"" Goe d6 hanh \1" Mere kicn t~ Mile logic " // /G6c de) diu trl\C T6ng h0P kien true ~/ MCre hlnh hQc Thie't k6 V[tt IS' lI'inh 1.4 Cic goc d ll quan \,\1. I!\lrC <16 Iri:ru Ilroll£'. \'il ciic phrtn dmlll !hie", ke. a. Tong lHlP kicn trllC G6c d9 V(lt ly M6 hinh hanh VI Ci mut kiei1 true co th0 (hf~X: the hi~n qua \{Ip h()p de phcp loan vi:11l10i quan h¢ phLJ thuc)c giiJa chung. Tong hqp kicn trllc yell d.lI ph,ii X,lc dinh cae laj nguyen phdn cung dn llLrqc sit' dyng dJ tlure !Il¢n de phep tmin. ,fn dinh trinh tty t1wc hien cae phcp loan va gtlll kG! chting vt'J"j de l~li nguyen. Vi¢c tlll;JC hi¢n Xfly (iL.rng m'Jch s,w !lay phl,! thuQC nl1l6u \'010 bIJ6c n:ly. Tlwc v,~y, de !hie'! bY ve il1{I\ kicn true .s;: xac djnh mlre d() Ilwc hi~ll ,-;ong song ella (,.\c phcp toano TllI;IC hi¢n toi 1111 hOit 111C.\ch 11"en llllk nZly Ch'lllg \"ai tro het suc quan trQng trong qua tdnh thlet le". Ta hay xct y[ d~1 sau: til thiet ke m;\Ch IhljC hi¢n Yi¢c gi:li phuong Irlnl1 \'1 ph[m), -; 3x)' -j 3y=O tren c1m.m [0, u] bi'l.llg phuong phap s6 "{5i but'J·c dich d\ va dlc gia tf! ban (.Hiu x(O)=-x. y(O)-y, y (OJ II. M<'ICh di~n co the duac bi~u dien btmg ng6n ngfr m6 til ph[in cling llhu sau: Diffcq 1 I~ Read( x. y. dx, i.l): Repeat { xl==x+dx: u 1 == u - 3*x*u*dx - 3*y*dx; yl =y+u*dx C = x < a: x = xl: u=uL y = yJ: Until (c ): Writd y): ~ 119 dieu khicn I I ':' I I Bo nh(1 t ALL I I Trong VI <lL,l n~ly. de dOll gi,in. ta ctl till:; coi c<le c111'ong dfr li¢ll Clb mach ;.;uSt phattlr hai nguon: til oQ nhtm ",'a lir h9 tinh to,in so hoc ALU. fill ALL 1l;1~' co th~ tl11fc hi~n dc phcp tmin cong. trir \'il so s<-ln11. M~\ch s0 g()ll1 c6 dc thanh ghi. h9 X,lc dinh dia chi va or) dieu khi~n. Goc dO diu Ink ella mo hlnh mi teh (1 mlTe kic"n truc cho ta Ihtiy dc cau trllc VI mo etta lhi0"l kc". :\16 hlnh 0' m(re logic ella 111<,leh co thc duqc hieu dicn btll1g dlc sO" c16 chuyen trang thai Clla dc o16mat hilu h;.ln. b,'ll1g doc sa d6 h'lgic 1JO~iC btll1g de ngon ngCi" m6 t,\ rhrin c(rng HDL. Cic lllO hlnh n~ly c1lt'(.K nha thiet I c' (hl'a ra hO(lC dunc tong hqp tir Ule mo hlnh ()·llllt'C kic>'n trlle. Cic thao tac 0' mlJoc k'lgic co Ih~ khae nhau tU)'" theo tinh ch,"l[ cLla mach (nhu lll'.ICh t() hqp hofle 111i,lch turin Il,r) va d'.lIlg hieu dicll ban t1:iu (biC:ll d6 ehuyen tn,mg Ihiii hay sa do l6gic). va'n de toi uu hOii dong \'ai tro he'[ slk quan tr9llg. N6 gflll lien voi qu,i trlllh t6ng hop lrung yi2c ,de dillh de C:\U truc vi mo ctl<l m' lch. Ket qua cuoi cung clla tong IWp ('j mu'c 16gic El hi~u dlCI1 CtlLl trllC dfiy uti. VI dl,l n!ur bang cac phan tlf logic ca h:1ll \'il kc:t Mii giu<l nhlJ"ng ph:in lir do. Trang VI dL.1 tru6"e cac d<:mg dCr li~Ll OUl)c dua vc hO nila va dU'<jC (1tt'a lU ht) !lha t6i ALU va bt.,'l nhfm. HO<.