非同步式计数器的运作课件

Chapter9

Counters

計數器AsynchronousCounterOperation非同步式計數器的運作SynchronousCounterOperation同步式計數器的運作Up/DownSynchronousCounters上/下數的同步式計數器DesignofSynchronousCounters同步式計數器的設計CascadedCounters串接計數器CounterDecoding計數器的解碼CounterApplications計數器的應用Troubleshooting檢修LogicalSymbolswithDependencyNotation具有相依註標的邏輯符號ProgrammableLogic可程式邏輯DigitalSystemApplication數位系統的應用1Chapter9

Counters

計數器AsynchrFigure8--40TheJ-Kflip-flopasadivide-by-2device.Qisone-halfthefrequencyofCLK.ThomasL.Floyd

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Allrightsreserved.Flip-FlopApplications正反器的用途除法器JKClkQQ00Q0Q0不變0101Reset1010Set11Q0Q0轉態2Figure8--40TheJ-Kflip-fFigure9--1A2-bitasynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作Figure9--2TimingdiagramforthecounterofFigure9-1.Asinpreviouschapters,outputwaveformsareshowningreen.100111003Figure9--1A2-bitasynchrFigure9--3Three-bitasynchronousbinarycounteranditstimingdiagramforonecycle.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作4Figure9--3Three-bitasyncFigure9--4Propagationdelaysina3-bitasynchronous(ripple-clocked)binarycounter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作5Figure9--4PropagationdelFigure9--5Four-bitasynchronousbinarycounteranditstimingdiagram.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作例題9-1如圖9-5所示為一個4位元的非同步二進制計數器,每一個正反器都是負緣觸發而且有一個10ns的極際延遲時間.(1)設計各正反器輸出的時序圖,(2)算出從Clock輸入加訊號進去到Q3輸出的延遲時間,(3)算出最高工作頻率.Sol:(2)tp(Total)

=4x10ns=40ns(3)fmax=1/tp(Total)

=1/40ns=25MHz6Figure9--5Four-bitasynchThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作Figure9--6Anasynchronouslyclockeddecadecounterwithasynchronousrecycling.7ThomasL.Floyd

DigitalFundamThomasL.Floyd

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Allrightsreserved.例題9-2證明一個非同步的計數器如何除12,從二進制的0000算到1011.1.非同步式計數器的運作Figure9--7Asynchronouslyclockedmodulus-12counterwithasynchronousrecycling.很尖銳的脈波8ThomasL.Floyd

DigitalFundamFigureA--21The74LS93A4-bitasynchronousbinarycounterlogicdiagram.(Pinnumbersareinparentheses,andallJandKinputsareinternallyconnectedHIGH.)ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作9FigureA--21The74LS93A4-bFigureA--22Twoconfigurationsofthe74LS93Aasynchronouscounter.(Thequalifyinglabel,CTRDIVn,indicatesacounterwithnstates.)ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作10FigureA--22TwoconfiguratFigureA-2374LS93Aconnectedasamodulus-12counter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作例題9-3證明74LS93A如何作為一個除12的計數器.11FigureA-2374LS93AconnectA2-bitsynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--10TimingdiagramforthecounterofFigure9-11.12A2-bitsynchronousbinarycouFigure9--9Timingdetailsforthe2-bitsynchronouscounteroperation(thepropagationdelaysofbothflip-flopsareassumedtobeequal).ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作第一個脈波第二個脈波第三個脈波第四個脈波解釋前一頁每次Clock來時Q0及Q1的變化13Figure9--9TimingdetailsFigure9--11A3-bitsynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--12TimingdiagramforthecounterofFigure9-14.14Figure9--11A3-bitsynchrThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作FF2在Q0Q1同時為1時,下一個脈波來會改變狀態,FF3則在Q0Q1Q2同時為1時,下一個脈波來才會改變狀態,Figure9--13A4-bitsynchronousbinarycounterandtimingdiagram.PointswheretheANDgateoutputsareHIGHareindicatedbytheshadedareas.15ThomasL.Floyd

DigitalFundamFigure9--14AsynchronousBCDdecadecounter..ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--15TimingdiagramfortheBCDdecadecounter(Q0istheLSB).16Figure9--14AsynchronousFigureA--24The74HC1634-bitsynchronousbinarycounter.(ThequalifyinglabelCTRDIV16indicatesacounterwithsixteenstates.)ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作17FigureA--24The74HC1634-bFigureA--25Timingexamplefora74HC163.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作18FigureA--25TimingexampleFigureA--26The74LS160synchronousBCDdecadecounter.(ThequalifyinglabelCTRDIV10indicatesacounterwithtenstates.)ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作19FigureA--26The74LS160syFigureA--27Timingexamplefora74LS160.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作20FigureA--27TimingexampleFigure9--16Abasic3-bitup/downsynchronouscounter.ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器21Figure9--16Abasic3-bitFigure9--17ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器22Figure9--17ThomasL.FloyFigureA--28The74HC190up/downsynchronousdecadecounter.ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器23FigureA--28The74HC190upThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器FigureA--29Timingexamplefora74HC190.24ThomasL.Floyd

