EECE 320 Midterm, Fall 2004

J,_/ , '. ',., \_~7;~-..:r - . ;ji;"~~.~ronl~rn 1: (10 poin!$] IQ U.sing 3 Mocre lIUIehioe WitJl D PUp-flops, design a sequence detector that would output a :z..l only after detecting . We sequeDce11001 on its single input X. Call the slates SO,SI etc. (use don't cares for illegal states and use simplest sl3t. assignment) .. " _/ t:: () LLI',.i:L:-;;.. g"..1~. . !:J,z tU't::! I ; -, \ . \ - '.Q~ ' ~() ~ .~ '" ,., ~, ~~ B ~ .:::-!?f ' ...,. .pp X ~ Z '8 , ; o 1 "'" <. (~ . ' ~. ~ ~ ~Q ~,O A:..~~ ; 1 ",~,.. \.,; & S:i.. c ',lJ'~ ~ :s-; S.~ c S", <S, 0. ("j) ..,'0', ~~ 0 _., of Se' S:~ .,.-!,. I _. S. ~. s S,,~ ~,~,Sl b.. 5.., ~ .0 ~ /~.. ",0 " C'" Gbl ~ 'I.",...", ; "':~:.r ;- i ~ C. The excit~tion equatiOIl$ arc given by: (3 points] " I Q1Q11 Q3X" od; 01 11: 10 I . OOIt)i (j c\ 0 01'0;/0 .er jJ! \ . - 1110/0 cl 0 101~l2-ldJ 0 DJ.-Q~. ~t X , -,-l. iO '"..f.\1i -) . "* .---- D3.. Q ~ ,t4t . y} \ Q{, Ai x: +&').. :;'~3 'X Q1Q% QJX\. 00 01 11 10 Q1Q% 00 0111 001~ QJX " .r"':", 10 ..' .,. .. - D2.. G~. C}:!J ... w +AJ/~ @; )<',.. .. .. ... -. -. .. .. .. , . -..-- .. .---. .-- :r~!e ~ _:,{11 - PrD.blem2: (10 points] ';( '"' ;~~ : ,----- CotlSider theflmetion: F.. :!:A.J.~(O, 2, 3. S,7, 8, 10, 11. 14, 15) a) Whal~e thepruneimplicantsofF? [2points] .... , " l ~./ '. CJ:J '. .Ar.: p.!C : ~ .: A: B1) ~.p,;, ~ ._~ J )9 b) Whatarc theessentialprimeimplicantsofF? [2points] ~ le -!lLC.:£:CiJ) A/An ('. j 1L' ...~ ., . t . ~"":. ., .' {.- c) What is a.mmimum SOP expression for F? [3 points] - \'. P>. ~I I I) AIBD h'" Q: ,~'..\- (-+ ~\ ..;..1)' . "- 1'(")\ - l'.t'oblem 3: [10 points] I ConsidertheBoole:1llfunctionF=:!:.u,c:.D(l,3.4, 11. 12. 13, 14. IS) , . . a) Implement F using a 4-input multiplexer ane! external gnt~'s. COlmeet A ilJe!B 10 the select line:. (S points] r '4-".-J>C+ j:[~~ D ~ 1 '- ~-.., - L/ '- .o::!::,,~i -I 'I' 1.0 . , I -I I. ". A r . i' l. 1 . ~ :::o .' I . V'\ , L'f . -.. ~A:::f L1 l' - V j . I . . I ..., ; /.: ~} . - ",v~.' ~ 1 ~ ' 11 .'. ~~ ~4"\~ 1." . "l I 1.._ l J' ,'. . j ! . . ~ . ',. " - b) Implement F using two 3-to-8 d~6di:rs.with enables. an iqvener and OR gales'wilh ma;timum inputS'oT4. [5 points] .' '.' , .' .~ . -v.:-J. )1,~.. ',' lJ,. . '';'-1 .\ I. '\( Y1j . 'I:" ,"1 . ' [cl '1.., . . .... t. ry ,~ ,,:., . , .,\..: ...:.. ---""",i. ,...'.'.. ';" '~"".. ...'," .... A , J.,.r::.j:.~ ~ '. ~.,.'"