~t o<)ng clla b9 dicu khien du'(.l'C bidu (hen hang sa do cllUy~n In.mg th,ii va so do logic. 15 ThllYI ke' \'(11 I}' 1<'1 qu<i. Irlnh lao ra ~o' d6 h6 lri eLJa ('/iiI} dien ILl'. Ceil' 16"r btl trf m"Jch luang lIng \'6i de 1ll,:11 n'.1 dung lrong qu,i Irlnh ehe" t:.IO ('Iill). ])0 ct6 c,k 116 tri hlllh hqe iii nwe IICU euoi cung ella Ihl2'1 kc" ole m,.teh \'1 di~n tu. Cie Ihao I,ic chlnh Ircn rh,ln elm,lll 1l~IY hI b6 trlm'.leh, di del)" dinh tllv(n. Trotlg eut'J1l ;;ieh n~ly chung: 1<1 khong di ~[tll \,~10 ph,-Ill doan ni:'y. 2. l'{ii un hna m: teh di~n l1~li lo<i.1I t6i Ull Iio;. me.leh Iw:m di dOl \'Cri h(li locin tc'ing hq'p m,.tell, T(\i U'u iW[1 m:,lch f h6ng nhO:ng d~ (1;.\1 dU\K ()' ll1u'L' <16 eao nil:11 n:: cltSt IWl'J]g nwch mil C(m 1',10 ra nhlrng llweh e6 trnh c.mh ttanh C,IO. Chling la chi :h:t c,le \:U\ de t6i uu hal d(l do eh,lt Im mg quan Ir9ng: di¢n tieh \'(1 hO' lt (h)ng ell,. mach. l\g(}~li ra 11l(lt do do ehAI IU'qng qu,1ll tn.mg !lila I~I kh,i n,1ng de kiC:m Ira \-il ph;'lt hi¢n Ibi eua Il1<)eh. DiC:n Ifeh eLla ll1'.Kh dUq"e x,ic dinh hill1g t()ng di¢n tfeh ella de ph,in tll' Im,ch. Do d{l dJ¢n tteh e6 tilt: "[Ie djnh duqc thcmg qua g6e d(l du true nla m'.leh nc"u ta bie"t di¢n tich ella Ilrng th~lIlh ph:ln m'.Kh. Thclng Ilnrh'ng de ph;:in tlf ec1 b,in ella m"ch 16gic 1:1 6e ph:in ILr [clgie, c.:ie thanh ghi, de pltan h'l' n~IY c6 dl¢n tfeh bie't lnr{re lu)' tllll<)e \'JO lung loai Ihicl kc", Di¢Jl licll dc d,'IY n6i d{lng \'ai trt) 4uan trqIlg \'il khong the h() qUa. C,k th:ulh ph:in di¢n l!ch Il~ly c6 Ihe X<.lc djnh IU mo hlnh m'.leh tren g6e d(l \',:11 I)' IH\le u6"c Im)"llg tlf ,-"ie rlH) hlnh 111":0 g(~le dt) (;j"u Iruc th :o cae phuong phcip Ihollg kc. l-liC:u n{lI1g ella m'.lch dlf(fe t6i U'u hoa til/a IrCII (h(\i gi'lll tre. Ihb'l gldll d(ing h(). c,mh tranh Iren ccie ph:in IlJ', Dc Ifnil to,in d() d,) ho'.11 cklIl)}, eua Illi)eil c:in thic"1 ph,ii ph'ln lieh c'lu Iruc "il hanl] \'J cLla mach, V:Yn d :: nilY kllelc nhau dui \'rJ'i dc IO' li mach kll,ie nhall. , HI¢u n,-lI1g eLla de m',lcll 10 h(JP dU(,J"c x,ic dinh th{ltIg qua thlji gldn tre truY~1l Ill' lUU \'ilo den dell! nl. TIt(lng Ihui\ng dl~ gr,illl dl) pln!c I'n) clla tlllll IO[\ll, la lut)]] giil thiet rang de gi,i tf! d{iu \'~10 Xll~ll 11I";ll IrDlIg dlllg Ill()\ Ihi)i dr(~ln \,:1 hicll m-lllg ub m',lell dU\1e tinh qua Ihr'ii gian tn~ truYCII tllLo lILt'ling dO Ii¢u dili