DigitalFundamFigure9--18Generalclockedsequentialcircuit.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計激勵線狀態變數線輸入線與狀態變數線加到組合邏輯電路產生激勵訊號線PreviousStatePresentStateNextState25Figure9--18GeneralclockeFigure9--19Statediagramfora3-bitGraycodecounter.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計步驟一:畫出狀態圖26Figure9--19StatediagramfFigure9--20ExamplesofthemappingprocedureforthecountersequencerepresentedinTable9-7andTable9-8.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計步驟二:寫出下一狀態表.步驟三:寫出正反器的暫態表.步驟四:根據下一狀態表及正反器的暫態表填寫卡諾圖.27Figure9--20ExamplesofthFigure9--21Karnaughmapsforpresent-stateJandKinputs.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計28Figure9--21Karnaughmaps步驟五:寫出各正反器的輸入端之邏輯表示式J0=Q2Q1+Q2Q1=Q2xorQ1K0=Q2Q1+Q2Q1=Q2xorQ1J1=Q2Q0K1=Q2Q0J2=Q1Q0K2=Q1Q0Figure9--22Three-bitGraycodecounter.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計步驟六:畫出電路圖29步驟五:寫出各正反器的輸入端之邏輯表示式Figure9-Figure9--23OutputTransitionsQNQN+1Flip-FlopInputsJK00

0x

01

1x

10

x1

11

x0ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計例題9-5使用JK正反器,設計一個如圖9-32所示不按照二進制計數順序的計數器.PresentStateQ2Q1Q0NextStateQ2Q1Q0001

010

010

101

101

111

111

00130Figure9--23OutputTransitionsFigure9--24ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計31Figure9--24ThomasL.Floyd

DiFigure9--25ThomasL.Floyd

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Allrightsreserved.J0=1,K=Q2J1=K1=1J2=K2=Q14.同步式計數器的設計32Figure9--25ThomasL.Floyd

DiFigure9--26Statediagramfora3-bitup/downGraycodecounter.ThomasL.Floyd

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Allrightsreserved.例題9-6試設計一個3位元的格雷碼同步式上下數計數器,當UP/DOWN為1時往上數,為0時往下數.4.同步式計數器的設計33Figure9--26StatediagramPresentStateNextStateY=0(Down)Y=1(Up)Q2Q1Q0Q2Q1Q0Q2Q1Q0

000

100

001

001

000

011

011

001

010

010

011

110

110

010

111

111

110

101

101

111

100

100

101

000OutputTransitionsQNQN+1Flip-FlopInputsJK00

0x

01

1x

10

x1

11

x04.同步式計數器的設計34PresentStateNextStateQ2Q1QFigure9--27

JandKmapsforTable9-11.TheUP/DOWNcontrolinput,Y,istreatedasafourthvariable.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計35Figure9--27JandKmapsfFigure9--28Three-bitup/downGraycodecounter.ThomasL.Floyd

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Allrightsreserved.步驟五:寫出各正反器的輸入端之邏輯表示式步驟六:畫出電路圖4.同步式計數器的設計36Figure9--28Three-bitup/dFigure9--29Twocascadedcounters(allJandKinputsareHIGH).ThomasL.Floyd

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Allrightsreserved.5.串接計數器Figure9--30TimingdiagramforthecascadedcounterconfigurationofFigure9-38.37Figure9--29TwocascadedcFigure9--31Amodulus-100counterusingtwocascadeddecadecounters.ThomasL.Floyd

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Allrightsreserved.5.串接計數器Figure9--32Threecascadeddecadecountersformingadivide-by-1000frequencydividerwithintermediatedivide-by-10anddivide-by-100outputs.38Figure9--31Amodulus-100Figure9--33ThomasL.Floyd

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Allrightsreserved.例題9-7試算出圖9-42中兩個電路全部各除多少?Sol:9-42(a) 8x12x16=15369-42(b)10x4x7x5=14005.串接計數器39Figure9--33ThomasL.Floyd

DiFigure9--34Adivide-by-100counterusingtwo74LS160decadecounters.ThomasL.Floyd

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Allrightsreserved.5.串接計數器例題9-8使用74LS160計數器設計一個電路,將1MHz的訊號從Clock端輸入,輸出端得到10KHz.40Figure9--34Adivide-by-10Figure9--35Adivide-by-40,000counterusing74HC1614-bitbinarycounters.Notethateachoftheparalleldatainputsisshowninbinaryorder(theright-mostbitD0istheLSBineachcounter).ThomasL.Floyd