~.. . . ~'c'" ..,:.' '~£~'~r':'~7'~'::~~~ "~',.._ .. .. , ,. r .!:U'J . -, . _,. ~:~~~;--A. '"~'H'!l'~~ ~1:2-~:'~:. ;;=~.~ . -....... '.. . '.,~.:i~ .~.~r:. ,-//~ . --. .,-- ,/ .. i:. - '.. :.u:- ,- '. .- " ... ..- . '': .. : 1'- ~ ..-- .. - ...---.- ..001' ..-- .'--- ~~".. .- ~. .... -- ... - - E'=:g-: 3 ~f 1 ~ . A'sequentialcircuitI1a.s2 flip-flopsA andB, oneinputX andoneoutputY. Its'St~tediagtumis sbownbelow. DesiplthecircuitusingD flip-flopsanddrawthecorrespondinglogicQiagnm. . \. X . . .~ 11'd £:), ()o B,eli.' ;_'1 'r ~ .o~~ 00' C1.60 L o Oi .:LO 11 i-L CO .10 .L'L1.0 :o~ ., UT' " . I ~ ~iU:r~JltN\ ~?Ll;ili.V'<iS~'K ;..rJlJt.d.p$.' -Llb \0 Q)L= ~/~~X + X).G.~+ GjfQ\{.J'. . :})~ =XJ ./ 1'-'_"-[Ff-'- " . ~, "~r . ~-- . ............ X .~ \ '~ LM ~A . . V (..Id L ;+ " "\, ,. \\__~=('w-I' . '. ' \' . L-J ~ ~:.:\. ..... , ': . .. .. '. ~..- :-~ . I . . . '1 I _ ___ _'~___'__I' , ." ". -:i '1 . '. .t .' '. f~' \ " . ~ I . , ,1 .- .-.;..."- ..,' . (:; ,.. ~. t 1i. I .::... \ : . .~ "::--~~"--r-c :-""-, '~.... . :. I , I i ~':.~'" e- 1'-. . -.---..---.------- ---._---_...._- .r ProblelJ!~: (10 points] ~ ..~!, :.- . ~: (10polats] . D . "Of allinvalidinPUt/ o inatioll$ ~ ~ . . gn ,\11E;m:ss.3 to BCD code converter that gives output code of don't-Cat"es ~ental1on. Completethet<lbleto includefor every integer the corresponding BCD code re9t / :BC!> :..;' EXCESS-:> ~b ..0 u 0 D 0 \ 0 0 O. 1 ... 0 0110 :. (j' 0 . '" 0 1 > 0 1 5 0 1 ,: .0 1 :J 1 0 5 (1'.0 . \<::) 0 -- -.-- \. 0 - ..., .... '. 1 j':";-: '.: cl, c;1:-;-~I" ,,": 1 . .', .c.,., ~ ~ ',', ., 1 I C;-":". : .. ., 1 t""Of1- ~.--e--- I> . ~..;~ ; f . . . . . . . . .. :. 'p0S]$0 13.81.gh and goin te:ms ~~W~nttodc:;ign~circuitthatperfot3llStheabo~econversion.WritetheeXPte$ . . . , . . o 3, b1, bl and bo. '/'.' . . b - .' ~:. 0 . I g3 ,;, ~" . /. J"' . '.:.; - ':;' ,/ ' - --, ;2.._ . / , I / ' "1= .i!I;,\..'i\f .\. ~ . .1':. . -I.I'I:~,11 .~ . I .,-' C J /- ;O"'~, I' _ // . ./' '-' I ./ .. ! I :I '1I iIt ! .o'C~ ~ Rnvi :D\ :- 'el~ ~(-o .00 o Cl o .\ ? ;,:()",. 1- . " \ I i . \ ':" c' :) .:, J ~ .' .-.,. ?~~~ 5~! ~l ..:)~ : '6J1~ R::::loo o ~ ~_.oI 0\ .1- ~ '\~ ' '0. o Q. 1\ 1- - o \0 1:'- o .h.tsl 10 ,1&0 10 ",,41)'%0 the followillg clocked synchroaous SIBle machine. x I A A .. ': \:: ~~A l;Joc;l~ -x) y A. Wrile the eext slate equations fac, A aad B. and output Y. [4 points] A''''~;X +- 'X. 5 '. /' . . y;.-,-f\ '..