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l. {?0 points} Use the rules afpres*icn to its simplest
s$fil
ELEC 22$s llrG'rukm"wm#ww w KffiiLi l SPring ?,0fi7Test
#1Boolean Algebra*f pr*ducts fcrr:t. {xtached} ta reduce the
fo$cwing ex-
,i -" t.+. ti*" e; i*' f" -' l'' +i+! r''Ee i"Er::'+'i; ,r"i{,i}
*. ,{ * I + il *r, * *;" i: -. ,*,t:.i; -i' i: ,n' + ,i."'*i d\
e-**",-..,*.-,.,,:.,.*'-.*****-",--'*. _ " +_.-,*ffi*J
J-**b* {F -+e i{'.eH* :+5 ig+ ei =s*rf *; {t** ii{} * #F} + f ,{
* i: #
* '..,_,i.;1.'..8
ftd"t\?* jJf !}*il/ I't*" L*'
'', 14G*, i+*.-t ,i 11: .,-:--'l *:-- .i r- i:i' f ir."" :-.
-j?r.I 1. 2 "^,. isi ,o- : *) ,;)
*'. :i? f-,-.,r _ .:| j?.&.4.. ,:::i.4.:i*:.\+
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2. (") (15 points)Use a K-map to findF{A,B,C,D) . ABD
4t: ri i ini ii! , rl :ltt:t ' ;.:, :
a minimum,f,um of products {SOp)+ trc +{AF+ Tlc+ An expression
for the function.:"''*,'; ' ;_ -= *: .t'., 'i , _" ','i - :_- , "
:i ,_
r*- t;-l
;
(b) (7 points)Give a circuit diagram that impiements the above
function using only NAND gates.
:,:
I
:. .\t.!; :-.r l":. :'F*;?j' it
i --.--..'-'
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t 'Use a K-map to find a minimum product of sumsF(A,B,C,D) _ n
M(3 ,4,7,12,13,14). D(1,5,8,9,15) {POS)
expression for the function
F+ l'tr-- " j
'.' t iiiit'Jti81-./'; l: E
; __,1-.--+ 1.j :r: r'1r i i;uJ -/*: *i+"*: ! ,j :\.:'i I "
,a t{.'efii gi+ i\,1t"+ 11.ri Fl -1-/
.'nt L\ltL: I Yl*J'-: I r*r !;{!3i 1:/: t .-1-^-i ; u-'
i--jsa'r:
J : r._.,- ::
t*j i.*':', i.*r.- *n, ,r,1 +{? i i,-{ 'lJ i ij'*r1
a\
(b) (B points)Give a circuit diagram that
'::, .
s--F*l,JJ
.." ]g -,
implements the above function using only NOR gates"
1^i:,; \* t fr.IJ *j:J*'*--=' : :'z4 :'"e' is,"""-"=-=**'l!'t
o--u!:t .*t *ts !e_',:: , r+ --.ss+
rj_'':.i" ,tt i":. a{{r-';'-'\j.i
;*t'?'
{
it ^\ it#.1I' i-f' i',, \ '::,,'"-* ,.L,, a'.r-*'**
#
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,i*Jr''
4.,f9*,points) The ?-segqqe 'di*play shown is to be used to
disptay the score for a,,garaewhere the score can fa,age.fron
&5, i.e. the digits 0,1,2,3,4,5- The display is to be drivenby
three binary signals A,B,C that encode, in binary, the number to be
displayed, lvith Abeing the msst significant bit, and C the least
significant (e.g. ABC : 011 represeats:thedigii 3. Since a va.l
'sioie must be 0,1,2,3,4,5, ABC codes 110 (6) and L11 (?)
represenidon't care conditioltf .,(i) Specify the,? functions
a,b,c,d,e,f and g required to control the 7-segment display fromthe
inputs A,B,C in Minterm form. For example: a(A,B,C)*
Xm{0,2,i,5).
be implemented using a single low activeTby to minimize the
number of inputs to theend gIAND or AF.ID gates. You da I{O" need
to show haw the rerna,i.sing functions ,fare inrplefileated.)
i:j ]:it1lFti
.*
'a
4:-";+.',-i:*.t
l1'if
;,i, "f
rffi""ir* :ih*\ t
AtsCL?:*Frs
?i. ,i:. ij''"1. i ;rr i'l- i i:.'-:-:\ "'-'l
1" i..'*
,, ' ,"rn!O'"...i iin!1.+J: '-..in ; ".., i.:. i, t;'_j:!!.
,"'ri i;e.-"i,' '. i
. ,i ,'' ,,: ni. r:i. ji.r'.i i ,+::.. ,: : i
" '\'* i '.#r-- f 1 :
il g,.,,"..Rqs$'ir. gj:iid
*,l^l . I fr|CIl ,l t(--l I'l- 1-er:trq)
ffit'.{ rt *- i:, i- \ru . * *t
*T":**^=i : .'iri fi{!