nhat. Dt'Ji \'6i e<i.e mi lell tu,\n t~f dong b<\ d(l do hi¢u nrlllg c6 lh~ uuve x,ie djnh Ihong qua thoi giall quay yong cua llli.,leh. Tho'i gian n;l)' IiI chu k)' dc)ng b() nhanh nhJ"t c6 the et,H \,~IO tlweh. Tel nh,)n IhAy dll1g tllb'i giaD Ire lruycil ct'la Iii thitnh ph::in m'.leh t6 hqp etta rn'.lch tu,i.n ~I! Iil. can d116i ell,1 thh'i gian quay vt'mg. Khi la :xct m6 hlnh trC'1l 111lTC kicll true nhu qp h{)"p d.e phep lo{m, d{il vll'i de m'.lch tlHll1 t~t" ddng bi\ m¢t trong nlllrng ci{) do hi('u lHlng li\ Ihi)i giml dn thiitt tte' tlll.TC hi~n d.c phep to,in. Th()'j gian nay co the dU'0C uo-e Ilfong Ih<'lllg qua d.c chu ky thai gian. Tich ella thoi gian quay \'ong vii Ih(Ji glan tlllrc hit;n eho ta thi\i gWIl thl!e hien tcing e(lllg ella 111'.lch. Thong tlmi::mg Ihi:J'i gian quay \'(lI1g \,ZI thai gi<1ll tlllTC hl~n dlTOC t6i Ull hoa riC'Jlf; r~ de' don gi"111 [10ii qu{i :rlllh leli u'U \,;1 Ih(x! man cae yell ([ill (t)1 ra d6i v6i thict kc". eic m;,leh d60g h6 c{) the' dune Ilnrc hicn day dc phcp toan theo chl:" dl) d.\y ehuYCll ~ pipdlll': ), trong dCllll' leh se tlll.fC hi~n c{le phcp loan song song tn:'lI nhung t~lp hqp dll' li~u khJe nhau. Nhu \'~\y hl~ll n[lIlg Cllil m' lch ellil e6 th~ dU(l'e thc hi~n qua kh,\ n:mg XLI' 15' def liC'Lt, luqng tier !t~u m;\ llI'.leh e{\ IhJ Xli' 1\'. Do do dt'i eni li\ th{llIg lunllt'. ella lIldeh. Doi \-(ii nhG"nl!. mach kh{llll!. •• __ L' ~_ L' L Ihvc hi~n qua ky IhU<)1 (by chuy~n, tIH'UIg hrqng hj glll'i h'.lll bni nglqch (j.\O eLlCl tfch giiIa th6i gian quay \'i:mg va thll'i gl:ln tlwc hi~n. K5' Ihu(\t (by ChUYCll cho phep ]\I'.LCh t~ll1g thong 111(l'Ilg dCl' liC'u dll'{~'c XLI' 15' nrot qua gl6i h'.1lI n6i trcII. V6'i nhG'ng dQ do n6i Ircn, tui uu hexi hi~u n:ll1g ella lIl' lch bao g()111 \'icc gle\m thicu tlli:ri gian (re truy'?l1 lt6i \'6i 111'.ICI1 t6 hqp, Ihai gian quay \'{'ll1g \':1 (he)'j gial} Illl,TC Iw:n d6i v6i 111'.1Ch tll<ln 1l/ d6ng bel: IZlln Uing t6i cb thong IlTong ella m'.lch d(ii \<'ri nhCmg: mach tlulc hi~lllhco \ 5' thu[lt d.\y chuyen. Ngoi\i nhu'l1g h~li 100In t6i lTli hoa vc kreh tl1Ll'(k \,~I thai gW!1 n61 In~lI, hlCll liang ella ll1' lch con lien qllan t6i kh,-'l ni"llIg phal hi~n l()i V:I d]llh V! \'! tr[ 16i lrong m:.Ich. (-l,:'11 10:ln x:ly d~mg nhCrng m~lch cho phcp de d:l1lg Illll It'll c111ng mot yai lri'l qllan trong trong qUii IrJllh tllle"1 kc' \';1 t6i lilt ho,1 tnach. NhCrng m'.lell de kicm tra cho phcp giam IhiJi gian Sll1h Ci\c b() gla Ir! thl! nghi('lJl \':1 gl'-'lll1 s6 lu'{.mg d.c h~) gia In IhlT nghi~lll. V[\n de (hlU lien dlH)'C giai qllyc-I h~lllg