数字电子技术(Floyd 第十版)课件Chapter 6优质PPT.ppt

数字电子技术(Floyd 第十版)课件Chapter 6优质PPT.ppt

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,DigitalFundamentalsTenthEditionFloyd,Chapter5,2008PearsonEducation,InSum-of-Products（SOP）form,basiccombinationalcircuitscanbedirectlyimplementedwithAND-ORcombinationsifthenecessarycomplementtermsareavailable.,Summary,CombinationalLogicCircuits,Summary,AnexampleofanSOPimplementationisshown.TheSOPexpressionisanAND-ORcombinationoftheinputvariablesandtheappropriatecomplements.,CombinationalLogicCircuits,SOP,WhentheoutputofaSOPformisinverted,thecircuitiscalledanAND-OR-Invertcircuit.TheAOIconfigurationlendsitselftoproduct-of-sums（POS）implementation.,Summary,AnexampleofanAOIimplementationisshown.TheoutputexpressioncanbechangedtoaPOSexpressionbyapplyingDeMorganstheoremtwice.,CombinationalLogicCircuits,POS,AOI,DeMorgan,Thetruthtableforanexclusive-ORgateis,Summary,Exclusive-ORLogic,A,B,NoticethattheoutputisHIGHwheneverAandBdisagree.,TheBooleanexpressionis,Thecircuitcanbedrawnas,X,Symbols:

@#@,DistinctiveshapeRectangularoutline,Thetruthtableforanexclusive-NORgateis,Summary,Exclusive-NORLogic,A,B,NoticethattheoutputisHIGHwheneverAandBagree.,TheBooleanexpressionis,Thecircuitcanbedrawnas,X,Symbols:

@#@,DistinctiveshapeRectangularoutline,Summary,Foreachcircuit,determineiftheLEDshouldbeonoroff.,（a）（b）（c）,Circuit（a）:

@#@XOR,inputsagree,outputisLOW,LEDisON.,Circuit（b）:

@#@XNOR,inputsdisagree,outputisLOW,LEDisON.,Circuit（c）:

@#@XOR,inputsdisagree,outputisHIGH,LEDisOFF.,Example,Solution,ImplementingaSOPexpressionisdonebyfirstformingtheANDterms;@#@thenthetermsareORedtogether.,Summary,ImplementingCombinationalLogic,Example,Solution,Startbyformingthetermsusingthree3-inputANDgates.,Thencombinethethreetermsusinga3-inputORgate.,Forbasiccombinationallogiccircuits,theKarnaughmapcanbereadandthecircuitdrawnasaminimumSOP.,Summary,KarnaughMapImplementation,Example,Solution,AKarnaughmapisdrawnfromatruthtable.ReadtheminimumSOPexpressionanddrawthecircuit.,1.Groupthe1sintotwooverlappinggroupsasindicated.Readeachgroupbyeliminatinganyvariablethatchangesacrossaboundary.,Thecircuitisonthenextslide:

@#@,Summary,Circuit:

@#@,+,B,Solution,continued,X=,Theresultisshownasasumofproducts.,ItisasimplemattertoimplementthisformusingonlyNANDgatesasshowninthetextandfollowingexample.,B,Summary,NANDLogic,Example,ConvertthecircuitinthepreviousexampletoonethatusesonlyNANDgates.,RecallfromBooleanalgebrathatdoubleinversioncancels.Byaddinginvertingbubblestoabovecircuit,itiseasilyconvertedtoNANDgates:

@#@,B,+,B,X=,Solution,Summary,NANDgatesaresometimescalleduniversalgatesbecausetheycanbeusedtoproducetheotherbasicBooleanfunctions.,UniversalGates,Inverter,A,ANDgate,A,B,AB,A,B,A+B,ORgate,A,B,NORgate,Summary,NORgatesarealsouniversalgatesandcanformallofthebasicgates.,UniversalGates,Inverter,A,ORgate,A,B,A+B,A,B,AB,ANDgate,A,B,AB,NANDgate,Summary,RecallfromDeMorganstheoremthatAB=A+B.Byusingequivalentsymbols,itissimplertoreadthelogicofSOPforms.Theearlierexampleshowstheidea:

@#@,NANDLogic,C,B,C,A,+,A,B,X=,Thelogiciseasytoreadifyou（mentally）cancelthetwoconnectedbubblesonaline.,Summary,NORLogic,A,C,A,X=,Again,thelogiciseasytoreadifyoucancelthetwoconnectedbubblesonaline.,（A+B）（A+C）,Summary,PulsedWaveforms,Forcombinationalcircuitswithpulsedinputs,theoutputcanbepredictedbydevelopingintermediateoutputsandcombiningtheresult.Forexample,thecircuitshowncanbeanalyzedattheoutputsoftheORgates:

@#@,A,B,C,D,A,B,C,D,G1,G2,G3,G1,G2,G3,Summary,PulsedWaveforms,Alternatively,youcandevelopthetruthtableforthecircuitandenter0sand1sonthewaveforms.Thenreadtheoutputfromthetable.,A,B,C,D,A,B,C,D,G1,G2,G3,G3,Inputs,ABCD,Output,0000,0001,0010,0011,0100,0101,0110,0111,1000,1001,1010,1011,1100,1101,1110,1111,0101010101,0110011000,0001111000,0000000110,0000111010,X,SelectedKeyTerms,UniversalgateNegative-ORNegative-AND,EitheraNANDoraNORgate.Thetermuniversalreferstoapropertyofagatethatpermitsanylogicfunctiontobeimplementedbythatgateorbyacombinationofgatesofthatkind.,ThedualoperationofaNANDgatewhentheinputsareactive-LOW.,ThedualoperationofaNORgatewhentheinputsareactive-LOW.,2008PearsonEducation,Quiz,2.Thetruthtableshownisfora.aNANDgateb.aNORgatec.anexclusive-ORgated.anexclusive-NORgate,2008PearsonEducation,Quiz,3.AnLEDthatshouldbeONisa.LED-1b.LED-2c.neitherd.both,2008PearsonEducation,Quiz,2008PearsonEducation,Quiz,2008PearsonEducation,Quiz,6.Thecircuitshownwillhaveidenticallogicoutifallgatesarechangedtoa.ANDgatesb.ORgatesc.NANDgatesd.NORgates,2008PearsonEducation,Quiz,A,B,C,D,7.T