phcp toan AND va XOR. Nhu v~y ht; eac phcp tOil.n AND v):t XOR t~tO thanh h¢ day du cua cae phep to{m. Ph[in tLr NOT e6 the duqe t,.\O thanh til' ph~in ttl' Hinh .lH X[ry dlrng phttn Itf XOR Itt elk phfin Itf NAJ'.iD. XOR bang d.ch eho 1TI9t duong tin hi¢u luon nh~n gi,i tri '1'. Phal1 ILr XOR dlf~K xtly uVng nl111' sal! tren cae ph[ill IV ~AND. Ngoai cac phtln til' 16gic hai dUll vao nell tren, trong eang ngh0 con Slf dl;lng nhung plu"in tir e6 nhicu h(m hai dtill V~IO. etc ph:in Ill' e6 nhicu d Ill V:LO c6 the (hl'qc bicll Ulen Ilhu ghcp noi nhieu lop cae phAII Ill' logic e6 s6 lwmg chtu vaa [I han ho,~e nhu m(lt ph an III duy nh[it. Cae phu'O"ng phap xtly dlmg cae JlWeh d6 dU,\1e ItJa ehqll dV<.l vZIO cae lieu ehurin toi lIll ve di9t1 Itch lmh the hall Mill eua nwch, nftng iUtyng ma 1TI' Ieh tieu thl;! va thi::ii gian tr-? Iruycn eua till hi0u khi di qua 1TI' Ich. §3.3. Thift kf car m<~rh t{) hqp 1. 'n;ng bqp m:;teh thco bien thlie 16gic Th6ng thuong de h~lt11 logic duqc bicu tlicn bang nhung hicu th{rc 16gic ch{l'a nhung phep toan AND, OR \,~t XOR. NOT. Nhung hieu th{re d6 Cl\ the duqe tlllJc hi¢n th<'ll1h m~\Ch thong qua nhung phiin ttl logic co sb. Bieu th{fe c6 the duqe phan tach duai d;~ng de ctly 1111h to{m wang: u:ng vai eac dfiu ngo(tc vii mt."ic dQ I!ll tien ella eSc phcp toano Dielt nay Cll the d;.I' , duqe neu ta ap dl;!ng phvc1ng phap pilall tich bi~u tilue loan hQe being deh viet Balan Va b6 cae dau ngo~\C. Sau d6 dl!a vao dch viet Rtlan cua bieu thuc 101 x<ly dl;fng cay bi6u dien \'i~c tlnh toan bi~u th{re. Dl!Ll vao cfl)! tl11h 4] to<in ta Xi.ly cll;l'ng so do il1i leh btlIlg each thay the' m61 bien lx\ng m(ll dui:1ng Ifn lu¢u, thay the moi phcp toan bimg mQt phfill It'r 16gie ca \1.I/l. Sau el6 la X[IY dl!llg m' lch theo uk h¢ d:iy dil dlI<Jc Irlnh h~IY IHlllg ph in Illr(le. 0,'lili ph[in tlf ea h;IIl eluC/c thay the bang sa do lUollg duong lrong h¢ (l{i:' dll duc:J"C lL.ra clHJIl va gii.lll uoe mach hAng nhling phcp hic'll ch)i l()gie, \'1 d~1 nhu Iwi pllfin tll' NOT !TItle noi tier e6 the: Im.li bO. Ta hay xct m()t VI dl;] thic"t kc ml.tch Ihue hi0n bicu thlre I()gie: f:::;: (x + y.z) EB 11'. fiicu Ihll'e n:1Y oUCjc viel du'6i d'.lIlg deh vic"1 Balan nhu sau: t = 11"X)'= . + EB . Cae bu6e phdn ti.l.eh clU\fC tlwe hi¢n bn 1u-r.11 cho den khi nhi.~n duqe Illt)t cfIy hOJJI ehinh, voi d.e nut trong I~l cae phep loan va cae nlil IS III d.e bic"n . Trong VI dl;] tn~n : ta sc co cae hu6e Xi'ly dl!ng cay nhtl' <.;<.lU: ~ ~ (x+ y. z) +.\ l0 +. mull 3.9 Xii}' dlrng <;[IY linil lo,ill bleu \V \\ Illlk.f = (x + y.i) EB 11". I C/+b ,/+~_ . I 7 Theo cay hi6u dien trcn ta c6 the xii)' dl!ng sa do bitu ditn m<'.lch theo de phcp toan eei sO: XOR, AND, OR va NOT. 44 llinh J.IO .