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1、Asynchronouscounter(异步计数器)Cascade(串级)Decade(十进制)Decadecounter(十进制计数器)Recycle(循环)Ripplecounter(纹波计数器)Sequence(时序)Sequentialcircuit(时序电路)Statediagram(状态图)Statemachine(状态机)Synchronouscounter(同步计数器)Truncated(截断)Truncatedsequence(无关态)Up/Downcounter(加减计数器)第1页/共123页KEY TERMSAsynchronous counter A type of c
2、ounter in which each stage is clocked from the output of the preceding stage.Cascade To connect“end-to-end”as when several counters are connected from the terminal count output of one counter to the enable input of the next counter.第2页/共123页Decade Characterized by ten states or values.Decade counter
3、 A digital counter having ten states.Recycle To undergo transition from the final or terminal state back to the initial state.Ripple counter An asynchronous counter.第3页/共123页Sequence The order in which several things occur in a specified time relationship.Sequential circuit A digital circuit whose l
4、ogic states follow on a specified time sequence.State diagram A graphic depicition of a sequence of states or values.第4页/共123页State machine A logic system exhibiting a sequence of states conditioned by internal logic and external inputs;any sequential circuit exhibiting a specified sequence of state
5、s.Terminal count The final state in a counters sequence.第5页/共123页Synchronous counter A type of counter in which each stage is clocked by the same pulse.Truncated Shortened.Truncated sequence A sequence that does not include all of the possible states of a counter.第6页/共123页Up/Down counter A counter t
6、hat can progress in either direction through a certain sequence.第7页/共123页 9.1 ASYNCHRONOUS COUNTER OPERATIONThetermasynchronousreferstoeventsthatdonothaveafixedtimerelationshipwitheachotherand,generally,donotoccuratthesametime.AnasynchronouscounterisoneinwhichtheFFwithinthecounterdonotchangestatesat
7、exactlythesametimebecausetheydonothaveacommonclockpulse.2.第8页/共123页A 2-Bit Asynchronous Binary CounterJ0K0Q0CHIGHCLK2134Q0J1K1Q1CQ1Q0CLKQ03.第9页/共123页ClockPulseQ1Q0Initially00101210311400BinarystatesequenceforthecounterinFigureabove.4.第10页/共123页A 2-Bit Asynchronous Binary CounterJ0K0Q0CHIGHCLK2134Q0J
8、1K1Q1CQ1CLKQ0第11页/共123页A 2-Bit Asynchronous Binary CounterJ0K0Q0CHIGHCLK2134Q0J1K1Q1CQ1CLKQ0第12页/共123页ClockPulseQ1Q0Initially00111210301400BinarystatesequenceforthecounterinFigureabove.第13页/共123页A 3-Bit Asynchronous Binary CounterClockPulseQ2Q1Q0Initially0001001201030114100Binary state sequence for
