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  • 7/28/2019 Sequential Circuits-Class Notes

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    rarrr."Linp-r O'J"-*9

    W ""* -iue**qa+a'7ff: A - . .- A^.an_o,( sa*r^=\V4-dglgt ,11 < nskA *|,n* bhoio-Jao J d,^k siano-L a-; A ;ylfuoY

    %tr;:ffi ,,(m, ff :r^7,ffiffircA?aLaL_ o* ,kny ore_ tr*] a/ h$rm^*ub. lo1 n s+*J/u /a_t,W "*r* # a, fl,-(loF , ";t!" O o- l,L

    (pr,-t}n '^"lc,ajl

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    Gr*l,.gffr,*ldr"e,r;* F t -f{opsdoolr*pw\l"Ot^Jrr*S

    n)l_r-fuin^ih9 d*ay,a-, ,Dcl+- p"-a-Tl,.a_ _}d_ f ]+& FF chaxy ],)"r^_+e "Lo"jr ,"E"l "},a,,y,{,,gt (f-*. 6 {o 4 o,-f,o^l +o O), ry t'g*{..b^.u*._ 9_ s{"_a _h +L.4_ *4J,# ,;_ ,",9a ^* +-_ re.d.dlu/.'',^";a A'd"*"A hrtl" ,J*p^,,L,

    S4oro*_ ebn^"^* ,LukheS'-,: r- -s{r,*e e_te*neJ, in a i{"{- ;dt co-,^* '-aj^l"-i-'- ,. }i'""t -JlaL in,tafi ^^t*l (as otP - Pa|,.: .laAre,e,t {p +]"4 o.',,^.9,,rn_l^\ J.t\_e.j +"^_ l,^ sigr,^,l_ $ swi{ch ,$},Jos,

    2

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    < Lod,.lLojol^ ;5 c.yq-*{ar, {{ua.-

    ,VOL G^*-x-ELYrys]",*t/- ele**nrt -{-t @?,o;r-al w',dL sw-L l,-"J4

    -rod114l .t-.6.^Jio wJ,-fr^ S < | q_+ck Ez_ c_c^+r*_J_e"( *) H^ +..^* e;o 9 3 -aou,QoJ, Norr-y*z a* +rJ. cJesr^c-DaV* FTAND *'j

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    T; bn' -i+- &+,J\ b {-i- ' *o , k= l) + (q=o, Q'=L)AtW LoW j^r^^j= r-*{.-^ -t , ?-A- , i4 js +#.^ po s gJUt" {* LiO-)h J,l^r. re-,o* sk*o t^^otfu\.^Je *tz ,?pfu;ry, L i, -}t",. R l^'^-,*,Il- r c-^.-^- +t"4,^_ t-.-rk- &-t il,A,er^- .V** ;,--o ,.44 f.L fL ln_ aroto- n*H, ca4,z-t.A\$o'r,^.Wu.J^_ b,t{. ^pJS { ]\4 l'a-tJ". 6",e- ei)uql k o ( s.o R:4 ,{t^_ [o_[",t- co,-- L^e- in e.t++g,i ++-_ ser * W *;*-r t"t,", J"r,"@o\,. "}a^ ;^+*,s. \,o-J l^os} 'ec2**{ 4, ,,r^rrs,*, ,*or+*jto (r=rr, R.--,,) --(Q=o, Q=o\\t a* L } *rllaa J.,, Vo+t* S o*LR l^-p,-,f -t {l'-Vo]+_a**p,^*, tr +o 0n zti ^rlion rcat---'u ae'us'wdLfted',re..l_s+^_r\ , *,r,,_,_ }l^" n_uxt ,l^,_ d'f,,^*A_, ot\ 1p >rJarin ,^,h,cra_ ..*-ed*nn +, ;, l+ ^-0-, u,t, ia-{o tt^- relu'trena'f ]}^rto u-+p-h' vn,,-r{* bc co*p\ew,4,,^f- o- e,l,\ o]4g ,\.. no.r_,J "r_r,\rn , ]L -r.t,h,^ ir a,,oiag q "^"k'"f

    f uJe-t{^r} 4' s ae r,_e{ ap72i e,L ]- D ,l[ i", p-,* ri ,*L$eo '*{1 {unrhVn @b - ,,lt"e, SR, lo.}k Covl,-_"Ae/ -,'tt" l*o;rr-**\2A \.\Ora tMQ'

    oo,t,lo

    oo4o

    ("(W S = 4, & =o) ". .ho*f_"- fr"lr} s{,do)(o{"l"- S -O , L- \)

