8.1 513131~1

aa~s~afi~a~us~oloiftdr::luaPia~naiulunaaGa~olai lua~ol~OaGa4;l')~us~olai rPluaad0dsduaPidfln 'laru?al5$ (counter) %flLma~L~aubya (shift register)

a::a~a~Onuk4la~us~olai~in~i8~~1run~an~~a~~flaa~1sCu ?iin~wai~~nu+aya ~m::iauQu 7 ananaaGaaaiviimu l9u~~mrfiariFlflla~usrmailIlunis~s"ia~~ ~ w ~ r u t A a l a a r ~ a i ~ r i ~ a o n u d b i o a n ~ ~icau~un~iun~iauaaW"adi~~~1irr f iu l~

rd u ~"ro~mw"nannaia rfiuld 'luuwtq::ndiabaaqsu"ua~mdia 7

8.2 3aorhlnrglunoaituu3saanndu Binary Ripple Counters

wqs6 magiuaaaaiia~dmula'lua~~~~aGa41~~usaai ~rda::Eu~nA $1

tjhaqsriu vii~iiirnis~t'uvlia~n~ ~assriu~ruuffiu~n~+~dfla::il"u duniiwss iiur~uur::nannih

g, 8.2.1 ' L ~ Q J I ~ I I ~ ~ ~ ~ ' P ~ " U O ~ (Count-Up Counter) ?a~niu~u3iulu;d 8.1 la' T ~Fiudaau 2 ih adnsnQn~Ad~iitjiu~n T

~ddnkrnaidFiudnau kaidyn Q ua:: B irolsmols~+iunirrau 61 Q ~awssn r (An). ij s::~Pluolssn o 61 Q ~3uarsn 0, ij .;~::~~uolrsn 1 ( idn)

ClNk input,

- Q

tbl

@ 8.1 ' Y ~ 8 4 ~ ~ ~ 4 l ~ l ~ ~ ~ S ~ L l J 1 1 2 fl1Fl (two-stage)

0 Q

T-

- z0 stage 0

(dl

T 5 Clock input

I l o J Suga toggles

on tnilino edw

311 8.2 ain~m~n~riajoo.n~ilsriu

, '*

n~ianju~n~iI~~~u~aa'~~^~n~n~~ia~~duu~niu:~d.jns".j~a~~.jnn"aer~"ad -n~ 8.2 (a) ~ ~ a n ~ 8 t ~ t ~ i ~ n ~ a n w unewifiwn Q Iw"8.j~nniidGu~aau~:w~n1nai . auaurm ~~af i tmi irmunu (trailing) 0~.~8y[111~nn"an ~ a d a d t ~ t ~ i ~ f m ~ n ~ d d u u qin I Id o w n ~ d 8.1 -a:duiimdvjn Q un.jd6u~aaunid i (A; EuniiAGudnau hA 20) ~ f l u ~ u ~ w daldwin m a ~ ~ f l 1 ~ v ~ n a 1 ~ ~ ~ 7 d 2 (B; duniivEiudaauoi?d 2')

dGudnauGY'?i?Gt 2 .~:111duuamuada~ai4~n Q ~ 1 . j d ~ m w 6 7 4 I ~ ~ d u u - ~ i n w s m I

Id$33lo R~iiu~&+ain$s.2 (b) L ~ ~ ~ ~ J M ~ U ~ ~ C ~ ~ ~ V ~ ~ ~ ~ $ ~ ~ M P I ~ J ~ G U ~ ~ O L I

A ~$rn~an . j i iA~ud~au B ~:n~n~nn~~~nu~iuua. j~n"anw"nd ? ~ ~ ~ d r l f i ~ ~ l a a u A

.~ariumuyiu~a~djiu"udi6t~u"~3u~~n ru:dGudaau B iiu~auylwda~3udiniyuin rd a dqn n i n . j ~ ~ a n ~ n i ~ r i u n n " a ~ ~ " a n n ~ ~ u ~ u ~ ~ iisnin.j 8.1