9、a 3-bit binary counter.510161107111 8(recycle)0005.第14页/共123页J0K0Q0CJ1K1Q1CQ0HIGHJ2K2Q2CQ1FF2FF1FF01CLKQ0Q1Q21111011111110000000000000012345678CLK6.第15页/共123页J0K0Q0CJ1K1Q1CJ2K2CFF2FF1FF0EXAMPLE9-1Afour-bitasynchronousbinarycounterisshowninasfollow:Q2J3K3CQ3FF3CLKHIGH第16页/共123页CLKQ0Q1Q21234Q311100000
10、0000000110010100110001111111001056789101112131415161010101111000011110011001100第17页/共123页J0K0Q0CJ1K1Q1CCLRJ2K2CFF2FF1FF0AsynchronousDecadeCounterQ2J3K3CQ3FF3CLR10decoderCLKHIGH7.第18页/共123页CLKQ0Q1Q212345678910Q3CLRGlitchGlitch8.1110000000000001100101001100010111010010第19页/共123页EXAMPLE9-2Showhowanasyn
11、chronouscountercanbeimplementedhavingamodulusoftwelvewithastraightbinarysequencefrom0000through1011.Q3Q2Q1Q000001011 1100RecycleNormalnextstate第20页/共123页J0K0Q0CJ1K1Q1CJ2K2CFF2FF1FF0Q2J3K3CQ3FF3CLR12decoderCLKHIGH第21页/共123页J0K0Q0CJ1K1Q1CJ2K2CFF2FF1FF0Q2J3K3CQ3FF3CLR13decoderCLKHIGHRelatedproblem:EXAM
12、PLE9-2第22页/共123页A4-BitAsynchronousBinaryCounterJ0K0Q0CJ1K1Q1CJ2K2CFF2FF1FF0Q2J3K3CQ3FF3CLRCLKB(1)CLKA(14)RO(1)RO(2)(2)(3)(12)(9)(8)(11)9.第23页/共123页CCCTRDIV16CLKACLKBRO(1)RO(2)Q3Q2Q1Q0(a)74LS93Aconnectedasamodulus-16counter10.第24页/共123页CCCTRDIV10CLKACLKBRO(1)RO(2)Q3Q2Q1Q0(b)74LS93Aconnectedasadecadec
13、ounter11.第25页/共123页EXAMPLE9-3Showhowthe74LS93Acanbeusedasamodulus12counter.CCCTRDIV10CLKACLKBRO(1)RO(2)Q3Q2Q1Q012.第26页/共123页Related Problem:modulus-13 counterCC74LS93ACLKACLKBRO(1)RO(2)Q3Q2Q1Q013.第27页/共123页 9.2 SYNCHRONOUS COUNTER OPERATIONThetermsynchronousreferstoeventsthathaveafixedtimerelationsh
14、ipwitheachother.WithrespecttocounteroperationsynchronousmeansthatalltheFFinthecounterareclockedatthesametimebyacommonclockpulse.14.第28页/共123页A 2-Bit Synchronous Binary CounterJ0K0Q0CHIGHCLK2134Q0J1K1Q1CQ1CLKQ115.第29页/共123页A 3-Bit Synchronous Binary CounterJ0K0Q0CJ1K1Q1CQ0HIGHJ2K2CQ1FF2FF1FF0Q2CLK16.
15、第30页/共123页1CLKQ0Q1Q2111101111111000000000000001234567817.第31页/共123页ClockPulseQ2Q1Q0Initially0001001201030114100Binary state sequence for a 3-bit binary counter.510161107111 8(recycle)00018.第32页/共123页J0K0Q0CJ1K1Q1CJ2K2CFF2FF1FF0SynchronousBinaryCounterQ2J3K3CQ3FF3CLKHIGHQ0Q1Q2Q0Q119.第33页/共123页CLKQ1Q2
16、Q3Q0Q0Q1Q0Q1Q0Q1Q2Q0Q1Q220.第34页/共123页A4-BitSynchronousDecadeCounterJ0K0Q0CJ1K1Q1CJ2K2CFF2FF1FF0Q2J3K3CQ3FF3HIGHCLKQ321.第35页/共123页CLKQ0Q1Q212345678910Q322.第36页/共123页ClockPulseQ3Q2Q1Q0Initially0000 10001200103001140100States of a BCD decade counter50101601107011110(recycles)0000910018100023.第37页/共123页
17、J0=K0=1,J1=K1=Q0Q3J2=K2=Q0Q1,J3=K3=Q0Q1Q2+Q0Q324.第38页/共123页 9.3 UP/DOWN SYNCHRONOUS COUNTERSAnup/downcounterisonethatiscapableofprogressingineitherdirectionthroughacertainsequence.Anup/downcounter,sometimescalledabidirectionalcounter,canhaveanyspecifiedsequenceofstates.25.第39页/共123页A3-bitbinarycount
