eic dlllh duqc hl~Ll elien b,\ng khat (.rlO) ehua trollg VIU) \,) V,M). \1:,It f h.\C c,ie dlnh duq'c bieu dicn himg khoi (xIx) cung l'ht:l'<.l lrung V IV) u \'If) vii kh6i (xIx) baa phil bai khl'li (xIO). Do do (xJ()) khoIlg phaJ [I [feh t{ij gl;ln. Kh(li duy nhAt bao phil (xix) li\ (.ux) nhung t(lp hop hicu dicll kh{ii (xLr) kll(mg Iliull trong V I (I) U V d(l), do do (x Ix) la lfeh d(m gi,l11 ella h~lln.t: ta cling co Cr.rJ) cfing.la Ifeh t6i gi,in. Ta k~1 hi~Ll P la qp hqp lal d e.ie lich teli gi,-Ill ella 11;lIn [('Jgic';: khi d6 ta ,0 co drnh 1:;- v~ baa phil Cl,re tieu sau: Hinh I)' vc han phLi qIC tieu: I\'cu t(lp hem \I(C) eila de dinh bi~lI dier} 1,:IP IH/P de kh6i (' dlf(l'C cho je(c) ~ UJ(a) ,,,I khi d6 t(lp h9'P (Hy du de tfch toi gl,in r sc llh,~n trqng s6 nho nh<.ll trollg tAt cit dc kha nflllg co tll~ co ella t~\P C tho,1 man h~ t!lu'c: V,(j) c V(C) c V,(j) U V,,(fl Hinl1 trqng s6 duqc gi,; tlm?t 12i dlJO"ng viI dun dj¢u t~IIlg v(ri c,le bl~'n dQe I<:tp I~I so luqng dc bien tham gia vao ceie tfcll 1{)glC ella tLrng khrii \';1 s{) luO"ng I[it ca de kh()l. f)~ chung mmh djnh 15' nay cllllng ta dtlng phuO"ng phi.lp ph.11l cl1lIng. Cii,1 '-;tr t61l lai tZtP hqp cae khoi C' co tn,mg sf) qrc tleu V~l khong tho,-I mall yell c:lu djnh Iy, khi do trong cae kh6i do ton 1'.li it nhAI m(J! kh6i kh6ng ph<"ti Et tich toj giilll. Kh6i 1l~ly (lLrqc k)' hi¢u 1;1 (", khi d{) la '\~t I,)P lwp: C" =( C' -{e'))u (e"). trung el6 (''' El tieh 16i gi,in bilO phil c'. Ta c6 s61U'<,mg cae kh6i (rong trip IH/P C' \';1 C" btlllg Ilhau. VI c" la (feh toi gi,ill (e " +- (') \,;1 bao pllll ( , lIen [["(.lll)!. s6 C" nho hun C. Dieu do lit m[\U (huttO d ta gia thiet C' co tr\lng s6 nho nhAt. QU'ltr1nh teli (hi~u h6a cae h~ul1 logic dl!<I (r0n cet Sli djnh I~I v6 ban phl! 16i thieu e6 Ihe dU'<!e ehia 1:1I11 hai giai dO:,lI1 sau: ill X<ic dinh W.'I d c.ie (fch t6i gicln clla hi'lI11 logicI( ltip hqp cae tieh t6i gian ky hl¢u 1(1 P ) b) Tim trung (,)p hqp dte (,)p can C ella t,~p PUlP h(iP c6 lrong s6 cJ!c (i~LJ c{le kl16i C'"ill Ihoa man Il~ (hue V 1m c V(c). 