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Allrightsreserved.5.串接計數器從63C0算到FFFF,即除以40,000.63C0H=25,536.40,000=65535–25536+141Figure9--35Adivide-by-40解題步驟(n,m,x,y皆為正整數)決定所需位元數n

（x:所需除數）

決定所需74161個數m換算計數器初始值y（換算成16進位值）畫電路圖42解題步驟(n,m,x,y皆為正整數)42計數器之解碼對計數器序列中任何指定狀態實作其解碼邏輯

使用閃控法（Strobe）消除解碼時的脈衝干擾計數器解碼器Output=1Atcounter=66.計數器的解碼43計數器之解碼計數器解碼器Output=16.計數器的解碼4Figure9--36Decodingofstate6(110).ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼44Figure9--36DecodingofstFigure9--37A3-bitcounterwithactive-HIGHdecodingofcount2andcount7.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼45Figure9--37A3-bitcounteFigure9--38Abasicdecade(BCD)counteranddecoder.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼46Figure9--38AbasicdecadeFigure9--39OutputswithglitchesfromthedecoderinFigure9-38.Glitchwidthsareexaggeratedforillustrationandareusuallyonlyafewnanosecondswide.6.計數器的解碼DecodingGlitches47Figure9--39OutputswithgFigure9--40Thebasicdecadecounteranddecoderwithstrobingtoeliminateglitches.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼48Figure9--40ThebasicdecaFigure9--41

StrobeddecoderoutputsforthecircuitofFigure9-49.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼49Figure9--41StrobeddecodeFigure9--42Simplifiedlogicdiagramfora12-hourdigitalclock.LogicdetailsusingspecificdevicesareshowninFigures9-52and9-53.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用50Figure9--42SimplifiedlogiFigure9--43Logicdiagramoftypicaldivide-by-60counterusing74LS160Asynchronousdecadecounters.Notethattheoutputsareinbinaryorder(theright-mostbitistheLSB).ThomasL.Floyd

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Allrightsreserved.7.計數器的應用51Figure9--43LogicdiagramFigure9--44Logicdiagramforhourscounteranddecoders.Notethatonthecounterinputsandoutputs,theright-mostbitistheLSB.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用52Figure9--44LogicdiagramFigure9--45Functionalblockdiagramforparkinggaragecontrol.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用車輛停車控制:最多可停100輛,當停滿100輛時指示燈亮起,同時柵欄放下,當不滿100輛時指示燈滅掉,同時柵欄收起.53Figure9--45FunctionalbloFigure9--46Logicdiagramformodulus-100up/downcounterforautomobileparkingcontrol.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用車輛停車控制54Figure9--46LogicdiagramFigure9--47

Parallel-to-serialdataconversionlogic.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用55Figure9--47Parallel-to-seFigure9--48Exampleofparallel-to-serialconversiontimingforthecircuitinFigure9-47.7.計數器的應用56Figure9--48ExampleofparFigure9--49Exampleofafailurethataffectsfollowingcountersinacascadedarrangement.ThomasL.Floyd

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Allrightsreserved.8.檢修57Figure9--49ExampleofafFigure9--50Exampleofafailureinacascadedcounterwithatruncatedsequence.ThomasL.Floyd

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Allrightsreserved.8.檢修58Figure9--50ExampleofafFigure9--51ThomasL.Floyd

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Allrightsreserved.例題9-10分析圖9-60測量的結果是否正確,如果不正確,那錯在哪裡?Sol:Truncatedmodulus=fullmodulus–presetmodulus=164-82C016=65536-32472=32064Thecorrectfrequency=10MHz/32064=311.88HzModulus=fin/fout=10MHz/637.76Hz=15680Truncatedmodulus=fullmodulus–presetmodulus=65536–15680=49856=C2C016比較82C016與C2C016就知道錯在哪裡了.8.檢修59Figure9--51ThomasL.Floyd

DiFigure9--52ThomasL.Floyd

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Allrightsreserved.例題9-11觀察圖9-61的波形看計數器是否正確?Sol:Q2正確的波形應為紅線的波形,所以若Q2的波形像綠線的部分則Q2的波形是錯的.仔細比較Q1及Q2的波形,發現兩者一樣,會發生這種情況,可能是AND下半部內部斷線,相當於接HIGH,因此ANDGate等於沒有作用所致.8.檢修60Figure9--52ThomasL.Floyd

DiFigure9--53The74HC1634-bitsynchronouscounter.ThomasL.Floyd

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Allrightsreserved.9.具有相依註標的邏輯符號61Figure9--53The74HC1634-Chapter9