.rail.iu'u 4 ninluld 8.3 imiaidni.iiiu6cmi~1~ 8.2 qnn.iddainalumin~~~a onmciinisrd~uunnmn I 4 o r iwn~f l~n in~naf ld~c4~~4naun"m~d ilin"ms6

Y d . jmm~~~dui in i . in inma~~a~nind 2 O ilr~fim~uynn8anGnn' mnA 2 l ninrnai Yn 2 n k n r i ~ d mnd 22 nin~nahn 4 Gad rSu6~ ~~~nid~du613uni~anr~uu"u i i~i~l irmac wn'yndnamn~acn"~i3::~~u~du~m rdu wiviynaa.jmnd 23 ~ilu63YSnmi 41 8 ~airiynd 22 YS9imid1~4 ~ain'yn~dcni~ 2' 9M"di 2 ~ain'yn 2O1$di ill anlu: g1u~a~aa~?~asriu~1u1.ind1u~6~ui1~u~1u3u~nduyn ~&aind~ca.iu"uld6.jdi 1 1 1 1 ~ J L ~ U ~ I ~ J ~ ~ ~ ~ J ~ I T U ' U T ~ U I ~ 4 mn ~wynfind6~id1dilavii1~"3~ila~"un~u11~ ~udi6u6u iia 0000 ~l i l~. i i l~ni ' i$~I~ld

clock input

&rug0 counter input -PC-

Input Pulscs

0

I 2 3 4 5 6 7

f4

9

10 I I 12 13 14 15

16 (or 0)

2' 2? 2 ' 2" Output Output Output Output

(Dl (C) (B) (A)

0 0 0 0

0 0 0

0 0 I 0 '1 0 0 0 1 0 0 '2 0 1 0 I 0 I 1 0 J 0

I () () 'a ( I 9 I 0 0 I 0 1 0

I 0 I 1 0 '1 0

. I I 0 I I I 0 I >

I

: > 0 0 5 0 I >

\t. I I I 1' output I 1

2' output 0 $. 1

2' output 0

. a cl a

8.2.2 24 Q%fd"fl ddflflfd"fla4 (Count-Down Counter) homda ~airiyn ae~rllurlnauudnzni~'bw"8~n5n ~ n a i 6 ~ ~ ~ ~ 1 6 n i ~ d a ~ d

13;wn~fIu2~lniu~~uuGuaa (Guoau~ W) ~ a i i ~ w ~ 1 6 u ' ~ ~ ~ ~ a i ~ ~ i i l i n ~ a i M ' ~ w Q am 2~wGu~~uud k d u 1 6 q i n ~ 8.5 L L ~ Y P ~ V J 8.3

T e

5 'a I-

,P mr

T 9 -

(h-

a - F 5 A

- a

2O nags 2? rnw 2' nrge

T * T

,Z .

Clock 4- input

pulses

1-

wiv~ 8.3 wi~?.~~Xu~la.~a.~q'iu"u 4 nm t~uui%uad

i u y n t d

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

b u u s n ~ m u n i s ~ ~ ~ n a ~ l s r i u (boiiyn o ae4d8udnnuyn 7 mn h s s n o)

i v n ~ d 6 a C ( 1 vii1fidGudno.u A M"rnmeBin o ~ 3 u 1 ninma4Cad~dGuAnau B ~ i ~ l i n ~ i i y n 5 an.sdGudnou A &~dioumn i ~ g u o d a w d i ~ r i i l i i v l b ~ n n u B q n n i n m o i ~ d u h ~aiviyn 6 ao4vl8udnnu B d~c lu i l in 1 d u o iddninmo4 d%Jdno¶~ C $4 6 UBJ C l d n k ~ n ~ ~ d i j u d n a u D ~ Y ~ M B . I L ~ L ~ ? ? ~ vii'LA6u"~1~3~ 11 11 64~1~114148.3 iuyn~lnA6aOiol~~:n%~no%Gu~a0u A ~ ~ o . ~ ~ i n & l . j ~ i w ($4