    ( ., b;J,t'^)

    ?

    a

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    5*-t op**{ion (S =l, f--o) fuJi.r =O,R;O in ++,2_ b* J{a_J"_T*- q2CI3=t+or+rrt,v S 'O,oLOeS 'rr} eo.Ae-

    c*to^ -Tabta

    lo ,/ '--(Z =o [n {La dr lfA

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    5L Ia{zJ^- _it"{^ d,, c_ro,! _ ca"|aA NA,D ffie,-^"*,11P$tnjsQ' ^

    O l C l -Qe9o-+*s+",te, I" t ("4l,-(llt.o)oO l t 4 (.f."lrlJ"e*)

    inP-^^*, rornoll1 & 4 , w|a,Jl*,["t-,X +l*- "l"trgr;t-$\.*" Cq=4 ,q'=O)resa.,t-st,-Je- (q -0 2 Q''4)

    L, pZ d"ra^_

    S = 4 ,, ?_,_-O -2x/

    1g,O R=4

    Qo o , Q': { , {4^,-,e;4ts\e,a, , 4+ +\. so$

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    Lt""Tr* [l4 !.l?dffirS,=q=0 tStt, o,e aL/. L.e_r. n c,

    E^ =_ L , 3 = A , ?=o *dt+, {r"-sa ta"tJ' {+'& g7 5h*e"

    h--(,, Sc-O1ft=4 " ? r " t, urR6f6r'l"afl" it rs 711i f:_^ Miffi"^ {4y

    *^*g:**::*- - ',, *r"+uff{r,MFo- 4,',^4 -^'*"^,Pt'*,""" o! "v,,_ s "[J,"'"-t,,uxls+"-rL^),-"|,'[*^ffian"'-ni+A,a,,J.c.'^

    3 ( t_a4esu- -i[ c oru*roL i rf tr*r^r;\}o,-1l",{lO X X lNochona1 O O l N, "h-,f^1 O 4 le=O1 resz}s}of,1tOiq-ltt 4'l l^a"S.o.-,-.",{n

    a 4*, o o l? o o { a\.n,b;n,Ys6p

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    D LcL+.h ( l,*s7ae.,i lq-+"h) wset ,.

    *rr)-*, {lL** elini"a-{a 1+,Li l8r. S n,nzldlr'o e(adLortag L%,-*UnJesire4Tlw fl tqt"l^ , a lop}cnl

    i n J akf,y,; nog-,qn d,t{io nbn)^f_ el,r"A+, 4- a*

    4 p,-nn^!.t Jt"r-{"h4 h-*q {{nn-a.

    S a,^.A e )^p,,.J,,Den

    qq'

    r\ Lo* "uoj) rq_.tginp.^tsso*..p\e.&*PE^=L,Th,-bin"'xl^{o..^o,t^PY

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    SroB*aL E Lal^^trs l, - P-o? ST_,q?_ : A ?n err-n^+". oLe^fl, w,Lvn ca_so_s ["ol on a FP_b 3w} ;+s sldo ,\ ,;!lal 4" ]r;nr , T,L D Q,d*?*, u i,}4*p;; a l, .,,n{.o{,\np^^t , ":g.-*u,0? \ =-l+'Ar iJ +tfe't::r" :,- y ffi#,**r;" ", "H ;:,ffia,(inyr* itaun-on"d^p,s* +1,e o.^J"_f a^rL +_""s}.te Gf ^Lbe^, T/us nu1 ca"__ao,*-"[Jt^;ve'l,*,t?tsu'

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    fl -${op b U"u(ta,)

    fuD lohJ,

    (nn as}e,.)

