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1、7SequentialLogicDesignPrinciplesEXERCISESOLUTIONS7.2SRQQN7.3ThelatchoscillatesifSandRarenegatedsimultaneously.Manysimulatorprogramswillexhibitthissamebehaviorwhenconfrontedwithsuchinputwaveforms.SRQQN119120DIGITALCIRCUITS7.5JENQQKTQQNCLK7.8JusttietheJandKinputstogetheranduseastheDinput.7.9E
2、xcitationandoutputequations:D1=Q1¢+Q2D2=Q2¢×XZQ=1Q+2¢Excitation/transitiontable;state/outputtable:ENENQ1Q201S01Z001011ACD1011010BCC0100001CAB1111010DCC1Q1*Q2*S*7.15Excitationequations:D2=(Q1QÅÅ0)()Q1¢×Q2¢D1=Q2D0=Q1Excitation/transitiontable;statetable:Q2Q1Q0Q2*Q1*Q0*SS*000100AE001000BA01010
3、1CFDB011001EC100010FG101110GH110111HD1110117.18Excitationandoutputequations:J0==K0ENJ1==K1Q0EN×MAX=ENQ1Q0××EXERCISESOLUTIONS121NotethatthecharacteristicequationforaJ-Kflip-flopisQ*=JQ×¢+K¢×Q.Thus,weobtainthefollowingtransitionequations:Q0*=EN¢×Q0+ENQ0×¢Q1*=EN¢×Q1++ENQ0××Q1¢ENQ0×¢×Q1Transiti
4、on/outputtable;state/outputtable:ENENQ1Q201S010000,001,0AA,0B,00101,010,0BB,0C,01010,011,0CC,0D,01111,000,1DD,0A,1Q1*Q2*,MAXS*,MAXStatediagram:EN¢EN¢ABENENENENDCEN¢EN¢Timingdiagram:CLKENQ0Q1MAX7.20Thiscanbedonealgebraically.Ifalloftheinputcombinationsarecovered,thelogicalsumoftheexpressions
5、onallthetransitionsleavingastatemustbe1.Ifthesumisnot1,itis0forallinputcombinationsthatareuncovered.Fordouble-coveredinputcombinations,welookatallpossiblepairsoftransitionsleavingastate.Theproductofapairoftransitionequationsis1foranydouble-coveredinputcombinations.(a)StateD,Y=0isuncovered.(
6、b)StateA,(X+Z¢)=0isuncovered.StateB,W=1isdouble-covered;(W+X)=0isuncovered.StateC,(W+X+Y+Z)=0isuncovered;(W×X+W×Y+Z×Y+Z×X)=1isdoublecovered.StateD,(X×Y+×X¢×Z+W×Z)=0isuncovered;(W×X¢×Z+W×X×Y×Z)=1isdouble-covered;122DIGITALCIRCUITS7.21Table9–4onpage804showsanoutput-codedstateassignment.Hereis
7、acorrespondingtransitionlist:SL3ZL2ZL1ZR1ZR2ZR3ZTransitionexpressionS*L3Z*L2Z*L1Z*R1Z*R2Z*R3Z*IDLE000000(LEFT+RIGHT+HAZ)¢IDLE000000IDLE000000LEFT×HAZ¢×RIGHT¢L1001000IDLE000000HAZ+LEFT×RIGHTLR3111111IDLE000000RIGHT×HAZ¢×LEFT¢R1000100L1001000HAZ¢L2011000L1