2. TIIIl (',ic lich hj'i ghlll trcn l'O' St't hieu dicn true quail. PhuO'ng ph,ip h~llg Karnaugh ele lfell Il)l glal1 e6 Ihc dU'Cie tim btll1g nllCmg so" (j() tr~rc quall f hi '-;(l hlc'n clla h:l111 r I1h(:). Twn)!. ph'ln Ir':n chung la aJ chi ra rtlilg. h~lI11 logic.l elU /I bien d(lC 1,:IP c61hc dune ell0 hilllg deh g;ln de gia tl"i 0.1 \;1 d ellO de dillh ella khr'ii /I Chll;LI. (llo-a de kh6i n chicu "~I d.c Ifch 16i gial1 e6 tn()1 mcii liC'1l h~ dUll glilll. Theo d1l111 nghia [feh [cii gian c6 thc hlCll dlcn hang IlH)1 kh(ii. [\VII kh;ic lll(yl kh(li cap III [;1 kh(ii con m chieu n;\]n lrang kh6i /I ChlCU \'~l liel! 101 gi,-lll 1;1 kh6i Ir'ill nhSI ll;illl Inmg I,-~p hop V 1(/) 1 ) Vit). Kh<il lH~1l1 kh61 lr'm nkll Irollg Inr(l'Ilg [](/p l1~ly c6 nghi<l Iii chua Itll C<t de dinh ella kh6i ";1 kh(ll1g 1{)11 IHi dc kh(ii e(l chieu 16n hem n;\ll1 Irong VI(/) u Vif) Tbu Il,le 111_'1 k1':-'111 1;1'1 C'I cele 1Jeb 1cii gi,'m cua h:l1n l\)gIC.I ell,ra ";10 Ilnll eh,YI n61 !rl'll dua 16i ' i('c tl1l1 t(lp [1l)'P e,ie f h6i co cAp 16n nh,lt c6 Ihe cluuc y()'j 1/1 < /I baD phlll;'!1 c:i c<ie d/nll-J \,;1 dlllll-d ella hi:11l11 Nc"u /1::;3 Ihu'~lt IO:tll e6 the duqe Iln.re hl~n tui:mg minh tren h,in \'c e:tc k1l6i; IWllg tnJ'l:ing h(,)p /I :: 1- \'i~c iip dung phu'o'ng philP trl,l'c tie'p Id1 nen kll{) khCl]l. Pillto'ng plutp tHing Karnaugh. Oic dll1!1 eua dc k!1(:i"i 1:1 de 6 cLla h'-ing. ele () dIll h,'lllg c6 loa d{y !lhu' dc dinh eua kh6i. (ii,i tr! lrong 6 l~l gi:t tl"i eLla h;llll r I,ll dc dinh tHUllg (rug. Cill" dillh dlf(.IC kl:'1 [H,l'p Ihc{) quy 1{IC ~au: 1 bi dlllh 1,111 dn ( hai f bul b(lc 0) 1 \0 Ih~Ulh J11()1 kh6i b~tC I. Ctc dinh 11;-1111 Ir0n bIen ella being cling !:I cac dll1h l:m C(lll \'61 nhau. C[IC 1\)<-1 d(l dtlC I{\p dU\l'e k~' hi~u 1;1 x. B6n dinh l:m c:tn c{) !h~ kC"1 IH,l'p 1,.10 th~lllh 11101 kh6i h(lc 2 ehl1a hai toa d(l d(lC lrtp, T,im c1inh [,In e(m 1,.10 thanh kh6i lxk 3. 'I 00 01 11 10 00 i 01 1 ! 1 11 1 1 , 10 IIlnh 2.61'11l((111g pli,ip h,)llg K,lrIl,lllgh 1 1 29 Vi du: h~11ll ]();;ie dU'(~e hieu dlcn qua 1(lp herp cae d/IlIr-J j = V J ~. 4. 5. 7.9. I I. 12. 11 ) = V xIX,X,X , V x,x,x,x-l v.\',x-,x,x. 1 Dc llil IIHCll hoa de hilm l"i dang cllU;in I{IC luycn la dLmg dIe ,1111"-/ '"it dillh-d. V6"i de ham ehu,-in I,k IH)j la dung cae dlll"-{) "il d/Ilft-d. J. Phuong phap h.lO h;ill~ theo d(' Im6c h~p. PIllJ'on~ pha!