    EdaL - Tnqau*d P Flk, F[,p},Aa-{

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    }k_: Sr ,4y, k_Bgy"*.f},n _ft"r--:7" su,i-lh do +- rEe-f" silct,o Ct}, = )i,2 D = o_--,*-*lJ=?oo+L

    (i ,|{o Swvtew "{, 4t^ s4+ gt,14 |

    ,Lo4'5" "6. cll,-=O

    V--z1-)-{". clk.OO fu. 6tX = ,l D,OL

    Q"qL- rS D dno_x,Azs *h^[a cllc=,,(,[ amo"t r^, J O be,c^,eq is o ,.T\^J,!,+h, Fe i:l" "1-al o,-b e"d does "ofr,espond, 1o chov,-s ,h +t"4,y?^^i .; J ku4^ |l,, doc,V ,e!ur|s)o _-qro , k ffos {o L,plac"g +}.4 ;"&"^} \ath

    i^ +h.a"f esu,,^,t cgnJI,"onu_i$,-o,^t' *r^^14 ++,-O.}r^*

    wt"J_a c-l[.= { ,or*1 ch"o-g", r, DJru_s ,^.l o-|,(eJ{Ia owt.r^-L

    ?r/o- e_tlc -- O :

    S = {, ? ?,l (1,q-,""^t ]{ltro. clL,_ =L r'( -, R.=ol- re;g1;}

    .-l

    D=L,'S-O *-h_a"^ JL goeS {,o"^, O to L ,o"-ct Q -+ j. '-->ICl]4

    =l-

    o.->L Q /=oc,:! s+*, "* d

    As a Su-*^v\atl_ ?or a_ posi*ie_eAq2__ *r,6ecd FF, _J)fuy\ *lnc_ c\ocl, rna],_es PoEi\rd+..*nj"r! +V* ol*-"+ is +f,J_{-"uot + Q, _ ^r^_t JL ^__ 4 ^aaJ-^^"< +ranj Jlio^ *J +l^,s__ ** , (

    a_> a) lo u vol- a#eet _lte ou,*Ft,Tt,e o*|._t is t,,r} ^+r"ia q lr,4 c"ha",gn_s, ,,.n 9 ^Jl,,,t_ c;llL ,'^ ++* ,, bgi,-l 0}^Nl"" -ll-" \o/-, O le*t,Q--rlp, 4r" d FF *Fonds k lA .l/tr|r)/rbn {ro* CI + t^ anot nall,Ynln"41

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    wtn/,,t *1 e^y-,MnEe,A FF'sfr'.^ *' "f{.a easPon^a *J a. FF {oing.,do*o.-^."L+ato"Jcn.,,4bz.*eawsjJ,f,e/,.S"r,P-_{1g i, -tU*_ ,,,i1,;iyv,r-,n J,i*c a,r."t ,^h-.cJn +t^' O t^r-} wu-| La",--}@[;+,-i",'\ a q-cois}a,^t "*-0^,a picr ,{, {, occ*Fenc, ot +1,.1-oc,V }rone }db n,t+rl& }i*. d_ l, ,r-}.^**\_ {i*-c- "r^",k *.r^*'^" ]4^L D *r'^* *^"| 'n..+'-chat4^ "W +*-L oce',r+-e-4 4o pai'n-, }dni*v'" q|-|+o a-Jo c'la 'P rrry}$**)hJ-F*hat^V-,roLLdt"a-\+.4{ilta-edo_*& *h4:ffi.r.f)r^ 1 1^a_ o^_+f o r^4{^] {.a .

    -fl^!-v,4l,;.ol

    lxr,,ba {". o*_ ul8o_h'3gn_*A D- {l,}, ,Floe i,h,n bz-l,r

    i-' Pos]tr,-e- -,l..b3e,",t\

    'flnur,t h oa-dl'l,a s1*-U,/-"hsie,na*e-l posi i'v

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    J* F{;e- orr,Je .,.* .l4r.e'_op,.,s,,]t;a* +h&t e,,' b- P*+orwadoJ{- o, flie,{to '4 _ .J. *t,e- eF t, 4 .,2- fu,"i +9 Ff *- o of3 * C-v^4ou,,,'* i lre o^;l#*i ,

    ^ o 'o f p _ .( top, has ":9 *,,^.{u!t:,ff:-^S"r.' o::# # :ff ''*"^ol^-* o ,1,

    .tln'- ,lo1',]- 1 *h4 D iy{rorntua,t, ell *hFe o,^r-*b,na

    *: )* 4* rv& ,are a{, ^_7/t_ FF lss,u,,., bJ":

    d,"rr;-t d"ot* 0{ ^f K FF Gro,t">Wb*l af adKtr"j Cl\a,,eeFgl Q Ct+)Q (*l no clto"noO Rc s.f4 SEQ'(+) Co*}eu*,d