deh It III ra nhling thui.lt to{m tclng hnp mach c6 hi~'u qu,'t: ctll1 \'an dc tilL!" hal hen quail h'ri \'l~e tIm ra nhLing thll,H to,\]) tIm j()j nhanh \'('ii llH.1C lieu gi;\1l\ thili glan ph,-i! hi¢n h')i V;I \'j trf 16i IUiJng l'rllg viii tlrng h(l ~;J{\ Irj thLr llghicl1l. T()m h,ll h;1l tOJ1I t6i lIll ho,\ thic't kC' du(,l'C (ILra vc ke'l h(),p hal h~\i 10,111' giall1 11\l~1l di~n lich tlu,re k' ella lIl'.Ich vi\ I, ng hi~ll n:ll1g ella llli.lch y(J'i J h,\ ll{lllg cao nhtlt e6 the c6. Bi:li loan l<li uu hOii e6 the ph\! thUl~C yilo cae ],;1111:' bu()C yi lIl.t nlllT gioi he.1ll tren \'e dicll tich Y~I gi6i h'.111 dll'l)'i YC hi¢lI n{ltlg. B~\J 17 lmin l(ii Ull hu,i co th~ duO"e b!~u (1Il.'11 lrong kh(mg g:iun vccW !lIlli' ~Ull. T:lJ) hnp c,ic c:lll ln~!C c6 the c() CUd mc.teh ,,;: dLroc IhlC'l kl: l.!n lh:lnh !Illll kh(mg ~lla!l. Khllllg. gian nilY 1;(,)/ b kh(Jllg gl<lll llu(:1 kc \ il chli'a llJ(.lL S(l jill'Ll han cac (hl;m tlong d6 mbi dl~llltU'O'J1g Ling \,{ii ITIi?! Ih!.:'1 kc' Cl,1 the, M{li (11':111 ( lUling L(ng 1~1 Ihl'::'1 l (Y ) :-,c c6 de gi<.i Irj d/~n tfeh \'~l hi.::u nilllg lU(illg (mg. Ta ,~C l(tp h~Ull gia Iri. lr~n cil "i) cic dOl !l(i,Jng nhu di~n lich. the)! gian Ire. lhi)i glill1 lh~rc hi¢n. thi)'i gu.lll quay \'ung, Ih6Jlg lu'tjng. Ru tmin ll1i Ull hoa mach 1m' !h:ll1h n(u tmin lim kicm dicm \<ie d!llllirung kh(lllg gl<.ln thic'l k.:: "ao l'l1O cac dlli 1Lfong: dat g,1J. tri t6i uu. 'Jhu "\y. 1j'()llg ChUUllg nilY Chllllg la dJ nghicn u'rll elc hlJ'('j"C Cit b,111 l!\lllg ljlH! trillll thie't k0 t(~lIg hop nwch. 18 CHlJONG II. CO SO ToAN HQC Trong chuong nuy chClllg \()i nh:-tc 1,.ti nlt)1 sCi vCin de loan hoc liull co _~(j cho C[IC chu'ong lier Ih(;o. Cell' kien there 10;111 Cllll )eu xoay quanh CO' so' X[IY d~rng d.c mach so dna trcn cac d',\llg ci1Uan lAc ella cae biel! thue 16gic. l\hD'ng vall de lien quan \(Ii qua trtnh 11m \/:'i !runt-' dIe Ill' lch logIC liell quan loi cae plllwng ph,ip ma ho<i vi:' 1~' thuy6t d6 Ill!_ Do d6 ChUD'llg n~IY (\uoc chia lum hal phiin chinh, m(l\ phfin lien quail tlij v[l'lI de 16i thieu I1mi cae hl0u lhCi'c logic, phfill thLi hai lien quan I(:ii I)' Ihuyet de; til! vii rna hoa. L~; thuy61 chlly~n Im,\Ch Iii co' '>()" Ihi(:', ke dIe h¢ thling so hi¢n (L,IL L)' thuye", nilY cI\ra Ircn logic ky Il.r do nha tmln hQc Bool s:ing li.\O nen. Unh \'~rc [()gic k~' t\f Iii phil! tritll ella logic hl.lc khi ta c1ua \,~lO cae ky' hi¢u hlnh lillie vii e,ie thao t,-Ie d<;ll s6 ilinh tillfe. Hai ~6 Bool dU(:il: dPlh nghla Iii m()t h¢ d~li sci Iho,llllan he de lien ck H,nh nghla: Doi Hii \,Jp hop B ~ { <.