ô ¤ ¾ þ ý ¤ s ú ù ø ª˜šCq ã ô ¥£ ¨ ¦ ©§¤ ~ } {t r z } • € Œ v  } ~ r ki|4ai1â‚k¬4XÝ s þ ý ÿ õ rx6q ¢½xä ô u’šCq ¡©Åä ô û s ú ù ø ÿ õ  Œ G4r s þ ý ÷ö õ rx6q ü©Úã ô u’šCq wƒƒã ô û s ú ù ø ÷ö õ › ~ r  } Œ Ž }  } ™ r ~ Œx w ™ r “ } ~x v ƒ p pn l d ih f e d ˜ „4Ãkii1auG|¢1a§¬|¢’@omkjxg0y™— – • • ‘ ” “ ‘ f € ‰ ˆ € R … € E c U vS V € s H YR S vS s F R U FSR p P h F fR U e c H Y P U Y W V U FSR P H F a40bx¢’8igQ‡†„ƒ‚xw1g[email protected]ig6#dda¢ba`[email protected] ...
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