DE Unit-2 Notes Part-2 PDF

uNrr*J! >::- COMBIU ITIQNAL LDGIC "=: digtto! (ot?c ci...

uNrr*J! >::- COMBIU ITIQNAL LDGIC "=: digtto! (ot?c circuitt Ittere q\Q ttrro tg peS oR \i) Cotnb'rno.No\As-! circuit q Senuerntlo.! c-ir cuib seXtrentroJ Cr.fCUrit o(p depends 9n p{ese\$ ilp s )F olp depernds s0 presq\t l 'itF's q po.st o[p's , I iF CorrtoirrS \o tqter.nrcr.$ marfioYu f contoing tvrtqVnq0 $nernof$i ,+ tt corn sists o R loXic 3"t.q XSt corcrS\StS o€ [oqic [o*Qs 4 vYpmo\ t ote,r"err,r i1 * Btoc< cl-ioqvum , * S(ocr< \ra,rrn ii if , o/e *-ole vatiob\el Vavtq[[g1 Des^?q.n. , \F D\ocad\NQ \*-- ds t"unb'.nqtionql srt step t '- Fsgcn \,,o- SPecre\co't'rovs oQ 't\No- t-"X tuit , v-eauired v'\\NI\Nhg{ eR itP's 4 olP'S de-tennirno- -tua- o.Sstgrn *. o. Sr6mtco,8. {o e-acl". slep g'.^ De-x\v Q -t\No- 't\Lr\h tqbb *tho$ de8ivrel 11^a fe-gtl*Xe&.6etcr.hlo\t btto i lp's 4 olp's Ste?-B:^ O btoi..r -\rxa_ stnnp(\R\ed toeo(ec.n (u,nchons {oY eCId.^ ofe o.l ^(utrC*sovr op -!rt^o ifp vaViqto(e3 , Dloo *u.q \oqt. &i o-X{orrr 0^^d u e-ri€t6 SSr-. +tl.a- C-oKrec}-rtess o€ -lt^a- desiSn , * Code- c.QnVeTte\S '.- crJ -5 > co\st\uc* 1:'":t E:S$ S S\ qe4--: rC 4 - bi\ Birrotn -tID g!o.\ et"d9 co\nvaTtQY aoNarts a.'l 4 - tatt \si.n'otr5 4 trit qR\ co&e ' c sj c"! e[B:o] jj * crrq\\ -a.H) G[:ro].J B Ls: o] --) Q * b.'t B-rqq\t numhq ' c= R= BsRrR,Ro c c,r[a'. o] ---) 4* btt Qrou nurnbe\ c G: r = 9r 9r9, 9o c c.fruth t-qb[e : - J olp J Bs Ba B, i Ip C Binurn) C Grro$) c o oo oo Bo 9s OOOO Qr q, Glo J I oo 5lO ol lO o o o ooll.1 J GJ 3 DO ll -o q t o q ot o().o t,. I o "J GJ s Ol o I -*-- Otll GJ b q3\ 10 otSl r \ I "" OIOO CJ ? o - I I I Doo I oo J"J 3 ,o fc I I ool o\o ltgl I 'l I J rl I o I|- "t \ I \ c).4 e{ leo r o o,l orl l6to J r3 3 l( l+ I r o-l to ol cJ I r l-1 J I r5 I t 600 t S\n gtot nu$ters I'S are rn"\ntefm S o's o.Ye Mqxterins- I  slo _ 1m( t,2, S,6,9,1o, t:, ltl) Cr,, = 6-ro ( z, 3, e, 5, lo, tl, t9.,t3) c,,a = arn ( at,s,6, 418,9, to,tl) ra3 = 2m(g,q, (or u I t9., t3,r\,ts) K:\oP Fc)K QO :- qBN o0 ot rl to a! Go= E,tsoB&-o = 8,6 For Q, :- B.eN-\ oo ol u Ito ata Q,= B,B"+ R,B" =. 