\, h, ) vZlllili 1001.n IV '+' vi\ ' " n(u h6n li('11 de ~all lho<\ man 1111 he Ih61l~ (t.11 sci g9i IiI d'.li s6 Bool: 1) Va. h E B. a + h:= b + ii, a . h = h. a: Tfnh eh[it giao hmln: (2. 1) 2) Va,h.e E It a + ( h . c ) ::::; ( <.l + b ) . ( a + e ). a . ( b + e ) = (a, b) + ( a . C): Tfllh ehtl! ph:ln phcii: (2.2) J) 3 IE 13, 30 E:: B: 7<1 E B, a + 0::: <I, a. 1 = a: Ton ti li e,ic ph,ln tlr dO'll q: (2.3) - 4) J <lEB:liaEB,a+ a=La. a=O:PldnhtL C~A) C{u: djnh I~' ella (h.li s6 Bool: \. a + a::: a: 2. a, a:::: a: J. a + I = I: (2.5) (2.6) (27) 19 c). a.{),-O: (2.~ ) 5. " -u C.9) 6. (a.h).c=a. ( b . c ): (2.111) 7. ( a -j- b ) + C = a + ( b + c ): (2.11 ) ~. <I+<I.11=a: C.12) 9. a . ( a + h ) = a: (2.13) 10. (/+h=a.h: (2.1-+j II. (/,h = u • h : (2 151 Vt'i'i he lien de ella dai so Boo1. ta c6 the chung l1linh de djnh l~' {rell. Cic llplb ly' eua d<.li ,,6 13001 c6 the ctmK tile hi~ll du6i (h,lng- l~' thuyc't t,~p hop n h Lr "~lll (Ila [hie'! c61flP hl/P A. xci 1(111 hlJP S lZI qp cae 1{1[1 COil eua A.lX<i \'ri'i hal phan ttr kit k.~' ell,t t;)p S :';:i\c d!llh phcp hop u \'~\ phcp giao n. Do S iii t'~[2 n'la Cjl' 1,:ljl (.",'11 eua A l1en llC:U [;Jr con (/ E.S thl ph<:in bLI ella a 11\'1l~ A IiI ,I Cllllg thUl)C S. V(\'j de khJI niCIl1I(lp !J(:P A \,ZI S, la c() the l\llnh iH.la c,le Jl11h \) (tl.l dc.li s6 Boo!. 2. Vai 6 chuycn m;~{'h \1()1 \ i ell,l Cl1<1 dal S() Bou[ h.hl up hop B = 10, [ I. Kbl d6 ta c() hl' llai ,,\') B(lul dun gi,ln nh,IL \Jm !tcn he 10'11-1:1 d:'l! s6 Bool nr'll trcn \'(ii 1)' (Iluy':-'t d{mg m.!~-\l mach d1011 duoe SIWlll1Ull dUd ra do ni1Q"ui.', n,-ll1l .:"i() ClICI Ih(: kv 20_ 1 h> L • _ • , • (L.II ~ll bao )!lim hdi ph'\1l1lf (0. 1) Cllll dl!\~l' goi 1:1 eli.!1 S\-j ehuycllll1ach. Cae lien d~ \'~I u\c d!lIh 1.\ Cl1.l dal ~(j Ik)d] h\l~\l1 to;'\l1 dlf(:'l' <ip dung cho dai s6 ellll\'l~n lllach. Dc 11l1et 1(1]1 mIll wong ql!<l11 glli,( 1)- tllu) c'l d61lg ngiil m,.tell dl~l\ \'6i c.ic lil'll de \':t dplil 1)' ella d,\] Sll clluycl1 IUOlch. 1,\ dua ra de sO' Mi llle.teh dU\K ,<l\' dung Ill' nhCrng ~()' dli co' Sl)'" == <l.h a 0 () 20 . '1 ph[m), -; 3x)' -j 3y=O tren c1m.m [0, u] bi'l.llg phuong phap s6 "{5i but'J·c dich d va dlc gia tf! ban (.Hiu x(O)=-x. y(O)-y, y (OJ II. M<'ICh. Tfllh ehtl! ph:ln phcii: (2.2) J) 3 IE 13, 30 E:: B: 7<1 E B, a + 0::: <I, a. 1 = a: Ton ti li e,ic ph,ln tlr dO'll q: (2 .3) - 4) J <lEB:liaEB,a+ a=La. a=O:PldnhtL. a.{),-O: (2.~ ) 5. " -u C.9) 6. (a.h).c=a. ( b . c ): (2.111) 7. ( a -j- b ) + C = a + ( b + c ): (2.11 ) ~. <I+<I.11=a: C.12) 9. a . ( a + h ) = a: (2. 13) 10.