> Quine - .\IcCluskey Tim ki0'1ll cae IIell 16i gi,in Iheo h<illg Karnaugh lrl1 nC:n nYL pink tap \.1 mift linh Irl/e quail 1l0'u s6 ILfl/ng Gie bi0'll ch)e 1<:lp ella halIl1 h'lgle \UO"1 li;t:! n':im. U"U diem eLla plwo"ng ph<.ip b,ing Karnaugh 1:1 (\ ehb eho pllep ",\c dil1h Itll)t deh In.re quan linh lien k6 ella cae 6. M61 phuung phar kh:i qll<lll In.lllg lrong de h;u 10,111 ICii thicu hoa de hitu Ihue 16gie 1:1 phllo"l1g pha]1 Quine- MeClu:-,key. PhU"O'llg pltap Quine - \1eClu,-;key eho phep x,\c (1Inll ~l.r 11l:Jl kc ella de dinh hill1g e,ieh [(Ip b,lllg. 10 11:1111 [()gle ctuqe eho h6i 1{lp hl/p de kh6i cap 0, ell' kh()[ nilY cllnie ehia Ihco nhllln. S6 luung don \'j lrong de khCii li(:n kl: eliCllh !Cell nhau m(l\. Trong \xlng ella uie kh6i dip (), la s:'p \c"p de kh()i 11ll'1l ~6 iLJ'(mg don \'! "il nh6m de kh6i e6 dlllg ~6 lHong dll,[} \ I llH'lt c;:iclt t,iell hl¢t. V I du: cho h"lmI bicll diC:n bllllg 1(lp h(:rp de d/IIII- I \;1 Iflp hop de dllllt-d f(.\'J.X2.,\,.X-l)= VJ(O.2.7,R.9.1:l) ",,(f) = ( :l, 12, 10 ) Qua trlnh klcm Ira t[nll il~n kc ella e,ie dll1h duoe Illl.re lti¢1J \(\j !:II l',1 ciie [(~ hop de kh6i d6i \'ll"i hai nhtlll1 l:lll C.)II. l\cu hai kh()l kh<ie nhau [x')'i I viI 0 chi ('"i m(ll V! IrL \'! Irf cl6 dlfl.!C dell ,r \'il llh,'\ll dU(il' 1l1(11 khhi e6 kle I{m hon. Kh6i nilY ctu"t,)'e dua \';10 b;'l!lg m6i \';t danh dflu 'I" \'i\O \'1 tri ella e,le kh6i ban dilu duqc bao phl! h6i kh6i e6 c,Yp lCm hon. Sau khl IhtK hi¢n bUel'e n~IY J{)i \'fij If It dl de kh{)i la llh~\ll dllqe b,'mg m6i c6 m()1 nh6m II han so \'t'J'i IX'lng ban dfiu. Nc'u trong h,'lllg ]w'ji Il~Y c6 llai hOi.lc nlllcu hcm c[le klH'ii gi(;!lg nhau Ih'l chung ,\L' bJ loal ho. QUii 11'inh Irl'll \0 duoe I(lp 1'.li \'(j'i de t h6i cap I elto 16i khi ehling la nh{\ll dunc h,ing d6i \"6i cic kh(li e:t'p 2. Ti"::p Il.lc qu.i Ir!nll \'()'i eae S,i IL~;~!o-' ~- Kilol c:;I;-()1Ki011111~ dOll \'1 I ~~O . ' OOO(j' -1 , ._ _ ,- - _~*()(ll() [(lOU =_: I (:)~~)i-~' : 1100 _,_ .' (J II 1 \ II 0 I \ I Kilol L,LP I - (1-' ___ +-' _ ~~;~~ :' 1 ()Oc,,'" f j 100" -+- , :;:DIU _~_I."()O '_~,~ ,;-o.\ II 'r ;I\() I II(h () Kh(ii C(LI?2 .,,0,\0 , -~ kh(li dp 2, cAp :~, V.