数字电子技术(Floyd 第十版)课件Chapter -04-st2.ppt
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数字电子技术(Floyd 第十版)课件Chapter -04-st2.ppt
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,DigitalFundamentalsTenthEditionFloyd,Chapter4,2008PearsonEducation,Examples,DeterminethebinaryvaluesforwhichthefollowingstandardSOPexpressionisequalto1:
DeterminethebinaryvaluesforwhichthefollowingstandardPOSexpressionisequalto0:
Examples,ConvertthefollowingSOPexpressiontoanequivalentPOSexpression:
Theevaluationisasfollows:
000+010+011+101+111AtotalofeightpossiblecombinationsTheSOPcontainsfivecombinationsThePOSmustcontaintheotherthreecombinations001,100,110TheequivalentPOSexpressionis,Exercises,ConvertthefollowingexpressiontostandardSOPandPOSforms:
Booleanexpressionsandtruthtables,DevelopatruthtableforthestandardSOPexpression,DevelopatruthtableforthestandardPOSexpression,Mintermv.s.maxterm,ThemintermassociatedwitheachinputcombinationistheAND,orproduct,oftheinputvariables.ThemaxtermassociatedwitheachinputcombinationistheOR,orsum,oftheinputvariables.,http:
/,TheKarnaughmap(K-map)isatoolforsimplifyingcombinationallogicwith3or4variables.For3variables,8cellsarerequired(23).,ThemapshownisforthreevariableslabeledA,B,andC.Eachcellrepresentsonepossibleproductterm.Eachcelldiffersfromanadjacentcellbyonlyonevariable.,Summary,Karnaughmaps,Cellsareusuallylabeledusing0sand1storepresentthevariableanditscomplement.,Summary,Karnaughmaps,Onesarereadasthetruevariableandzerosarereadasthecomplementedvariable.,Thenumbersareenteredingraycode,toforceadjacentcellstobedifferentbyonlyonevariable.,Summary,ABABABAB,CC,Alternatively,cellscanbelabeledwiththevariableletters.Thismakesitsimpletoread,butittakesmoretimepreparingthemap.,Karnaughmaps,Readthetermsfortheyellowcells.,Example,Solution,1.Groupthe1sintotwooverlappinggroupsasindicated.Readeachgroupbyeliminatinganyvariablethatchangesacrossaboundary.,Summary,K-mapscansimplifycombinationallogicbygroupingcellsandeliminatingvariablesthatchange.,Karnaughmaps,Groupthe1sonthemapandreadtheminimumlogic.,Example,Solution,A4-variablemaphasanadjacentcelloneachofitsfourboundariesasshown.,Eachcellisdifferentonlybyonevariablefromanadjacentcell.Groupingfollowstherulesgiveninthetext.Thefollowingslideshowsanexampleofreadingafourvariablemapusingbinarynumbersforthevariables,Summary,Karnaughmaps,X,Summary,Karnaughmaps,Groupthe1sonthemapandreadtheminimumlogic.,Example,1.Groupthe1sintotwoseparategroupsasindicated.Readeachgroupbyeliminatinganyvariablethatchangesacrossaboundary.,Solution,Thelower(green)groupisreadasAD.,Examples,MapthefollowingSOPexpressionsonaKarnaughmap:
Examples,DeterminetheproducttermsforthekarnaughmapsinthefigurebelowandwritetheresultingminimumSOPexpression.,Examples,DeterminetheproducttermsforthekarnaughmapinthefigurebelowandwritetheresultingminimumSOPexpression.,Examples,DeterminetheproducttermsforthekarnaughmapinthefigurebelowandwritetheresultingminimumSOPexpression.,Examples,DeterminetheproducttermsforthekarnaughmapinthefigurebelowandwritetheresultingminimumSOPexpression.,Exercises,Applykarnaughmaps,simplifythefollowingexpression:
“Dontcare”terms:
eithera1ora0maybeassignedtotheoutput,BCDcodeSixinvalidcombinations:
1010,1011,1100,1101,1110,1111,Atruthtablehasa1outputonlywhentheBCDcodefor7,8,and9,Without“dontcares”With“dontcares”,7-segmentdisplay,DeriveanSOPexpressionforsegment“a”usingthevariablesABCDandthenminimizetheexpressionusingaKarnaughmapSegment“a”isactivatedforthedigits0,2,3,5,6,7,8,and9EachdigitcanberepresentedbyaBCDcode,a,Exercise,Drawthelogiccircuitforthesegment“a”logic.Drawthelogicdiagramforthesegment“a”logic.,
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