a d 'L3nkmsiABurlaau B) awruid~uuqin o ~ 3 w r 6 d u v(GuAneu B c imr D qr C v A 2 ~~n~duldinisrdduwaniu::lu~1n"ac1w'a~wa~ 2 u nisGu4c~flu i I l o nisU"ul:riuu

naclwfinadnu q An: 1 4niuynwkdr#iuiiiacl 7 ~x~Cui ihunid j io in 'y !n o i i l unkms i juyn~~dAGu Anou G7n"m q l d u

a4ilsriu~~uus:nann8u ImdS~iiu(.raownn~inin~~aou~iua~~~nd d.RniCIw aa~sU"uauuriu:u aciiiiilfiioiviy ij tllunin~nn%~ddGudnouR"m 7 l d s d h n ~ a u a4lsU"uttuuU"uno diwiud~iuv(nau44n^sn~noin"aauuan~~aaourii (leadingedge)

a ~l:vii\jiu~1~17\jh~n"u~~uuu

PH 428 217

D c B . A

0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 2 . 1 0 0 2 0 0 0 0 1 0 0 0 0 1 1 1 1

. I

, 6d"su~Acluriimagiu~u

0 (w% 16) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 W ~ O 16

15

~ ~ F ~ ~ C ~ F J I ~ I ~ ~ ~ L ~ U ~ ~ ~ ~ I L C I U ~ I ~ L ~ S I ~ ~ B I L L Y Y ~ ~ U ;aiinisu?n tdd+~f~u A a ?ail5~u~Luu~u#u ~~a:viinissl~~ w a ~ ~ ~ u ~ a i l ~ ~ ~ ~ ~ u u ~ u n a du qailsiiu 6 rnn nulm

t: d ri~fia i i i i I I M% 63 ~LAII~IURU iinailsCugninn ilinuuuw'nd 9 87~iiui Cu t: Y d ilsriudiI6~ilu o o i o o ~ (nia 9 ) dannuumuw'nd~biuiZn 9 67 (aassdfiil:~uiaId

w A a wnduin 9 ddbi o ~ o o i o (M% is ) .railsdudiaiinuin ~du7agsu?n (adder nia accumulator) dirn%uu?uw'nd

8.3 ~~orwiiluqnic Modulus Counter

?ailsCudnciiabnnn"7lu~'7ia 8.2 ifllM"inisCuluuuuwn!m~aa 2. ;a 4. 8. 16 Q w rnr ~ ~ I ~ I ~ ~ ~ ~ I ~ ~ ~ ~ I ~ ~ ~ I L ~ M ~ L T ~ ~ Y E ~ ~ F J I ~ I S ~ F ( ~ J ~ J ~ ~ ~ ~ ~ ~ ~ C ~ ~ I L Y ~ I I S ~ I ~ 7 ~ 9 5 ~ u

d u Y nuu0I5auVjn q 10 $ad ~Llr~laail3Ih~lJ (decade counter) ~~mdilsC~yuRu (base- lo counter) M ~ ~ ? J ~ s ~ u ~ ~ B J ~ - ~ o (modulus 10 counter or Mod-10 counter) fl l ' lF(%d?dil5C~

~u~~~~ifloi~nhnidaunn'u~nd~da~M"?ail~b6~~~1~1udi~'uui~di~II n?o~~dmrngailin Cl'l6di~u~iudGaanis~~n"? ~~n:ni~#?ails~nn~da~M"~n1~~'~l~ia~ii&ud6aanis %n12 ~nd6il:~&ncii~daId

