CHAPTER5

CombinationalLogicAnalysisandDesign（組合邏輯電路分析和設計）組合邏輯電路時序邏輯電路components：LogicGatesCombinationallogiccircuitSequentiallogiccircuitcomponents：LogicGates+FlipFlops,LatchesChapter7,8,9,10Chapter5,6theoutputisonlydependedonthecurrentinputsTheoutputisnotonlydependedonthecurrentinputsbutalsodependedonthepaststateCombinationallogiccircuitchapter5chapter6CombinationallogicAnalysisandDesignFunctionsofcombinationalLogic5-1BasicCombinationalLogicCircuits5-2CombinationalLogicCircuits

Analysis5-3ImplementingCombinationalLogic

5-4TheUniversalPropertyofNANDandNORGates

5-5CombinationalLogicUsingNANDandNORGates5-6LogicCircuitOperationWithPulseWaveformCHAPTER5CombinationalLogicAnalysisandDesignAND-ORLogic（與-或邏輯電路）AND-OR-InvertLogic（與-或-非邏輯電路）Exclusive-ORLogic（異-或邏輯電路）5-1BasicCombinationalLogicCircuitsAND-ORLogicTruthtableINPUTSABCDABCDOUTPUTX0000000100100011010001010110011110001001101010111100110111101111000000010000000100000001101010110001000100011111XX=AB+CDAND-ORLogicAND-ORInvertLogicExclusive-ORLogicABX000110110110TruthtableExclusive-NORLogic

BooleanexpressionTruthtableTwoequivalentwaysofimplementingtheexclusive-NOR

Samelogiccanbeimplementedbydifferentcircuit5-2CombinationalLogicCircuitsAnalysis

(組合邏輯電路分析)LogicCircuitLogicFunctionX=F(A,B,C)?ThesensorproduceaHIGHwhenthelevelofchemicalinthetankdropsbelowaspecifiedpointBCABACA,B,Carelevelsensors.aHIGHisproducedwhenthelevelofchemicalinthetankdropsbelowaspecifiedpoint.AnalysisthefunctionofthecircuitX=AB+BC+ACBCABACX=AB+BC+ACTruthtableABCABBCACX00000101001110010111011100000000001000000110011100010111Thelow-levelindicatorwillgiveanindicationwhenmorethantwotanks’leveldropbelowthespecifiedpoint!AnalysisthefunctionofthecircuitAnalysisthefunctionofthecircuit(review)

Step1:ObtaintheLogicExpressionfromthelogiccircuitStep2:ConstructingaTruthTablefortheLogiccircuitStep3:Analysisthefunction

5-3ImplementingCombinationalLogic

（組合邏輯電路的設計）LogicCircuitLogicFunction1.FromanapplicationtoaTruthTable2.FromaTruthTabletoasimplifiedlogicexpression3.FromthesimplifiedlogicexpressiontoalogiccircuitExample：Implementavotingcircuitforthreeperson.Eachpersonhasonebutton.Pressthebuttonforagreementandleaveitfordisagreement.TheoutputwillshowonaLEDlight.Thelightonwhenmajoritypeopleagreed.Otherwise,thelightoff.三人表決電路每人一個按鍵，如果同意則按下，不同意則不按。結果用指示燈表示，多數同意時指示燈亮，否則不亮。FromlogicfunctiontoTruthTableTruthTableInputs:A、B、CAgree“1”，otherwise“0”Output:FLighton“1”，otherwise“0”Implementavotingcircuitforthreeperson(A、B、C):

Eachpersonhasonebuttoninfrontofhim.Pressthebuttonforagreementandleaveitfordisagreement.

TheoutputwillshowonaLEDlight.Thelightonwhenmajoritypeopleagreed.Otherwise,lightoff.

TruthTable2.FromTruthTabletosimplifiedlogicexpressionABC0001111001ABACBCABBCCAF3.FromLogicExpressiontoLogicCircuitAnd-OrLogic3.FromLogicExpressiontoLogicCircuitchap5-1a.ewbImplementathreeinputsparitychecker:Theoutputis“1”whenthenumberofinput“1”isodd.

(1)TruthTable

(2)Logicexpression

0000

A

B

C

Y0011010101101001101011001111ABC00100111101111Solution：奇偶檢驗器

(3)logiccircuit

(3)logiccircuitChap5奇偶校驗電路.ewbstep1.FromanapplicationtoaTruthTablestep2.FromaTruthTabletoasimplifiedlogicexpressionstep3.FromthesimplifiedlogicexpressiontoalogiccircuitCombinationLogicImplementation(Review)LogicCircuitLogicFunctionTextbook:Page168ch5-25-3TheUniversalProperty

ofNANDandNORGates

NANDandNORgatesare“universal”becausetheycanusedtoproduceanyoftheotherlogicfunctionsTheNANDGateasaUniversalLogicElementTheNORGateasaUniversalLogicElementNANDGateasanInverterTheNANDGateasaUniversalLogicElement?AAHIGH??NANDGateasanInverterxTwoNANDGatesasanANDGate?ThreeNANDGatesasanORGateFourNANDGatesasNORGateFourNANDGatesasXORGateNORGateasanInverterTheNORGateasaUniversalLogicElementTwoNORGatesasanORGateThreeNORGatesasanANDGateFourNORGatesasanNANDGateNANDlogicforX=AB+CD?5-4COMBINATIONALLOGICUSINGNANDANDNORGATEDeMorgan’s最簡邏輯電路標準門的個數最少每個門的連線最少門的種類最少

NANDLogicDiagramsUsingDualsymbolswhendrawingaNANDlogicdiagram,alwaysusethegatesymbolsinsuchawaythateveryconnectionbetweenagateoutputandagateinputiseitherbubble-to-bubbleornonbubble-to-nonbubble.UseoftheappropriatedualsymbolsinaNANDlogicdiagrameveryconnectionbetweenagateoutputandagateinputiseitherbubble-to-bubbleornonbubble-to-nonbubbleEXAMPLE:ImplementeachexpressionwithNANDlogicusingappropriatedualsymbols(a)EXAMPLE:ImplementeachexpressionwithNANDlogicusingappropriatedualsymbols(b)NORLOGICNORnegative-ANDNORlogicforX=(A+B)(C+D)

ANORgatefunctionaseitheraNORoranegative-AND.180三人表決電路:

Implementavotingcircuitforthreeperson(A、B、C):UseNANDgatesABCAnd-OrLogicGatesABCNANDLogicGates最簡邏輯電路標準門的個數最少每個門的連線最少門的種類最少Implementathreeinputsparitychecker:Theoutputis“1”whenthenumberofinput“1”isodd.奇偶檢驗器(3)ConverttoNANDlogic

(2)LogicexpressionUseNANDGates!EX5-12：DeterminethefinaloutputwaveformXforthecircuit,withinputwaveformsA,BandCasshown.5-5CIRCUITOPERATIONWITHPULSEWAVEFORMINPUTSEX5-11：DrawthetimingdiagramFindoutthelogiccircuitthatwillgeneratetheoutputwaveformfortheinputs.inputsoutputABCX000Page193:Problem30Homework:Page193Problem31DigitalSystemApplication7-segmentdisplayspage149共陽極接法共陰極接法gfedcba例：共陰極接法a

b

c

d

e

f

g

01100001101101低電平時發光高電平時發光共陽極接法abcgdef+dgfecbag共陰極接法abcdefg二－十進制編碼?顯示器件

D

C

BAa

b

c

d

efg00001111110000010110000100101101101200111111001301000110011401011011011501101011111601111110000710001111111810011