18、erthatadvancesupwardthroughitssequence(0,1,2,3,4,5,6,7)andthencanbereversedsothatitgoesthroughthesequenceintheoppositedirection(7,6,5,4,3,2,1,0)isanillustrationofup/downsequentialoperation.0,1,2,3,4,5,4,3,2,3,4,5,6,7,6,5,ect.DOWNDOWNUPUP26.第40页/共123页ClockPulseUPQ2Q1Q0DOWN0000Up/Down sequence for a 3
19、-bit counter.100120103011410051016110711127.第41页/共123页J0=K0=1J1=K1=(Q0*UP)+(Q0*DOWN)J2=K2=(Q0*Q1*UP)+(Q0*Q1*DOWN)28.第42页/共123页J0K0CJ1K1CJ2K2CQ0FF0HIGHFF1FF2Q0Q1Q1Q2Q2CLKU/DDOWNUPQ0*UPQ0*DOWN29.第43页/共123页EXAMPLE9-4Showthetimingdiagramanddeterminethesequenceofa4-bitsynchronousbinaryup/downcounterifthe
20、clockandUP/DOWNcontrolinputshavewaveformsasshowninFig.9-24(a).Thecounterstartsintheall0sstateandispositiveedge-triggered.第44页/共123页CLKQ1Q2Q3Q0UPDOWNDOWNUPUP/DOWN30.1000001100 1000001010000010111000100000011011100000000000Fig.9-24(a)第45页/共123页Q3Q2Q1Q000000001001000110100001100100001000011110000000100
21、1000010000UPUPDOWNDOWN31.第46页/共123页RelatedProblemShowthetimingdiagramiftheUP/DOWNcontrolwaveforminFigure9-24(a)isinverted.第47页/共123页CLKQ1Q2Q3Q0UPDOWNDOWNUPUP/DOWN30.11110111101010011011111110111010100000011011101100111000Fig.9-24(a)0000第48页/共123页 9.4 DESIGN OF SYNCHRONOUS COUNTERThissectionisrecomme
22、ndedforthosewhowantanintroductiontocounterdesignortostatemachinedesigningeneral.32.第49页/共123页GeneralModelofaSequentialCircuitCombinationallogicMemoryI0I1ImY0Y1YpQ0Q1QnQ0Q1QxCLKExcitationlinesStatevariablelines33.第50页/共123页Step1:StateDiagram000110011101001010100111Statediagramfora3-bitGraycodecounter
23、.34.第51页/共123页Step2:Next-StateTableQ2Q1Q0Q2Q1Q0PresentStateNextState000001001011011010010110110111111101101100100000Next-statetablefor3-bitGraycodecounter.35.第52页/共123页Step3:Flip-FlopTransitionTableQNQN+1JKOutputTransitionFlip-FlopInput000XTransitiontableforaJ-Kflip-flop.011X10X111X036.第53页/共123页Ste
24、p4:K-MAPPresentStateNextStateQ2Q1Q0Q2Q1Q0100000001011011010010110 110111111101OutputFlip-flopTransitionsInputsQNQN+1JK000X11X00001111001Q2Q1Q0K0map0001111001Q2Q1Q0J0map00000110110010X1011X1X1X37.第54页/共123页0001111001Q2Q1Q01X0001111001Q2Q1Q0100001111001Q2Q1Q01X0001111001Q2Q1Q01X0001111001Q2Q1Q0X000111
25、1001Q2Q1Q01X00XXXXXXX0001XXX000000XXXXXXXXX100001Q1Q0Q2Q0Q1Q0Q2Q1Q2Q1Q2Q1Q2Q1Q2Q1J2mapJ1mapJ0mapK2mapK1mapK0map38.第55页/共123页Step5:LogicExpressionforFlip-FlopInputJ0=Q2Q1+Q2Q1=Q2+Q1K0=Q2Q1+Q2Q1=Q2+Q1J1=Q2Q0K1=Q2Q0J2=Q1Q0K2=Q1Q039.第56页/共123页J0K0CJ1K1CJ2K2CQ0FF0FF1FF2Q0Q1CLKQ2Q2Q140.第57页/共123页To design