\" ehn I{ii klli ta kh6np. ebn nh{1Il du"c)c de Ixing ehll"a (hYu kl~llllh\ 'I". Trnng de hang nll,)ll dU(Je IL( phUlfng phap l:.lP lloi Irell. nhCl"ng klIcii kll61lg duc}c datIl! dau b(ii k~ hi~u '1"' I~I nhung Ifch tcii gi,in ella halll 16gJC hem d:iu. Trong vi cll.1 if hlBh b~n, nllll'ng tieh I(li !:P"111 IiI (OOIr). ((hi I). 1,'hO). (''')')' Kill Irong h:eu ellen hilll1 c6 nilling dlllli-d. 1.1't dlilillrng dlllh (t6 ,0 dU'9'C 'ill" dl.lllg nlllJ nhCl"llg d/nh-J \':1 I1lYu "all kIll l!t~rc hJcn cllll lal IlH)t kh6i ban plll'l l:il d c,ie dildl d till kh(ii d6 e6 Ihe IOdi bll. Plufo'ng phiip (Juinc- r kClu"kcy dlja Iren cae phcp 1~IJl do dl) eho phcp td ell the \:IY dlrng de chu"()'Jlg trlllh Il"en lll;iy linh tll~re hlen l(ii Ihil;lI hOil e,ie h:1Il1 16gie d6i \'6i nhL!"!lg h:\l11 d) ,,6 hie'n 16n, lIinil 2.7 I'IHf,illg pll~ip QlILIlc-lIlcClu,kcy. :\Jgoiu nllL"rng phWl"llg ph,lp IlCli Il"l'J1 eon llhL"fllg phuung ph:lP Ill! thicu hOii de biell tht're IllglC d~(a Iren Ifeh t6ng qual. phlflfng ph.lp t6i Ihll<u IlO,i Ih' ck 11,\111 j{"'Jgic, de phu(J'ng ph<.lp h~uristic. Cic phuo'ng phcip l1ilY c!to phcp gl.1111 Ihh'i gian l(ii thieu hmi e:le hilll1 logIC ph(rc \'.IP \'6i ,,~r 'rei git'l[J CLLI mii)' tinh. 4. PlllioUg phap fun cae tich tiii gian thong qua ticll kCt hqp Phuong phiip tn,re qUilll eung nhU' phuang ph,ip dLllIg [xing de tim de (ieh 31 t6i ~i'-ll1 yeu d.ll ph 'll bi~u. 'dien h;\lll i6gic ball duu kmg: nhang k1I6! Cifp O. Khi ,,6 bic'!l d('lc l~lp ell,\ h~l\n 16~ic \[l1lg 1cl1. sf) !Lrqng de khoi dip () ,,<: \,"lIlg theo 1)' I¢ h~\lll mo do do ct~ tim nhiIng Ifch 16i g[,ill Il1co cae kh6i co cYp Ill)' )', trong ky IhLl<~l Ihu(\ng <ip dung de phucl'IJg ph.:'tp chi so. Sau day (i1llng la nghicn Cllll phUCillg phar t{ji thi~ll ho'.1. elva tren linh \o,in de kh{ii. PIllI'Ong: phi.lp n~\y l~ll(}ng qu;i! hOii phuong ph,ip QuillL~-McCluskcy. Dinh nghia tiell ket IWp: Tfch kt\ ho'p c,' ella hai khoi (',. c~ l~\ kht:ii c6 C~\r cL!c dc.li thoa 111an: V(c, )cY(c, )uV(C~), V«(;)=t-V(c,). V(c, )oFV(C~). nJ co Iht nh(m dU'0C Ifeh kc't hqp la IhL!c hi¢n de phcp Ilnl1 thl'() hlnh 2.S d6i \'oi nhCfng hlll1g gi,i tri Clll1g len eLla cae kh6i. C'lC ],;,0'\ q:.:.'l sc dUde the hl¢n nhtr sau: T\6u trollg k(t qu,.! eua de thao t,ic d6 h.), lW:1l Y XUdl lHcn trunt! hal hang hm\c nhicu hcm thl khong ton \i 11 tfeh K0'\ ilnp. Trong tnrlmg lH)'p n~ly hai oinh kit k5' ll[(llll:'- (rllg ntlltl trong Y( C 1 ) V<.