Counters

計數器AsynchronousCounterOperation非同步式計數器的運作SynchronousCounterOperation同步式計數器的運作Up/DownSynchronousCounters上/下數的同步式計數器DesignofSynchronousCounters同步式計數器的設計CascadedCounters串接計數器CounterDecoding計數器的解碼CounterApplications計數器的應用Troubleshooting檢修LogicalSymbolswithDependencyNotation具有相依註標的邏輯符號ProgrammableLogic可程式邏輯DigitalSystemApplication數位系統的應用62Chapter9

Counters

計數器AsynchrFigure8--40TheJ-Kflip-flopasadivide-by-2device.Qisone-halfthefrequencyofCLK.ThomasL.Floyd

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Allrightsreserved.Flip-FlopApplications正反器的用途除法器JKClkQQ00Q0Q0不變0101Reset1010Set11Q0Q0轉態63Figure8--40TheJ-Kflip-fFigure9--1A2-bitasynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作Figure9--2TimingdiagramforthecounterofFigure9-1.Asinpreviouschapters,outputwaveformsareshowningreen.1001110064Figure9--1A2-bitasynchrFigure9--3Three-bitasynchronousbinarycounteranditstimingdiagramforonecycle.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作65Figure9--3Three-bitasyncFigure9--4Propagationdelaysina3-bitasynchronous(ripple-clocked)binarycounter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作66Figure9--4PropagationdelFigure9--5Four-bitasynchronousbinarycounteranditstimingdiagram.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作例題9-1如圖9-5所示為一個4位元的非同步二進制計數器,每一個正反器都是負緣觸發而且有一個10ns的極際延遲時間.(1)設計各正反器輸出的時序圖,(2)算出從Clock輸入加訊號進去到Q3輸出的延遲時間,(3)算出最高工作頻率.Sol:(2)tp(Total)

=4x10ns=40ns(3)fmax=1/tp(Total)

=1/40ns=25MHz67Figure9--5Four-bitasynchThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作Figure9--6Anasynchronouslyclockeddecadecounterwithasynchronousrecycling.68ThomasL.Floyd

DigitalFundamThomasL.Floyd

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Allrightsreserved.例題9-2證明一個非同步的計數器如何除12,從二進制的0000算到1011.1.非同步式計數器的運作Figure9--7Asynchronouslyclockedmodulus-12counterwithasynchronousrecycling.很尖銳的脈波69ThomasL.Floyd

DigitalFundamFigureA--21The74LS93A4-bitasynchronousbinarycounterlogicdiagram.(Pinnumbersareinparentheses,andallJandKinputsareinternallyconnectedHIGH.)ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作70FigureA--21The74LS93A4-bFigureA--22Twoconfigurationsofthe74LS93Aasynchronouscounter.(Thequalifyinglabel,CTRDIVn,indicatesacounterwithnstates.)ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作71FigureA--22TwoconfiguratFigureA-2374LS93Aconnectedasamodulus-12counter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作例題9-3證明74LS93A如何作為一個除12的計數器.72FigureA-2374LS93AconnectA2-bitsynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--10TimingdiagramforthecounterofFigure9-11.73A2-bitsynchronousbinarycouFigure9--9Timingdetailsforthe2-bitsynchronouscounteroperation(thepropagationdelaysofbothflip-flopsareassumedtobeequal).ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作第一個脈波第二個脈波第三個脈波第四個脈波解釋前一頁每次Clock來時Q0及Q1的變化74Figure9--9TimingdetailsFigure9--11A3-bitsynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--12TimingdiagramforthecounterofFigure9-14.75Figure9--11A3-bitsynchrThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作FF2在Q0Q1同時為1時,下一個脈波來會改變狀態,FF3則在Q0Q1Q2同時為1時,下一個脈波來才會改變狀態,Figure9--13A4-bitsynchronousbinarycounterandtimingdiagram.PointswheretheANDgateoutputsareHIGHareindicatedbytheshadedareas.76ThomasL.Floyd

DigitalFundamFigure9--14AsynchronousBCDdecadecounter..ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--15TimingdiagramfortheBCDdecadecounter(Q0istheLSB).77Figure9--14AsynchronousFigureA--24The74HC1634-bitsynchronousbinarycounter.(ThequalifyinglabelCTRDIV16indicatesacounterwithsixteenstates.)ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作78FigureA--24The74HC1634-bFigureA--25Timingexamplefora74HC163.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作79FigureA--25TimingexampleFigureA--26The74LS160synchronousBCDdecadecounter.(ThequalifyinglabelCTRDIV10indicatesacounterwithtenstates.)ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作80FigureA--26The74LS160syFigureA--27Timingexamplefora74LS160.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作81FigureA--27TimingexampleFigure9--16Abasic3-bitup/downsynchronouscounter.ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器82Figure9--16Abasic3-bitFigure9--17ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器83Figure9--17ThomasL.FloyFigureA--28The74HC190up/downsynchronousdecadecounter.ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器84FigureA--28The74HC190upThomasL.Floyd

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Allrightsreserved.3.上/下數的同