26、 in another way000111100111010001Q2Q1Q2Q1Q0mapQ2Q1Q0Q0n+1=Q2Q1+Q2Q1=Q2+Q1(Q0+Q0)=Q2+Q1Q0+Q2+Q1Q0J0=Q2+Q1K0=Q2+Q1Qn+1=JQn+KQn第58页/共123页0001111001Q2Q1Q011000110Q2Q0Q1mapQ1Q0Q1n+1=Q1Q0+Q2Q0(Q1+Q1)=Q0Q1+Q2Q0Q1+Q2Q0Q1=(Q0+Q2Q0)Q1+Q2Q0Q1=Q2Q0Q1+Q2Q0Q1J1=Q2Q0K1=Q2Q0Qn+1=JQn+KQn第59页/共123页0001111001Q2Q1Q0100
27、01101Q1Q0Q2mapQ0Q2Q2n+1=Q1Q0+Q0Q2=Q1Q0(Q2+Q2)+Q0Q2=(Q0+Q1Q0)Q2+Q1Q0Q2=Q1Q0Q2+Q1Q0Q2J2=Q1Q0K2=Q1Q0Qn+1=JQn+KQn第60页/共123页EXAMPLE9-5:UseJ-KFF001101010111PresentStateNextState001010Q2Q1Q0Q2Q1Q001010110111111100141.第61页/共123页QNQN+1JKOutputTransitionFlip-FlopInput000XTransitiontableforaJ-Kflip-flop.011X10
28、X111X042.第62页/共123页0001111001Q2Q1Q0XX0001111001Q2Q1Q0100001111001Q2Q1Q01X0001111001Q2Q1Q0XX0001111001Q2Q1Q0X0001111001Q2Q1Q01XXXXXXXXXXX10XXXX1XXX1XXXXXXXXXX0101XXQ11Q11Q21J2mapJ1mapJ0mapK2mapK1mapK0map43.第63页/共123页J0K0CCLKJ1K1CQ0J2K2CQ2Q1Q211J0=1,K0=Q2J1=K1=1J2=K2=Q144.第64页/共123页To design in anothe
29、r way0001111001X0X111XXQ0Q2Q0Q0mapQ2Q1Q0Q0n+1=Q0+Q2Q0J0=1K0=Q2Qn+1=JQn+KQn第65页/共123页0001111001X0X110XXQ1Q1mapQ2Q1Q0Q1n+1=Q1J1=1K1=1Qn+1=JQn+KQn第66页/共123页0001111001X0X101XXQ2Q1Q2mapQ2Q1Q0Q2n+1=Q1Q2+Q1Q2J2=K2=Q1Qn+1=JQn+KQnQ2Q1第67页/共123页 9.5 CASCADED COUNTERSCounterscanbeconnectedincascadetoachievehig
30、her-modulusoperation.Inessence,cascadingmeansthatthelast-stageoutputofonecounterdrivestheinputofthenextcounter.45.第68页/共123页J0K0CCLKJ1K1CJ2K2CJ3K3CJ4K4CQ4Q0Q1Q2Q3Modulus-4counterModulus-8counterTwocascadedcounters(allJandKareHIGH).46.第69页/共123页CTRDIV10CTENQ0Q1Q2Q3TCCCOUNTER1CTRDIV10CTENQ0Q1Q2Q3TCCCO
31、UNTER2HIGHCLKfinfinfin10100Amodulus-100counterusingtwocascadecounters.47.第70页/共123页CTRDIV10CTENTCCHIGHCTRDIV10CTENTCCCTRDIV10CTENTCC100kHz10kHz1kHz1MHz48.第71页/共123页CTRDIV16ENPD3D2D1D0RCOC0000ENTCTRDIV16ENPD3D2D1D0RCOCENTCTRDIV16ENPD3D2D1D0RCOCENTCTRDIV16ENPD3D2D1D0RCOCENT110000110110016C16316616CLKL
32、OADMSDLSDOutput49.第72页/共123页216=65,536(63C0)16=6*163+3*162+12*16=25,53665,53625,536=40,00050.第73页/共123页 9.6 COUNTER DECODINGInmanyapplications,itisnecessarythatsomeorallofthecounterstatesbedecoded.Thedecodingofacounterinvolvesusingdecodersorlogicgatestodeterminewhenthecounterisinacertainbinarystatei
33、nitssequence.Forinstance,theterminalcountfunctionpreviouslydiscussedisasingledecodedstateinthecountersequence.51.第74页/共123页J0K0CJ1K1CJ2K2CQ0Q0Q1Q2CLKHIGHLSBMSBDecoded6Q0Q2Q111152.第75页/共123页EXAMPLE9-9Decoding2and7J0K0CJ1K1CJ2K2CQ0Q0Q1Q2LSBMSBFF0FF1FF2CLK12753.第76页/共123页1CLKQ0Q1Q2111101111111000000000
