CSM51Ach10

CSM51Ach10 - Chap ter A r ithm et iccom b inat iona l m odu...

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Unformatted text preview: Chap ter A r ithm et iccom b inat iona l m odu lesandnetw ork s Inth ischap terw edescr ibe : Thespec icat iono fadderm odu lesforpos it ivein tegers . H a lf-adderand fu ll-adderm odu les . C arry-r ipp leandcarry-lookaheadadderm odu les . N etw ork so fadderm odu les . Therep resen tat iono fs igned in tegers :s ign-and-m agn itude ,tw o 's-com p lem en t , andones '-com p lem en tsy stem s . A dd it ionandsub tract iono fs igned in tegersintw o 'scom p lem en t . A r ithm et ic-log icun its( alu ) . C om paratorm odu lesandnetw ork s . M u lt ip licat iono fpos it ivein tegers . W enowadd ressanotherim portan tseto fcom b inat iona lm odu les ,nam e ly thoseu sedfortheim p lem en tat iono fbas icar ithm et icoperat ion son in teger va lues .A sw itha llotherm odu les ,theseareu se fu lfortheim p lem en tat iono f m orecom p lex( inth iscasear ithm et ic)sy stem s .Theinpu tstothesear ithm et ic m odu lescon s isto fb it-vectorsthatrep resen tin tegerva lues ,whereasou tpu ts canrep resen te itherin tegersorspec ifytheresu ltsfrom re lat iona loperators , suchasequa lorgreater . P erform ingar ithm et icoperat ion son in tegersrep resen tedbyb it-vectorsre- qu iresthespec icat iono fanum bersy stem thatdenesth isrep resen tat ion .W e beg inw ithadderm odu les ,wh ichperform add it iono fpos it ivein tegersinthe conven t iona lrad ix-num bersy stem ,inwh ichtheb it-vector x = ( x n ;:::;x ) C hap ter.A r ithm e ticcom b ina tiona lm odu lesandne tw orks ADDER n n n y x z c in c out F igu re.: A dderm odu le . rep resen tsthein teger x suchthat x = n X i = x i i Th isa llow stherep resen tat iono fin tegersintherangeto n . Laterinth ischap terw ed iscu sstherep resen tat iono fs igned in tegers ,and ex tendthebas icadd it iono fpos it ivein tegerstoadd it ionandsub tract iono f s igned in tegers .W ea lsodescr ibethefo llow ingaux iliaryar ithm et icoperat ion s : changeo fs ign ,i.e ., z = x ; sub tract ion ;and detect iono fresu ltcond it ion s :s ign ,zerova lue ,andover ow . F ina lly ,w ep resen tar ithm et ic-log icun itsandabas icim p lem en tat iono fthe m u lt ip licat ionoperat ion . . A dderm odu lesforpos it ivein tegers A n n-b itb inaryadder m odu le(seeF igu re.)isacom b inat iona lsy stem thathastw o n-b itinpu ts x = ( x n ;:::;x )and y = ( y n ;:::;y )rep resen t- ingtheoperand s ,andan n-b itou tpu t z = ( z n ;:::;z )rep resen t ingtheresu lt (thesum ) .Them odu leperform sb inaryadd it iono ftheinpu toperand s . A dd it iona linpu tandou tpu ts igna ls ,ca lled carry-in c in and carry-ou t c ou t ,respect ive ly ,areu sedtofac ilitatetheim p lem en tat iono flargeradders . Them odu leadd sthecarry-inva luetotheinpu tvectors ,andsetsthecarry-ou t s igna ltowhenevertheresu ltexceed sthem ax im um va luerep resen tab lew ith n b its(thatis ,aresu ltlargerthan n ) .Thear ithm et icexp ress ionre lat ing .. A dderm odu lesforpositivein tegers inpu tsandou tpu tsis x + y + c in = n c ou t + z Ah igh-leve lspec icat iono fthe n-b itb...
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CSM51Ach10 - Chap ter A r ithm et iccom b inat iona l m odu...

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