~) ~ 'i-1. / B*.. A .'1 ../. _ A \I } . Cl 'V ) _ ,,+D/\. B. Complete the e."'Ccitatloallrilnsitlon table. and the state t:lble (use the foUewing state names A.. 00. B=01iC=lI,D=10)[4'points] .. . I. I X C. D~w Ih. state diagram. [2.points] .' X~~ x=~~_ " ~(6 ~~X-=C . c./ ~ I: "- l~ do) I' A :..;:''t-J "/-' \ . r-.. .~~.r]) ~. ;' ./~~-'-' . ~ \ ,. -~---=::-:;- ~ X::d.. - ,..... .:":12:: : c: .~. 4~ ..:.l 1:0 ' ~'t\.tu ,! '~t;.ji~' ~-+ulotl r . ..------ - . - ..Problem 7 [10 points) ~ ~, ~+:. ~!~.;.~'.~:. ~ . .:'".,(' {"\ ..",,: ,..~. Consider the foUowing Master-Slave JX. flip-flop bUilt ~ing SR latches.. The S mpUt in the SR latches correSponds to aSE!. theR inputcorresponds to a RESET. and theC inputcomspOl1cUto ENABLE. (a) Complete the tiraiag diagram below. [3 points] (b) Do you see apote!ltial problem in thisJK flip-flop?[2 pointsJ .':1 ._ J. ~il "'= :rG.... Rt\0::0. H9,. 1 a aN a aN ' I .0 I '1 AB . A /0 00 / ' B 0]. "g 10 ~~~:~~~:f5~'~~:~~~~~~~~~~:~~~~:~:~~~(~~'~~~~~:~Tf:!:~~~~~~~y~'~~~!,~}:;~~;: .'~"~/;~~:~:~~,~'~~~~?:~:~:~~~:~:~;~ii~~;:~?~.~~"}. ~~':M', . _, _:.ldj,b/lJls}1'0 .~..~.::t.I.:."."'" '. ~,o??:"~':Mjy mp.floplIDS(ouroperauoa.s:clear to O.lJOchange. toggle; and set till. Wbellinputs M and N are 00,01. 10, -p'" ~nc/H. TCSpecuve/J" . . ' "'i- .1... J. <Z:lfI . .. . <"" , , . ~ - VI.V , a) Detc!llW:e thecharacte.'lSt:c e:sua!:c!: cf~ MN~p. (2pcmtsj ._ ~ . , ('1 .f- ~ 1 I £l H f"'j )\ 0 0 ~\. = --;q, I\.i c.\. -I- I ~\::::J,. ';1:. 6 ~ e.v V ;/ &./. ~s. "", / --- 1. f :L -L .. b) r'esigu a.aMN f1ip.flop using aT flip.tIop with enable and eXtra logic gate~ (4 poIntsj . .ikI . 'C. 11__~ . . , \-72- ~E~ ~-'i~~) ~ ' ..\ I '~GW~~/ I)-T. ~. . ,'; lr ,. <Q ~~ ~ '\ . '0;" ..~'.-' . ,., G\, ri.slgn 0ITC/lip.fIop using onUN fl:ip.flopand eXtralogic gates, [4 points] " \,) .. ,(" ~ ofoo 0- .'\...... If" "'V' ':!; I! ~ ~ :'\ .~,' ." t, .,-;'1..;;".: 7.... " I. U\\ " J' " Problem 9: (10 P,OIntSJ( Design i 4-bit Jowon counter using Dmp.flops, ~ J~c.vt. ~ .~ p , ~ ,__. r I..~ . t;JI,; ~' I L ; IIrU.-. ~ "I . r ... le. 0 ~' \. r" .----- f \ , r; j I , .I ; , I: 1'/ t" . . - )! if r IIi J ' !;, f 'L1) ~ NIJ- 1 ' '.l I C\.A- .' r-___ I, ~ --'1- i _J JI . .. / '-" -:::';"'-..I;.Q)'"; ~ ~,.. r- j...--. "-' - ..:;, ~J-t ' ,;:.\ ,." ..,...':'",., " ,: 0101, -'" ~~t~i~l ~ e1.G.1~ ho'''! -.... J.- :,\j "'", .,,,-,.\~'--. :.......- " , , '.. ........ ;,' ........ Q ...... ~~, ..... ~ '~ "Q ." . .'~ -.. ,,' '- '-. '" j ,.