34、000001234567827Decodedoutput54.第77页/共123页A3-bitUp/DownGrayCodeCounterDesign000110011101001010100111Statediagramfora3-bitGraycodecounter.Y=1Y=055.第78页/共123页Q2Q1Q0Q2Q1Q0Q2Q1Q0PresentStateNextState000100001Y=0(DOWN)Y=1(UP)001000011011001010010011110110010111111110101101111100 10010100056.第79页/共123页QNQN
35、+1JKOutputTransitionFlip-FlopInput000XTransitiontableforaJ-Kflip-flop.011X10X111X0第80页/共123页Q2Q1Q0YQ2Q1Q0Y01X11X1111XX00000000010101011111111110101010K0mapJ0mapQ2Q1YQ2Q1YQ2Q1YQ2Q1YQ2Q1YQ2Q1YQ2Q1YQ0YXXXX000X1X1XXXXX0000Q2Q1Y第81页/共123页Q2Q1Q0YQ2Q1Q0YXXX000XXX0X000000000010101011111111110101010K1mapJ1ma
36、pQ2Q0YQ2Q1YQ2Q0YQ2Q0YQ0Y1XX00X0X01XX000XX11X第82页/共123页Q2Q1Q0YQ2Q1Q0Y1XX0X0X0001100000000010101011111111110101010K2mapJ2mapQ1Q0YQ1Q0YQ1Q0YQ1Q0YQ0Y00XXXX0XXXXXX00X0X01第83页/共123页QNQN+1DOutputTransitionFlip-FlopInput000TransitiontableforaDflip-flop.01110011157.第84页/共123页Q2Q1Q0YQ2Q1Q0Y1111111111111111000
37、00000010101011111111110101010D0mapD1mapQ2Q1YQ2Q1YQ2Q1YQ2Q1YQ2Q0YQ1Q0Q2Q0YQ0Y58.第85页/共123页Q2Q111111110000010111111010D2mapQ1Q0YQ2Q0Q1Q0Y1Q0Y59.第86页/共123页TheBooleanExpressionsfortheDInputsD0=Q2Q1Y+Q2Q1Y+Q2Q1Y+Q2Q1YD1=Q2Q0Y+Q2Q0Y+Q1Q0D2=Q1Q0Y+Q1Q0Y+Q2Q0Logicdiagramofthe3-bitup/downGraycodecounterinpage
38、584Figure11-13.60.第87页/共123页Design problem 2-sequence detector Consider a synchronous sequential logic circuit that will detect a defined serial pattern appearing on a signal data input.Suppose the serial input to detect is 0110011,with Z becoming a 1 immediately after the last bit appears in the se
39、quence.第88页/共123页Design procedure1.Derive the state diagram.2.Draw the state table.3.Assign state variable patterns to states.4.Draw the assigned state table.5.Derive the flip-flop input functions,and in our design.6.Derive the output function of a K-map,and finally.7.Draw the logic circuit.第89页/共12
40、3页1/02/03/04/05/06/07/08/10110010010001111Statediagram0110011StatenumberOutputZ第90页/共123页1/02/03/04/05/06/07/08/1011001001000111Statediagram0110110011StatenumberOutputZ第91页/共123页State table present state Next state output x=0 x=1 Z 1 2 1 0 2 2 3 0 3 2 4 0 4 5 1 0 5 6 3 0 6 2 7 0 7 2 8 0 8 2 1 1第92页/
41、共123页State variable assignment For example:state 1=001,state 2=010,state 3=011,state 4=100,state 5=101,state 6=110,state 7=111,state 8=000.There are a very large number of possible assignments and each would lead to specific next state and output functions.第93页/共123页Rule 1 Assign codes which differ
42、in one variable to states that lead to the same next state.(次态相同,现态应相邻编码)001011000第94页/共123页Rule 2 Assign codes that differ in one variable for next states of a present state.(现态相同,次态应相邻编码)100000110第95页/共123页We make the assignment:state 1=000,state 2=111,state 3=101,state 4=001,state 5=010,state 6=1