.:-;i i r..---J \i3!
-i ---'Ji; - *'--l-.--"-'*-ea; F f].
ii
:#e
{}'f-"',l
:
:t '...-..*,... ..."..,tiI
J*i ..-"-: ir,-,, ::)---.-.,ir' ,1 ' 1, ' "'"tt ''.", '''
-t::le:' ::::!.!:ii::...-,: i!.,:: i.r..i:r.,_ - :
.Fl tt4:at*** =-l:',.=.r::.1
:: s;.,r,\! ar!+;
&*l4e{'3
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s.:r.t
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#ELEC 22OS DIGITAT ETECTRONICS
Spring 2087TEST #2
L. Find the state diagram for a synchronous sequential circuit
(ilso calted a finite statemachiae) that detects the input sequence
10101. Sequences may overlap. For exa,m-Ple,x :
01010101010001.010010101, - obod6-lilToi oooooooooilotl
':.1'r ',';' E^., t*"1-*,'... 1 :-t;l'ii* ,+""tt ,.*-if '!
1r'-ittid{"-*j i i.*.-'*- o'Y' l t *!' "'t " 'rl ' *"*'' .; lf' g
ry"''/* art
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2' The JK flip ffop ia the figuiJis positive edge triggered,
while t-he D flip.flop is negativedse trisgered' compleie *n.
ii*ios ai#**'iy liu*iog tr* *oJr*** of signals
ClackCLR
t\\*J r\I
:'.'t'-,.-
%
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' 3;' $*e a 2-to-4 decoder, basic gates, and edge triggered D
ffipffops to design & 4-bitshift registsr msdule that performs
the fallowing5s, 'Sr.Ss,Sl - SS:SoSr : S1:Sa$r T 1*:$'0,5r -
LL:
$yn*hrs$ous clear (all ffipffops set to 0) ' ' IShift rightShift
leftTwisted Ring Counterc?ff-
-"F"ir:j. ;::.: -4{-,.. 1:.
* f*r4 Fti?siI .-.i
tf. Y:i ,,j".""4tt\
',,,'S4 },,,,,,,",,,,.",:1
j,#.': t4::+:;!!-':t;1:lc
tr%dff
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i,i
;:l_!\:i I
A*!lt1t, .4 .i
i.: L.1i t-J !'-1 ;v' 11'e. i i\*:
tt!i
mww$$ffi*o*,,r"++.,*''. . *tf-.. *!-*t.
t.. t. -'.., ,,... *. .. r.l',,t 1. '*': -*%.i. :: ^= '.a.*:..t
.:i!:i.'::s, = J'Ir;,,,:'',t. . '. ,,,? ,:"*F1. **F
'a. .t'Fi-g *
'f12"{-tft:'f,
3K
A_ {}SB*01Cn-10
j: : .- .:
a.l.* zl.l ,, :S .F'" E'-=F-'.-t.{Ev,j_z F+ Tt.s*Hf1
zjgt"1+*%*,.4
kH -r Y, : K\;-i " - f i
_ ...-:-,; !:':i *'.i'..:.".li.i* , ri l,,i.1aE4
't!'-'.-$' ".
jt* l*,.e"-.*sniiu'ltgi *-;-'\-",Li f *'.*.n -ri. i *i;1g.'tiF
z.l\" =;dlE* Li
+ ..'u!r:;j:#;+l %:. : .,i:.r.,*!--;. j:.:t. ..-..
j..:fln:IJltftf 1*? ,,..'-t,t':
Clock.jr : H*t
3,;:I i-+:l ;: *.-L-._.--.F."tu':. iij g!
.F
r"5= fs=1{ i?+*: f i r't-j1fi".j
lrEo-. -l V iu*-{-r n $gn
-r**=-".
;i'-,g--S
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5. T:1.th: fogtt-So"*icas required to implement the foffowiag
*quential circuit usingJK ffipffops. IJs* afoq_gL+l:e___ n..:=
Y'H
.4ICD
1B/0*ic/0r"Df0.'Bf1
'*l)/s%/0r.gf*vlt
Jr= Y, R -L H 't'=4P J g*" :. ?.1 *Yi --,.;:t \ t#" ,f t";' f'
i**-
frLr'@ft i: X'y , 1- t ii,f .- lj'
{+ f,,
**'i u.i -,i i'i. ,'* '*i )i il, i i :;d"tj,i 'l '1 'J$4.. tu"ii
r,\ i i l'.1=i=' .r Fl *; Y' r- K
SXlxX1XO