\ Y( l', ) kh6ng e6 chung canh \tung ,",Illll 1/ ehi611. lIinh 2.S Ciic phe]) lu~ill 11m lieh kd hop. !\Cll .\ kh{mg .'\U[il hlen dicu d() dl nghla 1;\ dl !I1()1 ,",1)(')1 ehe rltll ,",h6i kl<.\ d ,",hCm)! ph,11 1<.\ tieb t6i gi;"1l1. Trong truling hup .\ xll[i\ hiel\ tiling tal !11()! \'! Irl. neu lhay \' b(')"! .\ lel nil.\n du()"c llH)! kh6i lhO,'1 man C,IC LliclI ,",Iell clla dPlh nglll<l IIell ke'! hO'p. Do ,",h6i Ilh'~ll duoc chua.\" IlCll khl'li d{l tho,llllJn dicu ki¢n: V( l' 1 -I- V( c 1 l. Y(c; ) ;i:. V( C C ); llg()~\i ra do kc'\ qU<.'1 ella rll0r 10;ln gil-fa.\ \';\ I Clll1g nhu' giiJa.1 va 0 btl11g 1 d,O wong ung. kh(ii 1111;111 duU'c thu,; lll:J.n tllCll ki¢n V( C; ) c V( e] ) u V( c] ). Thea kc't qu;'\ clla de than \,IC, ta nh')ll dw.1C kh6i ell b(\c Cllc d;,\i. Vicc tim de Hch l(ii gi<.in tfong t(lj1 11(.1p b.\1 k~1 dc kh()i (' d) the dl~ll r.\ theo ,,0 (\{i SHU: 32 LO,.li bb kh6i (", ra kh6i trip hCJp C n6u V( c i ) c V( c, ). c],c 2 E C. • Tilll'c hi¢n 11m tich ket iWp doi v('i'i (/' C.' E C va. IH.ip \'~Hl (' trong lnrcmg h0'P cho phep. Thu tl,le n;IY dW1C tlu.re hi¢n cho den khi ta khfll1g the them vao t(l(l (' ceic kh6i moi. Do thu tl,le n:1Y hao ham dl tllll ll:lc hqp ccie kh6i hen kc dd dw.'e m6 tei a pheln tren, kc"t qUe! ta nl1<.~n dUal' de lfeh t6i gi;in. Tom lai troll~ chuonu haL ChUlln ta da nubien ellll Cl1 <.;0 16"ic dl: x,h' . ~ e '" e e. d\rng de m~leh s6. Co su OilY bao gam Ch.ll s6 chuyen nwch - de.li <.;6 BooL bi~u dien d.c hlll11 logic btll1g ccic (l<.\llg churln ttle va de phu'ang pheip t6i thieu hOil ccic bieu Illlk i6gie. Nhilng \'[tn di': nay ntlll1 lrong nen 1,lng co' him eua k5' lhu(\l thie"! k2' cae mach 16gic. CHUONG III. CO 56 CUA THIET KE LOGIC CIC mi.lch 1ich hop xlr 15' dc Ih6ng lin dUQ'c bieu dicn trong he nil! pilC!Il. Khi xfly dlJng 1Il'.Kh, de ph~p loan t!UJ'(l'ng: dW.le hieu diell qua de h:l1n logic, do do bieu dicn c;k hihn logic lrong cae In'.leh tlch hqp b,\ng nh(rng rhu'o'ng ti¢n d~IC thll iil. co' so cua thie! kc logic. Thong thuong. de h~l1n 16gic co the lhll'e hi~'ll duai dang «.