816B, trov Q, '-- B.B. 5& oo ol t\ TD G- B"E,+ E. B" = 83@ BL EaBX 'ao I o, I rt tO  EL. c\\ault$ : - OA B, Qo = Bos B, Bl q, = B.ORL BL i", = B" Og^ s B3 33 = ,,Bs iB-Qvqrl to Ei-X JlzSUe-ttS\ i- QC= Gr6E3 RB= q3 rG BCb to EXCESS-3 co\va{tQY : - 6-- 4-btt Bcb - Bfs:q to g6cesS-3 E& :of BLt:ol -> BcS hum\e\ co\nvQ{tQ\ ECt:d -+ ExceSS 3 numbe\. Sutn tgble'-^ i[p ( Bco) olp Cexcsss-$ Re R, R, Bo E3 Er Er E- C) o oo oolt oool O I Oo ooro O lOt ootl o llo D 6 oo ortl BCS *a1*.5x\efs q\Q o*9 o I ol I o oo ol to I oD\ '. cons.\de\ (o -lS o-g dont co.TQt ot(t t D to. I o oo I O rl lool I I Oo  ZrnCo,a,\,6,4) + €d((o,\\r tar t3,tq, t5) -o (o \lr (3,1,*, lS) Er= t$0(c),3rq,+rB) +. 2d ( r ta , t== 5-ro ( t,2rB,q,q) + ,A Lto,i\,t2r (3,lq,ls) t\r ta, t\, t\,ts) Eg= 2mCs,a,a,B,9) + ad(to, K- \qP Stunp(t(.co.t\e\A '-- FoI E6"- E.q B"E,% E% E, R,Bo B.Bo %B oooturo. BaB, oo -il t B&82- ot \l rI BjBr ti x X x xl e"B, ro ID l/ x kt r------=-1.'. lEo = Bo I PL !,:- B^8.' 3aL ,S ol rl rb oo n l'rl ol I I tl x x x x to L' r8 x FO\ EL..- %-'\'t 6 ol u (o Y-B-  cg\it B3 @u ir > Eis.r P I Br\eS:- Trut\n tqtote:- ilp C ercess -R) olp Crecu) Eg E, F, E: 83 RL Br Bo oooo x "x x x ooot x x xx o oro X x xy O D I \. O ,b \O D o 100 6oc>l o tol oolo o tto Dott o rll o I oo I D Do o (ol lo ol Dllo lD to o I l'l lo { I I o. o o ll'Do I oo I x\x'x tr IID I llto x xxx lt) r x xxx. Snlqrq cov\vQtte\ : * - t 5 J- t& -fl Ex'-^ t ,}6r otB qYe 4or tD - tS fro.'s 3 MSRs ' ots ' nqq te e* 3 MSR'S. 0 T\Lr$n tqb\e'-- ooDo o o o oo ooot o o oo I oor6 o o oi o ooll o o oll O r oO o o I Do o tol o o to, o llo o o tto ootl oolll I ooo o I o oo lbot o to.o I lD lo I O. o o o lo tf lo ool lt oo lo o to Itot lo otl lr16 lO t oo rl l1 lolol Bcu to, ho.\SrV\qy u Cc)*s\\S{\g-\ : - -ll tr.ntr-\J ( ecs) olp ( Binov$ D,* b3 br D, !p Bo B- B, Bo. o\ooo t ooo o o o o olo ooo o\ool t ool oDoo'lo ool \ oooo \olo O o o ' olo oIo I o o.o I \ o tl oootllo oll I e o \o \ \ oo o o 1oo[o too 1oo\l I lol o D I D r\o 1o I 1D tOo \ o \ol \ r to o o \ I o\o t Ic  AooEQ.s '-^ s Addqr is o\ diXit u_8 qirctrtt tlst^ich Pe\eot{cr s qddi+\ on opesl.*rorlr.S l. B$ N!s:- tvre toXtc c-.r cr"*it tr:hicU pqv€osms o.d&it\olrr og zhirl ts c-o.\\ed o, " Hq\( Ad.det ". tt colrrloinS turo S'rUrX ffp- ( AuXeu,.A 4 Ad&qnd) ur,rd tu)o R\rru\\ olP ( S.rrr..,r S QrrUJ A S.r\ B c_q\y\A Txuth 1c.b\e'.- 't1p's.1p' s A R Sutr\ Co.v\$ O o o o O I I o I o I o t \ o 1 rs SiwpLtRi c.s._trem..- FoV S,.rtn : tsr___ls$s r- B A ol a c) -o A() A ? o Ar ,o. St\rq Ats+AB ooo ac\\\t = AR AOB li bti.. 50 c-\yq\L\t,.