8.3.1 2 4 0 1 l h l % ~ ~ ~ 8 ~ n f i (Fedback Counters)

d i n s ' ~ d i ~ u ~ & a ~ n 1 ~ ~ : : 6 a a ~ ~ 4 ~ u ~ u d 6 u ~ n a u ~dafi i~f l~nisCudi~6uinn41 diCudGaani3 ~~n~ni9ilaun~ufiilM"ini~ar'uiia~iu~a~iI~ ~ a t i i a ~ $ u n12Cu 6 GaJq# dRudnau 3 didu?ailsCu (~aGd&~fiad z3 nia e 61) Tm~lbinisflaun~uiuldaCuiiu dl111 2 61 ~ a i 2 nuaanilin e l&wnifltcdiiiu 6 dl 74ilsCu 3 ni~l ' i lsj i4n~hii o ~ $ 4 Fnn 8 ~d I L ~ : ~ ~ ~ ~ ~ ~ I ~ G Y ~ M ~ ' I . J F I ' I ~ ~ I L L ~ J ~ ~ B 6 (divide by 6 counter) il:nGuddl 0

nnjilin 6 irn~(a;sa~~nisU"uI~d

k~l~~Idi iu~ud~udnaudlQidiu"u 2" di~~mnniii iu~uu'uG(6~3ani~ (N)

~ ~ n ~ 4 1 w ~ d i C u ~ i i a ~ d ~ ~ ~ n i ~ f l a ~ n 5 u d i u ~ w ~ i n n i ~ ~ m N k n u :

0s 1 Q-crutput 0

Imoehanga ldvrncrr count

&output going 1 to 0 of 2'

(b)

@ 8.6 1595%l Mod-6 \ ~ d ~ ~ ~ T l % J ~ ~ i l ' I ~ ~ l l ~ l ~ ~ i l

I . ?dils~u6ajl+7'u#o81 (one-shot) ~ i a ~ m ~ d 4 ~ i j n ~ i u n ~ i ~ i i a u n ~ i ~ ~ ~ n7iu nii~aadm5andCasinKamg~qm ~lndil1n~u~aOild~1qil:: IM"ddqd8~~ii~ld~~~~&a;0d

A d ( ~~~ailsiiu~i~mwadu~~~di~~innis~~~auau~dkdiiiu~arfiuwnnnw'nd~aun~u ~ d u rj,dilaunGufidn?r~~naiqdils i psec ~kilinw'nd6u6~ 84~~7.silsriubiaa

d m~isn~ii~iu6~un~iun 1 MHZ (111 psec = 1 MHZ) ~dMq::nn-~LhudLLn:nisiile6adm q~qsi~#an ~ ~ u f f ~ ~ i d 6 a ~ 6 1 6 ~ ,

4 4 8.3.2 ~qo~uirr~.rtrnrhniun'i Jfl~d~uudM'i~'tdda%g~uara~ (counter

Reset For Binary Equivalent Count)

iinisjuwddun~n~n"lv~aunws!aa#~]f f i a ~ a a ~ a d ~ s ~ " u ~ u ~ ~ d ~ d ~ m i 3 a u n n ' u A d( fi~o~#n~snamM'Ecassn~~n::nis~~#n ~~uuddi~~ilsrwuvu~~iuFii~urna~iuda~ LL~:

i l ~ ~ ~ ~ ~ ~ n " ~ i l i n f t a ~ ~ i ~ " u 4 f i a ~ n i s ~ ~ ~ ~ Tmuni.inamsfi~6qo~nn