43、10,state 7=011,state 8=100第96页/共123页 present state Next state output y3y2y1 x=0 x=1 Z 000 111 000 0 111 111 101 0 101 111 001 0 001 010 000 0 010 110 101 0 110 111 011 0 011 111 100 0 100 111 000 1 第97页/共123页Flip-flop input functions The input functions for the three flip-flops are obtained as befor
44、e by mapping the next state variables in the assigned state table onto Karnaugh maps.第98页/共123页xy3xy3Q0Y11111111111100000000010101011111111110101010 xy3y2y1y2y1xy1xy3y2y1y2y1111111Y3Y21y3y2第99页/共123页xy3Q0Y11110000010111111010 xy2y1y3y1y2y1111Y11y3y2y1xy2y1Y3=xy1+xy3+y2y1+y3y2Y2=x+y3y2y1Y1=y3y1+y3y2y
45、1+xy2y1+xy2y1+xy2y1OutputfunctionZ=y3y2y1Drawlogiccircuit.11xy2y1第100页/共123页Mealy model designsThe Mealy model state diagram indicates the outputs on the arcs leading to the state,together with the inputs that caused the transition to that state.Often the Mealy model state diagram has less states th
46、an a Moore model state diagram for the same problem.第101页/共123页The same design steps1.Derive the state diagram.2.Draw the state table.3.Assign state variable patterns to states.4.Draw the assigned state table.5.Derive the flip-flop input functions(on K-maps)6.Derive the output function of a K-map,an
47、d finally.7.Draw the logic circuit.第102页/共123页MealymodelstatediagramThedifferenceisthatonlystate8iseliminatedinMealymodel.21/0StatenumberOutputZ3415670/01/01/11/01/00/01/01/00/00/00/00/0Input,x0/0第103页/共123页 Present state Next state output,Z x=0 x=1 x=0 x=1 1 2 1 0 0 2 2 3 0 0 3 2 4 0 0 4 5 1 0 0 5
48、6 3 0 0 6 2 7 0 0 7 2 1 0 1第104页/共123页 Present state Next state Next output,Z y3y2y1 x=0 x=1 x=0 x=1 000 111 000 0 0 111 111 101 0 0 101 111 001 0 0 001 010 000 0 0 010 110 101 0 0 110 111 011 0 0 011 111 100 0 1 第105页/共123页xy3xy3Q0Y11X111111100000000010101011111111110101010 xy3y1xy2y1xy1xy3y2y1y2y1
49、111X1Y3Y211XXy3y2y11y3y2y1第106页/共123页xy3Q0Y11110000010111111010 xy2y1y3y2y111XY11xy2y1Y3=xy1+xy3+y3y2y1+xy2y1+y3y2y1Y2=x+y3y1Y1=y3+xy2y1+xy2y1+xy2y1OutputfunctionZ=xy3y2y1Drawlogiccircuit.X11xy2y1第107页/共123页Exercise sequence 11011/02/03/04/05/1110101000StatenumberOutputZ1第108页/共123页 Present state Ne
50、xt state output,Z x=0 x=1 1 1 2 0 2 1 3 0 3 4 3 0 4 1 5 0 5 1 2 1PresentstateNextstateoutput,Zx=0 x=1x=0 x=111200213003430041101MooreMealy第109页/共123页20/0StatenumberOutputZ3410/00/01/00/01/01/01/1Input,x第110页/共123页PresentstateNextstateoutput,Zy1y0 x=0 x=1x=0 x=1000001000100100010111000110000010001111