C7T (Digital Systems and Applications), Topic:- Counters

Prof.SurajitDhara SACT,

Dept.OfPhysics,NarajoleRaj College

C7T(DigitalSystemsandApplications),Topic:-Counters

 Counters:Counterisasequentialcircuit.Adigitalcircuitwhichisusedfor acounting pulsesisknowncounter.Counteristhewidestapplicationof flip-flops.Itisagroupofflip-flopswithaclocksignalapplied.Countersare oftwotypes

 Asynchronousorripplecounters.

 Synchronouscounters.

 Asynchronousorripplecounters:Thelogicdiagram ofa2-bitrippleup counterisshowninfigure.ThetoggleTflip-floparebeingused.Butwe canusetheJKflip-flopalsowithJandKconnectedpermanentlytologic1.

Externalclockisappliedtotheclockinputofflip-flopAandQAoutputis appliedtotheclockinputofthenextflip-flopi.e.FF-B.

LogicalDiagram

Oper at i on

SL.No Condi t i on Oper at i on 1.

^{InitiallyletboththeFFs}

beintheresetstate

=00initially Q_BQ_A

2.

^{After1stnegativeclock}

edge

As soon as the first negativeclockedgeis applied,FF-Awilltoggle andQAwillbeequalto 1.

isconnectedtoclock

Q_A

inputofFF-B.Since^Q_A haschangedfrom 0to 1,itistreated asthe positiveclockedgeby FFB. There is no change inQ_B because FFBisanegativeedge triggeredFF.

=01afterthefirst Q_BQ_A

clockpulse.

3.

^After 2nd negative clockedge

Onthearrivalofsecond negativeclockedge,FF- AtogglesagainandQ_A

= 0. The change in acts as a negative Q_A

clockedgeforFF-B.So

itwillalsotoggle,andQ_B willbe1.

= 10 after the Q_BQ_A

secondclockpulse.

4.

^{After3rdnegativeclock}

edge

Onthearrivalof3rdnegative clockedge,FF-Atogglesagain andQ_A become 1 from 0.

Sincethisisapositivegoing change,FFBdoesnotrespond toitandremainsinactive.So does not change and

Q_B

continues to be equalto 1.

=11afterthethirdclock

Q_BQ_A

pulse.

5.

^{After4thnegativeclock}

edge

Onthearrivalof4thnegative clockedge,FF-Atogglesagain andQ_Abecomes1 from 0.

This negative change inQ_A

actsasclockpulseforFF-B.

HenceittogglestochangeQB from 1to0.Q_BQ_A=00after thefourthclockpulse

TruthTable

 Synchronouscounters:Ifthe"clock"pulsesareappliedtoalltheflip-flops inacountersimultaneously,thensuchacounteriscalledassynchronous counter.

 4-bitSynchronousupcounter:TheJAandKAinputsofFF-Aaretiedto logic1.SoFF-Awillworkasatoggleflip-flop.TheJBandKBinputsare connectedtoQA.

LogicalDiagram

Operation

SLNo. Condition Operation 1. InitiallyletboththeFFs

beintheresetstate

=00initially.

Q_BQ_A

2. After1stnegativeclock edge

As soon as the first negativeclockedgeis applied,FF-Awilltoggle and wiQ_A llchangefrom 0to1.

Butatthe instantof applicationofnegative clockedge, , = =Q_AJ_A J_B 0.HenceFF-B willnot changeitsstate.SoQB willremain0.

=01afterthefirst QQ

clockpulse.

3. After 2nd negative clockedge

Onthearrivalofsecond negativeclockedge,FF- AtogglesagainandQ_A changesfrom 1to0.

ButatthisinstantQA was1.SoJB=KB=1 and FF-B willtoggle.

Hence QB changes from 0to1^.

QBQA = 10 afterthe secondclockpulse.

4. After3rdnegativeclock edge

On application ofthe thirdfallingclockedge, FF-Awilltogglefrom 0 to 1 butthere is no changeofstateforFF- B.

QBQA = 11 afterthe thirdclockpulse.

5. After4thnegativeclock

edge On application ofthe next clock pulse,QA willchangefrom 1to0 asQBwillalsochange from1to0.

QBQA = 00 afterthe fourthclockpulse.

 Classificationofcounters:Dependingonthewayinwhichthecounting progresses,thesynchronousorasynchronouscountersareclassifiedas follows–

 Upcounters

 Downcounters

 Up/Downcounters

 UP/DOWNCounter:Upcounteranddowncounteriscombinedtogetherto obtainanUP/DOWNcounter.AmodecontrolM inputisalsoprovidedto selecteitherupordownmode.Acombinationalcircuitisrequiredtobe designedandusedbetweeneachpairofflip-flopinordertoachievethe up/downoperation.

 Typeofup/downcounters

 UP/DOWNripplecounters

 UP/DOWNsynchronouscounter

 UP/DOWN RippleCounters:IntheUP/DOWN ripplecounteralltheFFs operateinthetogglemode.SoeitherTflip-flopsorJKflip-flopsaretobe used.TheLSBflip-flopreceivesclockdirectly.Buttheclocktoeveryother FFisobtainedfrom Q=QbaroutputofthepreviousFF.

 UPcountingmodeM =0-TheQ outputoftheprecedingFFis connectedtotheclockofthenextstageifupcountingistobe achieved.Forthismode,themodeselectinputMisatlogic0M=0.

 DOWNcountingmodeM =1-IfM =1,thentheQbaroutputofthe precedingFFisconnectedtothenextFF.Thiswilloperatethe counterinthecountingmode.

 Example:3-bitbinaryup/downripplecounter.

 3-bit−hencethreeFFsarerequired.

 UP/DOWN−Soamodecontrolinputisessential.

 Forarippleupcounter,theQoutputofprecedingFFisconnectedto theclockinputofthenextone.

 Forarippleupcounter,theQoutputofprecedingFFisconnectedto theclockinputofthenextone.

 Forarippledowncounter,theQ baroutputofprecedingFFis connectedtotheclockinputofthenextone.

 LettheselectionofQ andQ baroutputoftheprecedingFFbe controlledbythemodecontrolinputM suchthat,IfM =0,UP counting.SoconnectQtoCLK.IfM =1,DOWNcounting.Soconnect

QbartoCLK.

BlockDiagram

TruthTable

Operation

SLNo. Condition Operation 1. Case 1 − With M = 0

Upcountingmode

IfM=0andMbar=1,then theANDgates1and3in fig. will be enabled whereastheANDgates2 and4willbedisabled.

HenceQAgetsconnected totheclockinputofFF-B andQBgetsconnectedto theclockinputofFF-C.

These connections are same as those for the normalup counter.Thus withM =0thecircuitwork asanupcounter.

2. With M = 1 Downcountingmode

IfM =1,thenAND gates2 and 4 in fig.are enabled whereastheANDgates1and 3aredisabled.

HenceQAbargetsconnected totheclockinputofFF-Band QBbargetsconnectedtothe clockinputofFF-C.

These connections will produce a down counter. ThuswithM =1thecircuit worksasadowncounter.

 ModulusCounterMOD–Ncounter:The2-bitripplecounteriscalledas MOD-4counterand3-bitripplecounteriscalledasMOD-8counter.Soin general,ann-bitripplecounteriscalledasmodulo-Ncounter.Where,MOD number=2n.

 Typeofmodulus:

 2-bitupordownMOD–4

 3-bitupordownMOD–8

 4-bitupordownMOD–16

 Applicationofcounters:

 Frequencycounters

 Digitalclock

 Timemeasurement

 AtoDconverter