    5=|V*o + si (Q=4,q'=,o),, - l5=o h- , rel,t (Q = o , Q'= l)5 =4 ,K,| t o"tp"r is eompta"9,,Jre{ooollol,i^p,^t; !D=Jql+K'EV.4^ 3*A2 K= OrJ

    ++,-\)V.l^ j=Or(* 4 ,-,-Z

    Qhr,. T= K -- 4- --+whn T=K= O --+

    .qo)h= qiq =L*l.o_ nac{ a--\oc,l. eA se*s \o*irJ ,tp .L (+{^",E , q ='|;Ja-*s+d")!= o-Q'(t}'K=+o= ); fl,ue_ nt*t c]ocl. edg" se",lstha oJr* ' C+{,* , Q =o)resLtcl"k)

    Q = 1 . Q '+ ( )'Q = Q ,|* ?* q,,l"o.1+.4 "*tF-t.o *h.o v.*t* c)d- eAY cova?leD= o.Q'+(o) e =0* -- a )1V.lJ.'.' _a**, ow}p,i nch,.*),ti

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    -Tl..r- -r_( r"u!q) fl,,- tll:hL _T t? is a_ eonnPlo,nne*.** Ftr ar.4 co.r_ bz o6{_o,i, {r" *a f E_ t , [.r^ i^ rJ' sr +J {"g4lr-.r

    CLILKT FF ob,*#,.,.ad -{rc, a5K FF '

    fu. *Io K ff w?- haA th, {"\Iowt'*5,P= TQ'+ Kq6.oh*t sg*Ua0 of r rr,

    el uoir" {"- O* O l,-* ta,,a_.^,- it T in p*,*Wh,O.tn. ,4ra, dJa ++^2--Ta,^,d- K lnPy*s,*'w{ cor_ o'b*ar, +t^2 {"tLo,,tq eT^o\D--TQ'+T'Q a -re Q

    ,ror 'T>O iN\.J^ T =,t " D=oe q=a (l^o*S=46Q:Q'(+L* v.o o,o,*'\.+t,4 o'J+le^)

    Cha--Je-,}l,e Tablo d \T ry'r " "h""S,

    (,l",,\ta,[o"J"t)

    qt. t lqtt*,tlQ(++)

    4+

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    Ch orac{

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    !-$. Rese-t ^ OQ=O Q/=l',;1"llwb rcr+}s,l"teinJ2pal6{1g ot D: i

    '(ur:t:*"" 4 oDftp-ft"p wilh q*ci+ronotrs -

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    Dire lnputsoneS{al- FFs hant_',,a_s"6n

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    4NALYsls 0F cLocKED sEquENT,tAt cetlTAnat5sls "f a c)o

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    The l"(+sile a{{h. J]d{1u.hi,'rn, ,.J)+h (++) Jur,o k thgncrts}o{. .{ +h.FFs one c),ur ia*er. llr.Qiph+sH_C +t^4 s{""l.e Eato*'n a B*.l

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    -'tl e s*^le *ra^houn v)ou

    -(ha ne*t sl'z.k val,s a" fhar. de*4r-'"AJ fo^*h. *ak elu*'e,s(or fun lhe logi"- Jro*),ln gzrr.erl-, L sJp4+'ol ok;.*,ui*l. rn FFs, onA n npu*: nead,s 2^*nnovJs in *he s}at bte- , -T-lnp-"nu*| shJb|| eo,, h*s rn g,lonas, onF. eor FF- :.w?Vi,ca|ly. I.n a. s}a.}e )lot,n,n,-B ,fu| i. *lo,5qa+. bt n ,r.Oa.,- (e l".k 4n',af^.L) fra-"sl'o w bllwav 's,lz.:]g5 a.e hJ:oJe"t b6dcec*l ltnel co,,na

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    The FF irp,,i y'a{lans i^plnY fur" ./ *lA tr {*^ .l&4- l,Lt4Q-g^bil, anol *2 rllx 7e.'{{.o"bno,na4. a.l,z,i*" +r^ Jr*'.qstLn FFs ,Nale U^t *l,z ixp} Eai,o, o D r is iJenl'coy' h t-h* stal.o-Q4 *ah'on- Th B b-u:" /to chara,earthL eryation tha* Eurz ]hz-wxL *h{e lo *1,2 ual- of li'L 9 h7*t : Q (+ ; = DLA na l,,ts ! wilh D trli> - F/oP5Suporo \ #4 "l."r.jil""t-6a* ]. oor"!ia_ is J,zsc-.'b.ed bx,lha_inp,r* qq,J-al;on