NMLR>LLUIK@S

Nf1 (u!&~L) L, P PM~O L~R>N~~~~\R$u~~~P.L$~,L~uMIsEo~u~~ P P wrn 6 kn>ULOP$MgEyRpPy

neupngp L uiropu~pg+ uenurcgnu~~unpap n -I np~utnine o =

n~l~~w~ou:bu~nn!? nt n (0101 = KNL~) n O$ n~n>~pnh+1:bp1\@pn>e~ .Z

(1001 =

n>Lp) 6 $~>E~~BP~~L~R~~~L~~LL~~~E~L~~>K>~~EL$~~~~M~~~~~ w '2

nlzln>rLun@m+i:b$~@,sMn,nrort (oooo = v~p) n>rbrtupgrLunt$ -1

~P~~~LUIJL We nlzlnernlo I ~pnptr~rluprtrgyn 6 ry o pip L nnrin~n~l Pn PXP

iV$LU#lP~~UUL~L~t~11 n Lj) 91 P~~1\L~~~P~~~I(U@U%~~11~~SOEL~~~LOEt @Np1

uuyukpnln>ntn~o~y nn$~fiLg~buin\n>~p~ rs $nl or -POW ny~rt >

3

p:~iuilinmint 8.5 ii ciiciunn 9 (1001) I d 6 10 ( to lo ) il:~iiniiubiam: d d n'aunilrs~#dd~ih o (0000) ~~uu~nneIfl~aiG+ndu 1 iluns:~.jciir7Y6cii l o iiriu

A a i o i lmnoansm'~~au~#~uqn~ssn'~~~~du " I 1 nunddiriu i o dodiCu ~3u i o ~ruumn il:~rn+iqn~~u~lssn o tiomm~duuilin 1 rflu o iariIunin~na~Ifiriu<u#o~1 44

ilil:wCGndrwu 7 l d i kv(Guv(anuynC9 i?mlI#8qj~i~*~in 0 rwn:dimsmdn6 aa~$iu~fiudig~ ~~hn. j~msrndi~i~us:ni i~~iu ~?niaa~7"u#am nsfihv~~uvlnau~n d a 5L+?SYl&3~'1~~8qj~1tUd1dl (active-low clearing) ~kdaa~<u~amdiodu13wa~~u~dil : :

d w d C: d i~#nv(Buv(nousr?nnnqn d~d~m-~du: ~(iiurlnaunin~ 2l LLn: r3 iviiuunqni~3n A a udynv(Guv(naui~4n LW ~~~u~n'nds:n"uiisa~~nisu'u~~bi 6u6u nn::&qudir?u oooo

3ailriiuaQni~%MniX~1G#i]~~uz dr::nir fla I. diriuduin~uilusr~fin~~at~:n'au~il::l11r~~~iu,vi~#n ,

2. 3Jil7flEId#<~#i]91 L L ~ ~ d i ~ ~ a ' s l ~ . j ~ ? ~ ~ 7 ~ 1 3 ~ ~ d 3 . j n 7 ' 1 ~ 3 0 ~ w ' n ~ ~ M ' L ~ ~ 1 ~ ~ ~

8.3.3 w o ~ u i r r Q a B M ~ u ~ 1 4 (Direct Reset Counter) d a ! l l d ~ ~ u ~ ~ a d i ~ d i ~ ~ ~ ~ ~ s u ' u ~ ~ m ~ ~ ~ n ~ ~ u o l z ~

i ? J B S ~ U ~ U (Mod-10 or Decade counter) ~ o l l ~ ~ n l ~ ~ U d l 6 ~ ~ l ~ d 1 ~ ~

D C B A

8

J - 1 c - Q 0 J - 1

MEi CK MIS CK- M/S CK #-.l, MIS CK-2;

4; ulll 4 5 Kll 0 1 2 3 4 5 8 7 8 9 1 0 1 o r 0 1

l nput p u b

@ 8.8 ? ~ Q ~ % L I ~ L I \ $ MIS JK *I~%~*IRDu

a aaesiiunn (Modd Counter) ~ 9 1 1 ~ l 4 n ? ~ i i u 6 ~ ~ 1 ~ d l a u

.nnwinanisr?lr e:du<i A L ~ u ~ ~ u w ~ I u u ~ ~ u L L ~ ~ : : ~ ~ ~ w ~ " ~ ~ B n h ~ n a i vlnmkd A iddouqin 1 flu o un~?udo c $74 1 l a B nanniu:ir& ABuAnau c n a ~ m u : i ~ ~ v ~ n n k d A ~dLouein i ~4% o oniTu&a B d u i ~ o ~ n m d i f i l f l u n i s aanLruuaa-~s¶iu Mod-6 lmol# JK Ai\ydaau6a:d 8.9 (a) I P I U ~ ~ ~ ~ R ~ ! U P ~ J ~ ~ 8.9 (b)