\c 1l1' lch ttl [](/P, nhung lrung ph:in [(m d.c tlUo-ng hop de l1l~\ch c6 do tfeh h0P cao tlll.J'C hi~'l\ llhl'tng ch{l'c nang l~\p h.li theo thoi gian. De lUll IrQ" dc kel qw.'t trung gJan ell<\ uie phcp to[]n \<1 t[uyc hien qLtLi trinh lc}p thea thll'j gi<lll de chue n{lJlg 16 hqp ctUCiC th~rc hien tren llhCl'llg 111i lell thao tal' turin tLL Co 'i(j tllle! kc de n1<.\cl1 tic clong lur\ll IV elva 1:1 m6 hlnh cae l1!6mal huu hi,lll. Trong chucl'ng n:l)' chClng la <;\0; nghi('n CI'I'U van (16 tiliet ke de mHeh t6lH:p \'~I 1111et k6 d.e IlWeh lile ch)ng tufin IlC §3.1. D:;ic di~m cu tlU{l trinh thic't kc' l11<:ich may tinh Trong ehuCing nily ehClllg ta ngien eCru eac phuong phap Ihie! kc' de kh(ii chIle n,lng CUd de Ihiel bi tll1h to{tn. Cae thiet h.i Ifl1h IOilH 1l~ly thve hi('11 de vi thao 1{le d6i v(l'i eac tIn hl~U lac Qt)ng. Cae vi tlmo lac lu'ong Cl'ng \'fii Ihang 11'(11 11,1' Ih~Yp nhflt trong Ihang ph[m etlp dc phuong phap bi~u dicn C<1e th!c'\ bi 1 fllh IO{lI\. Ctlu true eua cae kh6i c!nk nftng phLre t' IP hon etlll IrtlC eLla de ph[lI1 IU higlc. Do do Yi¢c nghl ?n CUll ule hoc.11 d6ng ella ({tC kh6i do Ir2n cO' '-a:~ m,.tch di~n Ill' !le'li chung kh6ng th":" thy-e hien elw:c. Trang ky Ihu(lt thi,:'t kc'. ngl((\i ta nghicn eCru hOi.lt dt)ng eua c,ic khai ehue nang ll1t)t dch gfln dung 1Ili:1 kh{Jn~ dn thi6t phai tIm hicu cae so (16 nl<,lch di~n lrung IfUt'ing hQ"p kh6i 1;1 nhO'ng cflu true h)gic. Cae cflu truc logic nuy ciuQ"c xfly dung III nhCrng ph:in ILr It)gie I)' !U'lillg. 1. Danh gia tho'j gian tre trung nit' Ill',lch 16gil: Trong quit trlnh tilie't k6 C,-IC thiel hi tlnh Imlll. nh~1 thiC't k6 kh()ng dl! quwl_~~~n~g(h~hi0nck~p_l~~c~am~h~~n~ . '()'i eae S,i IL~;~!o-' ~- Kilol c:;I ;-( )1Ki011111~ dOll '1 I ~~O . ' OOO(j' -1 , ._ _ ,- - _~*()(ll() [(lOU =_: I (:)~~)i-~' : 1100 _,_ .'. II 0 I I Kilol L,LP I - ( 1-& apos; ___ +-& apos; _ ~~;~~ :' 1 ()Oc,,'" f j 100" -+ - , :;:DIU _~_I."()O '_~,~ ,;-o. II 'r ;I() I II(h. I{IC luycn la dLmg dIe ,1111" ;-/ '"it dillh-d. V6"i de ham ehu,-in I,k IH)j la dung cae dlll" ;-{ ) "il d/Ilft-d. J. Phuong phap h.lO h;ill~ theo