Download Next-State Logic: External I/Ps and Internal Wires - Prof. Shantanu S. Dutt and more Exams Digital Systems Design in PDF only on Docsity!
8 :9 12;=<^ >^1 ,?@-BAC04&$'!)DFEG1HJI^ DA^9 ?LK2-NM4-OM,PQ"+*SRT-OM2PLUNE
< > 1 ,? 8 ,$'?L1V"W-CXC;Y,! K[Z]^42_ DA=* "%12;=U * 9 3"%!)-a`bI,P
?Lcd2$%"+12 3"aef "+K,gdhdiWjlkVm#m n7opirqtsVi%uwv)xOx4y)iWj z:u=i)zt{|(;YK[1 $};~HLOknVm#zOkV ^otsVmBv)k2qpum#zq#=[j qpou:zotOkV
nVi%u:k|otsVm,k2v)x4v)k qpu=m#zq:Oqk i)om kViWjV Ws4
. &,2Kb!#" 9 *, g=m# WOk|byrztm v)n OkV av)xx4[jVm qtotiWk qv)k n7n i/otsViWqpm2zqpoots v}oy)iWjots OkV{ay)iWj{bk i+uTm qpo#
A9?9 JEGK["%04Z,;Y*, HF- sVm#zmaOqvc^0 12!^ K#xi{)m^ n qpm^ bjVm^ k[otOv)x^ #z^ #j2o^ ~i)zNu^ s ^ s^ ots m^ i
,Ok v}otiWk v)xxOi)
W |Oq^ W)m kJ3m xOi+u Yi)z qt 2xO #o y) du=mv)qtqtjam|ots v}o otsVm#Oz #j o/s v)qkVi mbopm#zk v)x
iWj o2jVotqt sVm av ^n m xOv y^i 4v
Wv}opmOq W)m kaby^otsVmm ztm qtqiWk "! k qpm##q k qv)k2n/otsVm$ak/nVm xOv y
i vB
Wv}opm qF W)m k[y^otsVm m zm qtqtiWk ! k q# [u:sVm#ztm$! OqdotsVm k[j Tm#zi 4Ok%,jVotqFopiBots m: Wv}opm)'& i)opm
ots2v}oOk)m#zopm#zq(&()
Wv}opm q=s2v )m(!+* -, qtqtj./mots v}o/ ~i)z:otsVmmbopm#zk2v)x Ok%2j otq# i2xm#/m k[opm n
k%2jVotq v}ztmNv)xOqtiav }v)OxOv}2xm) Vv)k n|k i)opmBv)xOqpi^ots v}o 0 Yi)zv121 Ti)ots3Gv)k n 543 v}zmNv }v)OxOv}2xm)':sVmnVm xOv y
n2v}otv 6 ~i)z v87 9121 Oqv)q( ~iWxOxOi+u:q#g;:=<9>* "? @=AB :DC6FE @=A 4o y2 #v)x :GIHJCK E @=ALB aOkM: GIHNC8* @=A
oy O, #v)xP: GIC#HQSR ? @=ALB aOkM: GIC#HT E @=A '1FOk2v)xOxy) Vv)qtqtjamots v}ootsVmBqtybqpopm#+#xi{|qp{)m#uwOq$U/k q#
A
B Q C
Q
Next-State Logic: External I/Ps: A,B,C; Current state bits: Q0, Q1;
y
x
Master FF excitation inputs: x, y
v M, qtqjaOkV
Cots v}oots m( iB2k v}otiWk v)x4xi) WVOq Ok iWkVm2xi t{rTm#o u=m#m k|otsVmNqtxv )mBv)k n6 v)qpopm#z 0121 Fq
m) dotsVm opzv)n otOiWk v)xdi)z#xOv)qqt #v)xM iWk2
WjVzv}otOiWkPt dnVm#opm#z akVmots mK#xi t{WTm#zin4& i)opm|ots v}o^otsVm
#xOi{Tm#zinqts iWj xOns2v )m/v X?LY qv" ~m#o yZav}z
WOkW m) 3Tm X?LY )ztm v}opm#zots v)klotsVmaOk V j ots v}o
Oo0#v)k7Tm)[]\sVi%u y)iWjVz:u=i)zt{8#xm v}zxy) P
=_^ kfi)znVm#zopi ztm n j m^otsVm#xi t{Tm#zOibn4 3q2xOOo:otsVm iB,Ok v}otiWk v)xxi)
W ^Ok[opiro u=i62v}ztotqqpirots v}o
ots m`av a2v}otsQnVm xv yqBOk otsVm ou=i2v}ztotqBv}ztmaztiWjV
Ws2xyfm bj v)x `bxOv maots m qpoc2v}zoNv" ~opm#z otsVm qtxOv+)m
121 Fq m) Ok%2jVotqdopi otsVm 2zqto'2v}zto=v}ztm ots m:mopm#zk v)x3Ok%2jVotq-d BfeKBhg v)k nrqpotv}opm ,otqM3(i B 3 cj#t kv s
iWj o2jVoBi :otsVma2zqpoc2v}zol otsVm qpm iWjVo,jVotqc i)ztzm qTiWk n opilotsVmu:ztm q ots v}o^v}ztmWm#jVofnlby otsVm q2xOo