    Da=Aoxey7he D^ s5rnbot impiie a, 1) FF ,i ov*p,** A. The x and- y vluaca **a inp.,ls ,lo +l,,e rJJr*, Na o*ta e7*bn3 a-Fe g^lwr, ,^. keliqplie lho ,lde o":}p*f c-on43 {rn ,ll.c oui7*of lha FF.t'/ze logL d,'an^ s oLh;ne fu*, [he hp,..t eyat;on a.s $lloos:

    Presentte Inputs Netator} AAA&)a xo/

    000000010100001

    A(t+) -_= D1-- A

    01, {)(c) Slate digramEquenqL circuiL i{h D FF

    (b) ae table

    (ru, ll 00.lt(a) Circui diagram

    ,+ *.*-.: :*( t^22-

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    Ihe stqh lob* hos ora ol,^n $*ila.v.- ycse:* s+d-t , A FF ; |ua catwn3.fo" 1hc-{"o i"puJ (x anAy)l one 6olnn {2n h,* ne*|slaJeaA . AXy a

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    Ano!#Fpr a_ D rF /te_,/a/+ e,a.Lbn ) {lresam *E *h. kr} e.'niion.u1ha^ a "Fp olhu ffi*, tlr-e_ D w id,r 5cA as TlLor Tr,.t 's nelLor T, t is nea,s*1*o JJa I.* ctaraate,n:hb ,ro,t*n' /o oblo.l /},a rz*t e h b- Va[g-s ,T* ne* sl"Je. -"-9rzr - *futlJ;rr. d*^^: J+rrt ,e TlLor r ,rffs an* bLprWJ as follous,1, Dp_l(,-,-iw,, l+,L rc ^nJ e{ulja^s in ,lyyrJ o{ l,L 7r

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    Tle_ s*al* L*bla o lire rywJraL, ci,e,i.t ;Prg*snttatt lnput il|.gxtrt r*p.fupl,nputuI fr4 g l(g00l0000lll0l00l00ll0000ltl000

    l00ll101l0001l

    t}0CIo00100t,t*e i*p^* Ee.*,i*,",{s-E 4,pr o{,tlra *{e +Ak ) b't ae. "dg/* {".|t,,a"ra.laJ o{ Jha vxt, +rk (os spaueL in s44f 2. 1-1r* po*llu " The.,o[u^r.s a

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    5"ls${.*l7 .-val*es .* JA , |14 r Ig, u,L(-E 'n ***ohove elua}ionsW e ot>{on hhe sJaJg.- eg-oas' :A&ffign,)'A = A,rr+(a)+x)A. A'b*AB'+ Ax,

    B(t+) ,>'B' +(Ae x)'B= B'u'+ (*qx+,Ax')'b- B'.' +[a' *)', (lv')' ] o= b'xt + L$ + K') , ( A'+* )]g=gL|+ (*Ar+4'xo= '*. + Atsx + At xl

    Thesc s}aJe eqatl*s 7on,'Jas +tL brL vol*s &. *ho_ .o|rra heo{pj|' N"b S{ok" in the s{,-r/+ fublc, No k **at +^a aolgytns heo-{ed" Fl'p-{lop lnp,*| " a,

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    Anahjs w{ T pltp-Flops-Thu o,.*Ltr i Q a" solr*Ll cj,-u^t i-tl T r",s i.+K FFs , 7h4 me*l "*"{e vo&-u, in *lu s{.al ]ohlo,ra*l" ,Tho cAorcfu,tblI #ta "f a T ft'e-floPT QC*+ )

    si^ita,^ {p {dJco- |n obhuador *:Lrp-cnaracJe.4zt

    Q&+l) = f@ = T'0 +Tq'

    o4

    q c+)q'() No ahary_Cor*p l+rfue-bThe h'- E,"otran e{ a T FF i

    .xawpte Obk,; *,e. s |o&-la+b a-,.a,5+*Se *}* ouq ,ey,,,ra,.aaircJ,it she urn b-Low , d;a8J7,!*

    rast

    FFs A andB ,, ong irpu* xro-d^2?*

    AlcJthas l.,. ohe s"l"-h' q'r,curi or* orrlpo|* y,

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    lhe ,:rp't anal oulp,t Eua}'ans :TA= BxTB-x--AbS{ql EuaJbnr afe otta-'rned Uy suls*{r{ n?.lM i"p eq,J-blons T:and:f,g i" ]le