6 1 3 ~

C B A

'a J 1 a J- a J-1

MIS CK * MIS GK -1 M/S CK E

B K - 1 i i -5 K - - 1 a K-1 -

C B A

- Input

0 1 2 3 4 5 6 b O l Input p u l r

$8.9 94973U Mod4 1% MIS JK V6UdFi~l.l

7 4 8 3 i i ~ 7 (Moe-7 Counter) ~011514nl3~lI&4Vll¶4 8.8

Vll514 8.8 ~ l l 5 1 4 ~ 3 ~ ~ ~ 4 7 4 8 S u ' ~ Mod-7

0 I 2 S 4 5 6 7 (or 0)

Input pul-

Synchronous or Parallel or Ckscked Counter c Y .r~qsriuuuuauiu~~u~~ssiiuA~n 7 v(Gv(nau~nnin tnaswsauriw airiir

x Y waa'~daad~dn:~ftudna~auadn'u~nn~1~~u~ (gating input or synchronous input)

rr 1 uwn 1 s n n d n i f i r ~ l ~ i c u u d ~ ~ ~ ~ ' ~ ~ u d ~ ~ ~ 3 65 \u?o~sriu~oanuuu6

8 i u rl uun 2 L ~ U U ~ J I S L ~ ~ ~ R U V ~ ~ U ~ ~ U ' U ~ ~ ~ J 6 dQtnislk&dld 8.12 rr i run 3 6uumn~~d~.s:naudi?u'i(n~u:i~~~~'u nmu:ouinol~m:~u~n%adrl~~vJnau

nuuh.smihd~n~8on , JK v(51jv(nw n n m i 7 ~nii~nnt~~nals~wiru%ad JK * ~ b ~ n o u p i ~ d .

fig 8.1 3 (b)

t! 4 run o dew~rsciuuuuauiu .ba$u 6 d i m ~ ~ d i a ~ n i d 8.1 3 -- (c)

C 0 A Clock

,+

pJ 8.11 ? ~ m i u 6 uuunuiu (a) @ i ~ t n i 7 ~ ~ (b) niiuad~~iw (c) awuniwarsmssn

8.4.2 n i~aanl luu?~~nPt , t 10 II'UUSIWIM A

?J?.ilkI 10 LLUUDUlU (parallel nod-10 (decade) counter) B J L ~ ~ U C ( Q ~ I I ~ ~ ~ ~ % J r r lv lnul#AGuAaau 4 83 <mlflMiCu to ~ i r m o ~ n i 5 6 d 6a

duuaam6~$ 8.14 (c)

aoiurilil?Gu D(t) C(f) B(t)A(t)

0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1

-

aoiuzilu1~1~1 D(f+l )lC(t+l) B(t+l)A(t+l)

0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 . 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0

-

~ U W M ~ M ~ ~ U A ~ E ~ L I

iJD(t)K (t) D

i

JA(t)KA(t)

1 d

1 d d l 1 d

1 d d l 1 d

JC(t)KC(t)

0 d O d O d O d O d l d d l O d O d d O O d l d d l O d d O O d O d d O l d d 1 O d d O d O l d d l d l d O O d O d d l O d O d d 1

J&t)KB(t)

1 I - L - Clock

8 , s ~ a o n u u u ~ ~ ~ f i i u ~ m ~ u ~ a ~ a u i m 3 Cn d~ubiufii 5 uas 7

8.9 s ~ d u u ~ n i u n a c ~ ~ ~ n i u 12 sQmi~4hTmuns.r