\:;ly dllng 'it) dci Ill<tell 111<:0 e<ly hl~LI dil'n Ill' e,jc ph[lil III ,\: ID,OI~. XOR, MH. Dc ;";'[1), dung so' ell) tren dle pli:in !If cO" sCi NAND vii NOT hO(lc :'-JOR \,~I NOT Ihl la ~C X{IY d~fl\g ctll' ph[ln tu A:'-JD. OR. XOR Ilr de phfin tlr ella h¢ (Hiv (h'l Iren: -2=J" = , .\-y = 1I1nh J.lla Bic'u dien luang dUlTllg. ellJ eic ph;in I{r AND. OR. XOR trang he d,iy till ~r\ND. , = , I1)nh J.II h Uil'U dlcnllrOng dnOn.!! ella [lh in tlt XOR trong hc d:iy lIll NAND. Sau kIll ap dung dc bieu dicn luang duong ella cal' p!ifin IU logic Il"Ollg eic h¢ d{iy dLI khi\c nhau. ta nh,)n dW:K sa d6 sau: 45 JIlnh 3.12 So do llldCh tlnre hl0n hiQu thlre f == lx + \'.::) ffi )1" trcn he NAND vZ. NOT. :'-Jc!u phtin tll' XOR Iham gia \'~.o trong thiel ke. ta Ll1 the ~Ll' dL.\ng e[le h¢ thCre tl((1ng du:ong tren hinh 3.11. Oie h¢ Ihere n:ty dU'(/e ,uy ra tnre IIC;p tll' IlllJh 3. U (\ic so cia \UO'llj! dlrong ub phep hll Irlr kigie XOR Dieu d6 co nghla la toan tu NOT trong bicu tlnk eva long XOR co the' ll{im l1 mqi \'j Iri. T(llll 1<.li phuong philp xtly d~(ng tni,teh tn!e tier tlr de hi6u Illue 16gIC nlnr dJ neu trcn \:J. phuong pluip don gi,il1. V(1i phuong ph,ip !lilY' la u\ the ,\:IY dLl'llg dlr~K 111Qi 11;:1111 logic v()i nhLing dQ phue 1' 1]1 khac nlwu. PhU'(1ng pll,ip nit,v c() mol nhuc)c di~Il1 16n lien quan Wi thbi gian tri': ella tin hl~'Ll dl qll,l m',lch vZt d() d:lj cu,' tin hi~u. Tlf vi dl.1 tn:n ta thti!" d6i v(}'i cic (tlu vi\() '\. y. L. \Y. cae tin hi¢u tac d(lllg phai e6 dQ dai khac nhau. Diell d6 1:1 do e[lLl trCK philn t£ing CUil nwch. Tin hi~u:: d~ di fa uU\:iC (!iiu rat ph"li lii qu,1 b;'ry p\l['in Ill'. trung klli do lin hi~u \j' chi can (II qua ba plliin tlL 7\hLl' \,,~y 1;1 plHii 11nh to(1I1 de) dZli de lin hi~u tae d<)llg V:l thoi diem I;ie ct(mg -;;JO eho nlIrlll duO'c gia tr! dC\!lg (} d:iu raf 2. ThI!c hi~n eac ll1~eh hai hing Ta e6 the !w':i !\)ug phl(,1ng ph;ip Ir\':n \'~I dlfa Ir\':n co' Sl'j CitC ph,ill ILl' e6 nhieu diiu V~IO. la co the x<'1y dlfllg de s()' do du6'i d~ll.g chinh lile: A!\U-OR. OR-AND. A; JD XOR. Trong cile phuong ph(lp thiel kc' e,le 111'.ICI1 kl! tang trell cCi S(1 cae phfin tt! AND-OR va OR-AND. ben Ci.lllh bic'n x, ta dn thcm 46 de gl<i Irj u'la x, . KlIi (.I(J (;~lU Ink mach trb thanh lXI t<lllg do Slf dL.lng 1Ia:"m ph:in Ilf l\OT de t;.IO nell ph£ill Ilr bll. Phuung plI<ip X,'i)' d~rng 1ll<.ICh tr~fe lle'p IiI cue Ch.lllg ehuCln (ill' (.hrq·c rno li\ trang plI;ln lrul~je trell thL.rc 16 kh"m,g. c6 hi¢u qua. Trong Ifw"ing hop bl~ll di':Jl h;tm IClgle du6i dang t6ng e.ic Ifeh 