y)iWjTm#zf Yi)z 8 Oq v)klk%2jVo opi vrj k [jVmZmav)qpopm#z nK7;9121 v)k nm v s iWjVo2j o i v8av)qtopm#z;7;9121Oq
v)kOk%2jVo=opiaotsVm k2n82v}ztoi otsVm( iB,Ok v}otiWk v)x4xOi)
W }'1FOk v)xOxOy) [otsVmBiWjVo2jVotq i otsVm k n6,v}ztov}ztm
k%2jVotq/o p opiaots mNo u=iqtxv )m(7;9121Fqots v}o:qtopi)ztmNotsVmBqtotv}opmB2otqqr3(i B 3 cj#t
s^ xm^ v}zxy7nVzv^ uGotsVmt^ it2xm#opm/qpm^ bjVm^ k[otOv)x2#z^ #j Oou^ v)xiWkV
^ u:Ootsfv)xOxztm^ bj ztm^ nv7;9121^ qXztm^ qtj xotkV Yzti
ots mBv}Ti+)mBq,xOo y)iWjTm#zf Yi)z 5 Yi)zotsVm
W)m kv iB2k v}otiWk v)x4xi) WV}
1 FOk2v)xOxy) nVm#opm#zhaOkVmotsVm:ztm qtj xotkV
q#xi{tTm#zin] i)zztm qTiWk n Ok opi otsVm:v}Ti+)m q2xOOoFi 3ots m$ iB,Ok v
otOiWk v)xxi)
WV})k m v} Wv)Ok4 ,k i)opmBots v}o otsVmc#xi t{8Tm#zin|qtsViWj xn|s v )m^v X?LY qtv" ~m#o yav}zt WOk \sVi%u
v)xx4y)iWjVzu=i)zt{8#xm v}zxy) R P
R
b A=Kb!#" 9 - /1 i)z otsVmc#z #j2oqtsVi+u k 3m xOi+u u:Oztm qv}ztmBxOv}Tm xm n|k|otv)xO #qtg
v (1FOk2nLv)xOx=opm qpo^)m# opi)zq` ~i)z^m v s Yv)j2xo iWk2xyQiWkSotsVm|Ok[opm#zk v)x=u:ztm qKrU B B j qOkV
lotsVm|c1V"'0D
!+Kb ! 9 " 9 9 L? K["%0*4Z & i)opmots2v}o=ots m#ztm u OxOxVTmvBopi)otv)xTi q[ Yv)j2xotq# bo u=i/iWkm v s|Ok[opm#zk v)x,u:ztm)
^ P
= s iWk qpopzj. o v 1 2&;"^"+1;YK Yi)ziWk xOyaotsVmNOk[opm#zk v)x3u:zm qqrU B B i otsVm(#z #j Oo=v)k n v)q:nViWkVmOk
#xv)qtq# VnVm#opm#z akVm v/? 9 9 ?L12;"+K[! "^!+K" Yi)z=iWk2xyaotsVm qpmOk[opm#zk v)x,u:zm q- Yzti ots Oqotv}2xmj qtkV
Bopm#s
k2O[j m qqtVaOxOv}z opi ots v}oFj qpm nu Yi)z v b-^ Lopi sVibiWqpmv ak Cj qpm#oi b-^ qopi; i%)m#zv)xOx[otsVm_aOk[opm#z aq#
m#ztmotsVm opm qpotqv}ztmqt OxOv}zdopib-^ q# botsVm; Yv)j xOotqv}ztmqtVaOxOv}zdopitakopm#z qv)k notsVmq iWqpo i mv s opm qpo
q t;& i)opm^ots v}o otsVm zti+u:q i dots mc v)j xo:otv},xm qts iWj xOn7iWk2xy|TmNotsVmCopm qpo)m# opi)zq ~i)z otsVm^qt[7Ok[opm#z
k2v)x Yv)j xOotqFv)k n^qtsViWj xOn^kVi)oFTm v)xOxotsVm i 2Ok v}otiWk2qi 3otsVm$EOk2jVotq# \VsVi+u v)xOxVqtopmX2q #xm v}zxy)' P
x x
x
x
1 2
3 4
f
x
5 6
7
8
10
9
Internal wires
External wires
1 2i)z y)iWjVz iWk[)m k m k m) i 2m q:i FotsVmc#zh#j ov}ztm
W)m kOk7otsVmc YiWxOxi%u:OkV ` ,v} )m q#=hdiWjfkVm#m nopi
n m#z)maotsVmopm qpotq] ~i)z mv s Ok[opm#zk v)xFu ztmt v)j xoNiWkLm v sSi otsVm
WO)m kW i 2Om qNi otsVmK#z #j otq` j qpm
iWk m; i by Yi)z=m v s 8 Yv)j2xov)q=Ok n V#v}opm nv}Ti+)m mv sr,
WjVztm) $ 9 "+K H3*,&$a 12?LK *, S"%0K !+0K[K["
$%3 3" c1 2Kl12 Z6!+&? 9 " 9 " 1 2;Y, 9 "'0 H,*3&$ 1 2 !^K[$!+0K[K["W
E
x
x
x
x
f
x
x
x
x
x
f
x
U
Q 3
x
x
x
x
f
x
x
x
x
x
f
x