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    i'4eah_anl Noo"e Mod,)s al Finik S*oJq MachinB_s-T|e-u--are- -l-u ^o/nJ' * *1ue--,h'o!* "lr-c-;fu, Tfu lea\ moal[and 1,1zMoorZ nodt slr1o*n bo|.ow .7712 only lfu,ena r orLto_gprrakbn 4 E ,Ja* -

    Owuu(Meal_v-*pe

    lllooe Mmhinc0upus{Moorc-rype

    Block dignams of Mealy nd Moo sttt n*hlnec

    h Fig, ,l{is o-,fic*'or o} +i"4 booL (/l,auxa"plo,d be itp r a-^A-**ap,

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    Ano|lrf e*ctrr\ple o! ._ ,oore ^oAlL is,l,\a se|uent1 o!* rrr;)*.rith 1uo T rFsshon in Fb, ZO "/ 1* bgoh*. He.e, a+,-o,-.*p,^t aa"

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    TATL k$.croN AND Asl6^J MEI,]TStak redAo " is re#-ed, h as W,2- re_d.r.a n ir| ,lla nurvh,. nl Fsin a 3*r^a"l akJr^Ut,, ,,l,-l. @ ,tl- ;ry-a -o,,*p,.* ry;Mt"odarfu

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    a-bLJe L=l ,N1

    efaq ,,{affr "."{ ,f

    In -h col*,,^ we_ har.- +h1prl-'on proczssro],r {haw }]na_4u- c/*l dlb,{nh , t.}Q- ,,za-L--lo obw )4,.* {uJe_ "l"U-,S}a]e Tahle

    Npxt {+4k Ou}p4tP,vsprrt El"l,e- X=O X=./ Y=C v+/a-hoocdOoadoo oo,p',

    41J/,f

    -Tc,o slok arc- .ro.J J, b equLivalr,b i, {"r efu"la- inp'- +4_ 3**-.}-{-sa-y.-- o.,.lpr* -^a u^A $hr-dre+;,r e|+1^4 +o +4 taJ/^,a [a},.or Ah Eui*lo*t s{r,tL. ..l,,z,^^ *t,e. {o _rlJea a"*, exulla-Or* oh.a*"]ra^qr* fu,, ney,no,,l_ w{lro "t al{

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    nL re/Jk./- sl& lalolo: : ,)P,erQ}"h Nerl- Stak odr^,*S+4]-, ,r,-O y-J *=o "-_ 4flre adur g*n{n" e'arah

    alo/o, r'\

    oo l c

    ,)c | , /0 /oa Uo

    q,abobc)0OC,.adOOdLJ04L&J04llq- Qllo wi"p Lsl, "o."- fo- /a',^ed- f,* al,- reilrrr,al_ s/ak a'qp*, Sl4Je-a,Lbcle-JJed4a_lnpro1o'lO14o1ooo"lp^,to o o o o 4 4 o 4 o @

    Lt is oL -*

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    SrArz A ss GN N erfn daElnn$ t441uenl;al .t"rrr;hz, il is neags%! =l- ass,git u^|,qu-cod"ed brnon4 ,air,s +- }he s*e.*-s ,4fo, a c,'rtri* *ilh. n staks , 1+r4,. eo&.rusl eortoi^ p bt t ,, whr*Zr*}rn (o. "Z bo^), For e;.oJ^{lq .,iH. 3 b\h, iS is fossib|e+. OJ,ir+ e.oatas + k-s+a*e.r , lt "^ly sta*

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    DEs t6N PQ7CED4F,E-Tlre olei3n o{ a clockesejuen},al ccuj* stor}s wifl a se} o "cr(La{rb nsfu,\d. end,s q t^i{,[ q. lo2l'crr1y o. : 'l tf, BooleaJ^ {,,a^onsf-io"" ,^.h,'eJu r!,l lOglL otlz^,\ ca_F be obtrai^e_*.Du, ,^"-l^Zr1,4 - {=r,- l*.e- *o4 d.a-scn'p{bn ar.at spLicaibn, al +r,2- Jesireatopozhin,4e,r'vg lAe slole- &.a1an,,* o{ 1+r4 clrc. )2, arr"e t+r4 n,,,bZ , ft ss igr- binar1 ,u-L,as+ , O b }an +]r4_ 5 in3 q JeA s*{a +relg.