16g,ic, tfUll"l1g hqp X~ill nilfl! t< 1 c<'in (2" - 1 ) tich ey'c tJ(:;u V:l khl do dn ( 2" - i ) phi.ln tu AND Wyi /I d<.lU vi\() \'i:1 Ill(lt ph~in tll' OR \'6i ( 2" - 1 ) cl[iu \·uo. Trnng [ruling hqp tham gia x, vii .r, khi dll din thC:m nillcu nh~lt EI /I pll<i.n Ill' : JOT Irong llUang: hqp xily dung: lm~ch lll~ll dUll'J1g. NC:\I tfeh CLTc Ill;U cLla /I l)JI.Yn Iln,le hicll nhu ('r pllan lnr6c, khi d(\ Cilll [{ill,!; c0ng ( n - i ) ph;lll IL'r AI'<U v6i hai (UU van ho;K m()l phii); tu .'-\1\11) v(J"i II d::iu vilo. TUong I~f ]1l,?t ph:ill Ill' OR v6i m dau vi\O e6 th~ thay b,'ri (Ill J) ph:in tu OR \'(1i hai dihl V:'IO. Klli x;iy elL.rng m;.tch Cal' pldn Ill' 16g,ie C{) /I d[tu \'ito cfln nhiC:u elien tieh trl'll tinh Ih~ bun (WO !Jon kill x;ly d~r!lg trC:n !lllling ph,il1 tlr ell hai (till \';\0. Do c1{) gia thiUlh clJi1 mi.\Ch cling phu thU(ll' \';10 srS iU<Jng drill Y:IO ella de phtll1lL'r logic. D()i YlJ'j \'l¢e thll"t k6 c<.ie 1I1;.Ich tI~ h(rp SLr elyng SlJ' d6 hal (iing tilClIlg qua de ph[in (If AI'<!) \';1 OR. dicll quan (I\lng la gi<illl dm/c sCi Illljng. de ph,ll1 tti Ar"n) \';\ OR. DC:n cdnll I'i¢c gi<.'tm srS Iwmg C:lC pl1<ln liL 1l1()t diell quaIl trong I;. gialll s6 Ill't.;l'Jlg, (hlu V:IO CLl"o I de ph~in ttl do, Ta (;6: t;)p hup eic kiJ6i e6 gd thilllb nllo nhilt chn ta so' do Ilai t:lllg C(l g!it th:mll nhl) nhill tren eli SlY A.'JD-OI·C ClUing la h:t,Y xC! 1110t vi ell.!: la thiet ke m;.tch tlll-!c hi~ll h;lJn 1= V (0.1.2.5.7.X.IU.15) Sau klli t()1 thicu h6a. t<l c(): 1= {xOxlJ. OxOI, Illx. Olxl J SO' (ki thie! k0' me.teh (h~re hiGll h;)!l) /dlf~J'c dua ra IrC:n hlnh 3.12 tlwo hal thiC't kl.Y: thic't k(" then eI;.mg chu;ln t~e wycn tn,rc tiep viI (hiC'1 kC:' ,au kill thi thieu llO:\. Ta n1irtn thil)' thi":'! k6 lrl!e lic'p piluc t<,IP hon (hiet kc'sall khi d;lt(ii t[ll~L1 11m! .:,i \'~ s61u0llg C:\C ket n<:li. d \'c s6Iu(f!1g diu V~lO cLla de philll It'!, IClgic. Khi la tLli thicu ho;i cic halll j()gic. tn:l!lg sCi cLla t~IP h\rp c<.ic kil6i dU'(,JC x;ic djnh bflll~ (h.ti luqllg (ttm diGu Wng then s6 V! trf bic'n trolll:', khiii ng();li Ini \'! (ri ehL"ra x tLre Iii eile \'1 Iri cua kh6i m chi6u ( /I - fII ), vit so llfl.l'Ilg ele kh6i tham gia vao t~p ilQ'p. Tu I,)p hqp kh6i nay ta e{) tll.:! dU'a ra In.rc tiep bi~lI there logic duoi eli,mg elwin t,k tuyen. Mot kh6i tl1ung LIng \'6i !l10t tfch IClgic 47 vi:' eo Iht dW1C X[IY dl,fng tren ph.tn tll' AND c6 /I - J1/ dau vao. Rien x, Wong ll'1lg v6i gIC't If! . I' trang kh6i siS n6i tn!c tiep "oi plJ<i.1l IU AND con hien x, tlfong u'ng n5'i gii.l trj '0' -;c n6i v6'i phdn 'trl6gic AND qua philo tLf NOT. Khi ta x[IY dl,l'ng bieu there