非同步式计数器的运作

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1第一页，共六十二页。Figure8--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2第二页，共六十二页。Figure9--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.100111003第三页，共六十二页。Figure9--3Three-bitasynchronousbinarycounteranditstimingdiagramforonecycle.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作4第四页，共六十二页。Figure9--4Propagationdelaysina3-bitasynchronous(ripple-clocked)binarycounter.ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作5第五页，共六十二页。Figure9--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=25MHz6第六页，共六十二页。ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作Figure9--6Anasynchronouslyclockeddecadecounterwithasynchronousrecycling.7第七页，共六十二页。ThomasL.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8第八页，共六十二页。FigureA--21The74LS93A4-bitasynchronousbinarycounterlogicdiagram.(Pinnumbersareinparentheses,andallJandKinputsareinternallyconnectedHIGH.)ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作9第九页，共六十二页。FigureA--22Twoconfigurationsofthe74LS93Aasynchronouscounter.(Thequalifyinglabel,CTRDIVn,indicatesacounterwithnstates.)ThomasL.Floyd

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Allrightsreserved.1.非同步式計數器的運作10第十页，共六十二页。FigureA-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.11第十一页，共六十二页。A2-bitsynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--10TimingdiagramforthecounterofFigure9-11.12第十二页，共六十二页。Figure9--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13第十三页，共六十二页。Figure9--11A3-bitsynchronousbinarycounter.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--12TimingdiagramforthecounterofFigure9-14.14第十四页，共六十二页。ThomasL.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.15第十五页，共六十二页。Figure9--14AsynchronousBCDdecadecounter..ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作Figure9--15TimingdiagramfortheBCDdecadecounter(Q0istheLSB).16第十六页，共六十二页。FigureA--24The74HC1634-bitsynchronousbinarycounter.(ThequalifyinglabelCTRDIV16indicatesacounterwithsixteenstates.)ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作17第十七页，共六十二页。FigureA--25Timingexamplefora74HC163.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作18第十八页，共六十二页。FigureA--26The74LS160synchronousBCDdecadecounter.(ThequalifyinglabelCTRDIV10indicatesacounterwithtenstates.)ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作19第十九页，共六十二页。FigureA--27Timingexamplefora74LS160.ThomasL.Floyd

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Allrightsreserved.2.同步式計數器的運作20第二十页，共六十二页。Figure9--16Abasic3-bitup/downsynchronouscounter.ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器21第二十一页，共六十二页。Figure9--17ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器22第二十二页，共六十二页。FigureA--28The74HC190up/downsynchronousdecadecounter.ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器23第二十三页，共六十二页。ThomasL.Floyd

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Allrightsreserved.3.上/下數的同步式計數器FigureA--29Timingexamplefora74HC190.24第二十四页，共六十二页。Figure9--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PreviousStatePresentStateNextState25第二十五页，共六十二页。Figure9--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26第二十六页，共六十二页。Figure9--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.27第二十七页，共六十二页。Figure9--21Karnaughmapsforpresent-stateJandKinputs.ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計28第二十八页，共六十二页。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第二十九页，共六十二页。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

00130第三十页，共六十二页。Figure9--24ThomasL.Floyd

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Allrightsreserved.4.同步式計數器的設計31第三十一页，共六十二页。Figure9--25ThomasL.Floyd

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Allrightsreserved.J0=1,K=Q2J1=K1=1J2=K2=Q14.同步式計數器的設計32第三十二页，共六十二页。Figure9--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33第三十三页，共六十二页。PresentStateNextStateY=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34第三十四页，共六十二页。Figure9--27

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

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Allrightsreserved.4.同步式計數器的設計35第三十五页，共六十二页。Figure9--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36第三十六页，共六十二页。Figure9--29Twocascadedcounters(allJandKinputsareHIGH).ThomasL.Floyd

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Allrightsreserved.5.串接計數器Figure9--30TimingdiagramforthecascadedcounterconfigurationofFigure9-38.37第三十七页，共六十二页。Figure9--31Amodulus-100counterusingtwocascadeddecadecounters.ThomasL.Floyd

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Allrightsreserved.5.串接計數器Figure9--32Threecascadeddecadecountersformingadivide-by-1000frequencydividerwithintermediatedivide-by-10anddivide-by-100outputs.38第三十八页，共六十二页。Figure9--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39第三十九页，共六十二页。Figure9--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.40第四十页，共六十二页。Figure9--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+141第四十一页，共六十二页。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第四十二页，共六十二页。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第四十三页，共六十二页。Figure9--36Decodingofstate6(110).ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼44第四十四页，共六十二页。Figure9--37A3-bitcounterwithactive-HIGHdecodingofcount2andcount7.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼45第四十五页，共六十二页。Figure9--38Abasicdecade(BCD)counteranddecoder.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼46第四十六页，共六十二页。Figure9--39OutputswithglitchesfromthedecoderinFigure9-38.Glitchwidthsareexaggeratedforillustrationandareusuallyonlyafewnanosecondswide.6.計數器的解碼DecodingGlitches47第四十七页，共六十二页。Figure9--40Thebasicdecadecounteranddecoderwithstrobingtoeliminateglitches.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼48第四十八页，共六十二页。Figure9--41

StrobeddecoderoutputsforthecircuitofFigure9-49.ThomasL.Floyd

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Allrightsreserved.6.計數器的解碼49第四十九页，共六十二页。Figure9--42Simplifiedlogicdiagramfora12-hourdigitalclock.LogicdetailsusingspecificdevicesareshowninFigures9-52and9-53.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用50第五十页，共六十二页。Figure9--43Logicdiagramoftypicaldivide-by-60counterusing74LS160Asynchronousdecadecounters.Notethattheoutputsareinbinaryorder(theright-mostbitistheLSB).ThomasL.Floyd

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Allrightsreserved.7.計數器的應用51第五十一页，共六十二页。Figure9--44Logicdiagramforhourscounteranddecoders.Notethatonthecounterinputsandoutputs,theright-mostbitistheLSB.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用52第五十二页，共六十二页。Figure9--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.53第五十三页，共六十二页。Figure9--46Logicdiagramformodulus-100up/downcounterforautomobileparkingcontrol.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用車輛停車控制54第五十四页，共六十二页。Figure9--47

Parallel-to-serialdataconversionlogic.ThomasL.Floyd

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Allrightsreserved.7.計數器的應用55第五十五页，共六十二页。Figure9--48Exampleofparallel-to-serialconversiontimingforthecircuitinFigure9-47.7.計數器的應用56第五十六页，共六十二页。Figure9--49Exampleofafailurethataffectsfollowingcountersinacascadedarrangement.ThomasL.Floyd

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