    o{ s|-ol

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    -l.kL {lr]H unsechk l- seAds +{4.8- J,-A^, {"t",{e 5t, lf r",ore. fsefe J*ftJ-/ .++u* cd,"cf ;Sags l. 3 _ antr o ;rp,,* s d.J +A .*u,tboJ*{a. 5o -This ! a. Mooe w,o&A r.x,rur^+JAl ,;nrhrsinc.e ++,J^ o,Ja-r, U L,rrhen +h_ c.s,crlt i} in r}{-S, .,'A O a{,,ala, 7h"* \ rl4**o,r&p,,.* *-*r4'o" ". r^- p,es,* fub.or1r'bo* ,ro}-a f'..*chb n o}++,L ;wt.'To JzJ ,'1 L Jl^L dnJi-t \ ha",d, ) ).P, neeJ, *, asin_ bina4 codes +" ++4stat, aJ\L trtl +t4- st_la-hbla ( n ^ *lk ^*tl*l+n "l*oo.- Des e^p i \o n la,gwgn f. *h- o hi d"'ax--Stu-t Ta$la fon Sef

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    A(++ {) = DA (Lts, n) , 2(z ,r, +)ts (t+ t) = D, (A,g,x) = 2 (l,?) lJ inp** naJrr"8-11a *s

    gCa , Br*) -_ '(6,?) J o,*p-i eo,,Jl'oLs s;,nnp\iQ +hr,'"p-d ey,.fio*s % ^T*' nl ,,--J- } l,$eal iap,,vtD^, Ac+ t

    TDa= Ax + Bltelua,l'on, at- ,,,j Dg=Ar+Blr y, AB

    Tr.-0_ *ria*+ay_ ,lnr;a'i.4,'1r1, ,D PF ,s +fut +la i"p** E*efansarv-" |cd13 "b,!u,d, {pm.}lnJ* shk- bble*u oTuJ"rw,rn,f lhe *f ,,fu,*d,eJ

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    Excih,hoa_fuL!,)he,-_ D FFs aJ

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    7h? FF inp*k tn *lra s]--{a Aoble- spaF1 ]*e +rr^th, +ab._ {or t},.a_np,r Ea"kors 4s a l/'.,"h'a,r" o-{i4r- prsts{ala A, p.es4 s4o1*, B,s]oJa loble-dd, ' i'P't *,*!'''o,* 7* * s1",ph' 9e/,h *,,l,f +L,+ y.nfu.fbLnll+,,,od. IW nex| slab,,, ry ac" no l- se L dr^3"+ r r* l.+'"1vce- P^n- r1o*t E u"aij,o*s ar a lrrrlr'o n -f rl* an"L lfa lpl,.t enlg ,

    Logk dlarm for eqnd Gitilrit udth /f,fflp-flops\.For s/,npia,ly lhL :e' s;7ial k nol-,,u,wn ind-l* loy? onrt, br.fr3 de.l6* lhu"lJ i,.J,,tb e. ,.J.t iq,,,al_.

    JJa= Bt

    T*Je:sMrys fot J ud i lnF.rt antfu

    (: Et

    .rlKg=(/t &xr=Ar+A/*l

    Clack

    .b9-

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    S,{}*eis U-in& T Ftp - FlorsT" ll,Lilila" t/r* fvab},,-r' .l** * dagn a_ b;r+ e,nA

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    TLe hhrel- FF< a< Sg,bolizJ b1 Ar, A|ra,,,al-Ao . Bingf! coun+is a.e consJtua/e^d}'o,l- e.ff,ta'e^+\ with T trFs becae h* wf len** papra,Th FF inp-t ey*.t*r6 simp|i;ea Jn +t\^, yvo(S a_ {*,tlows ;

    .46Iat *.'lA AT * dnMap fr three-b$t binary cgutr

    Lagle dig,rar of tiree-fu]t b-n*rytount*r( 7*" ra* S'gnal s no* 3hou{o.inpl;.+,!l