l6gic duai ch,mg ehutin Itlc tuytn. n1<.leh chr0c thlc', ke sc co d' tng AND~OR. 56 JU0ng d£iLl V~IO cua ph un tLf OR se btlllg sO' hrqng de kh6i tham gia V~IO \(Ip hqp kh6i noi tren. Tu do suy i'<\ khi ta 'hie', ke Ill~eh Ii.) h9P thr.:o de mach IlJ.i 'fing AND-OI( h)p lWp khoi e6 trqng so nho nhat sc tHong ung vai 111<.,lCh co gia thi'mh tlwc hi~n nha nhfiL 48 :. , .', o/~'~ ·'!: - >.::;, !,::: ~ '. i I., ) , -I al IIInh J.14a So ~,illh hal rhie'r kehiun!trcn lllach AND-OR_ Trollg hlilil ,\, Ihiel kc' theo ch,lllg chudll rac, I IlInh _~.14h So ~linh hal thie't kc"h:\ll1 {tf<.':ll mach AND-OR., Tl'Ollg hlllh b. mach dlrac thie"l ke' \'01 f!,la thil11h nha nil!!\. Khl ta bieu dl~n bicu thuc logic du6i d'.lI1g ChU{lll tflc h()i. su do s0 dU"q"e tlwc hi~1I c!mJ-i tL.mg e{lc ph:in tlr OR-AND. Ul[fa de so dil d'.lllg AND-OR \"~l OR-AND C() Sl:! chu.y~n ti6p v~ de d:'.lllg NAl\D viI NOR nhl1 lr011 hlnll :1.15. DJ(::u d() dU\K ~uy ra true tic'p ILl" dinh Iy de Morgan: f[ + fc 0= f[ j",. OR-AND NAND a) IHnh ].15 a. SIr I.l.fang dLlling: giLr<lIl1<u.:h .·\1"'1)-01< \i\ :"JA~D. t>. Str lLIL1Ilg dtldllg: gill<! mach OR-!\ND \':t NOR. Trong phan nay ta khong quan 1,1m loi ,'An de giOI hi.1ll ~l)' lu~mg diiu VilO eua d.e ph,in Ill" co ban (gi6i IWIi thea d.e nh:lIlh di \'aO d.lu V;IO ) v21 gl6i h<.111 theo lai d,~t VitO (UU ra ( s6 ILrqng 1"0 nhanh d d;iu ra ) eUi! chung. Bi¢n philp lh6ng thu6'ng de 1m.li b6 d.e gi6i IU.lI1 n~\y 1<\ Irmg sci lu'qng d.e ph[in tu logic va tang s61u1ng de lap phill1 IU. J. Tlwc hi~n I1Weh to IWp tren co' sa cae PLAiROl\'1 Ma tr~1I1 logic 1~IP Irlllh i~1 eac khai ph[ill IU: VI 1m) dLJt.:iC ~U dl.lllg de thi0'1 k6 nhli'ng m:.\Ch LSI. VLsr theo du truc d.e nweh hai t:ing. Cac PLA hao g611l ma tr(1I1 AND \'~I ma tr(1I1 OR dl1()'e mile noi tiep. Ma Ir:1I1 Ihu nh:it l~\ ma tl"<)n At'D. ma {r(1Il thu hai ia ma tr~1I1 OR. Tu un.lc tnJ'6e 1<'1 Ih.'I), dll1g cfiu trlle hai t:ing AND - OR Wong dU'(llIg \'(')'i du true hai t[ing eua de ph[in Ilr NAND. Thell nguycn I)' d6i IlgtlU, e[iu Irue do eung lu'(mg dLtang v(ji CiYU tnie hai dng NOR - NOR. Do do trong ky thu(\1 Ihiet k6 de cau true hili Hing NAN D-NA l'\D v~\ I'.'OR-NOR duqc Slr dl.mg n)ng rili. 49 . hO(lc :'-JOR ,~I NOT Ihl la ~C X{IY d~flg ctll' ph[ln tu A:'-JD. OR. XOR Ilr de phfin tlr ella h¢ (Hiv (h'l Iren: -2 =J" = , .-y = 1I1nh J.lla. chinh lile: A!U-OR. OR-AND. A; JD XOR. Trong cile phuong ph(lp thiel kc' e,le 111'.ICI1 kl! tang trell cCi S(1 cae phfin tt! AND-OR va OR-AND. ben Ci.lllh. h()i. su do s0 dU"q"e tlwc hi~1I c!mJ-i tL.mg e{lc ph:in tlr OR-AND. Ul[fa de so dil d'.lllg AND-OR "~l OR-AND C() Sl:! chu.y~n ti6p v~ de d:'.lllg