^ A^ r )}.Suvq CAOB) -EcqY\B (AB)  6 X. jlr\\ $d.c}.qX Fu.\\ Adder ts o\ co\hnbinq\ornqQ q\rLutt\ -\\^o.k futoos -t\q o.X'*\nqnl.p*tc Sq\Y\ oR :-btnpu* \oits. f,b -rhq lhird tn Put is a Lovrststs o( ts itP's q 2- o[p. \, usholcln sap{asqvtts tVrq cq\\t *rerrrcr -t{^o Pvev\ous \\t (^ " -tY\ s\td(\ c-qrnt f:oS\t\e\t A S\r\ B c. cqY\B Lo\) Cst-rr Txut\ tu'.ote '- ^ t(p's otp's A B \C S..rSA,j co.rr\, ol o ol o i o ol o \'lo ol I o\'\- ol I riD lt llo o\il' r \o llo rio \r l lt Di" \' \[r rirlr. t: wrqp ,,::. :l-, si$c\p\i.(icqrbns: ^ Fov a\.-r\- Sq\0n _r". tu A\. OO Ot t\-tO o o o I 0 o oon SrxNn= AEc+IsE+ AEE+ Aec = TCEc* ts_c )+ ACBa+BO ('.' a xY+xY= xov) = A(s@c) + AC B@e) * AOR@c' trox *a:a-aPU CqT\q A\" oo e>l tt o I ooo c-u\\f, = AB t Bc+ Ac' S'. w1 ( *o 4 - b?t Btnmi 6 vruv'nbqr s.{ dl A = AsA, A,Ai R = BrBt B,8o *l "dl ca q AL Ar (o - -'ot 11$ Auqend..1 A3 Ao -->..1 B3 B! R, Bo *> --) Rddend fe.sukt. c Blgss- &rq$o:-.----a-_ Addo'nd Auqpnd s J J A_rAr4fto cin=o $  43 Sgbtvoltqxs: * Srl\stXo.Ctol iS q. d^1ito-I c\rtuit r,.in\cJ,\ per €o.mqs Su.\atYq$\o[t Oeq\C.JttO\NS I. Ha\e Sqbtro.tlor : - ?s o.. co\t\bt\^0*to',rc^! eircuit u:\tcta Pa\ S,.lb\xo(\on o€ *{rJo " 6!vru\t b^'tS. tts \"c8 tuco tnpu.ts -- (nnl,nue-.nd 4 su-btru\r'orv.d) otnd tqro o \AD\rtq t digter e\^\co 4 borrou$ B(oCls dioqrqtn :- A #D'{{Q\e\isQ Brybvrcl.r.r Tvuth tqb\e :- '.[P's olP'S A B D\Pf. RottotO o o o o o I I t I o I o I I o o k - tv\op SirnpLiftco.hon :- -Por DiP4etencQ:- -dot Boxrou: EB ot A\.- Io A A AI oif{. = Ier.AA_ As -..Bsr[oLrJ: AB  Loqtc- circutt A DiR €erencg c AoB) B Bo\ \ot f, C AB) 2. tru\\ SubtxqctoY -l : - qtto( iS co,nnblnqt\oy,oj circuit trr.r\\ Su\stx : q,chich Pqr€oftns Sub\sqClio\x o( ?* h.irrroxX b^ets bg t+ tnal covrst&erirnX bo\xouo oR *t\l.q PYe\,\o\L\ Sto-Xe ' o \r.fFutg B inputs Btoc-r( diqurosn'.- s A b\8 $etqvrce B Itut\n tqb\e ',^ ik' s ole\ A B Rirn Di(8 \"t o D o o -o D o \ I I o 1 o I I D I I o I I o o I o I o I o o t o I o o I I I I -. K- no.p stnnp({ice\r.o\\\ '-- For biR Rqxenqe t- e Ru\ BBin RS-iq ol r\ ro AO D\R Rex.ence :- A 6 BG Btq AI Si € Re.rence = h.BR'.n+ AeR,o *- ARR,*. * ABR,n A( BBrn+ BE,u) + A (R'Eio+ eei*) A( aoRrn)+ A(BoRifl = A(Roei$tn = AOBOBTn = AOeORiq. trD\ Boot '-- E sin BKin eEi n A o\ t\ to h Roqt : aR r-E sr^t B.Ri5 A Bout = Aet ABtn+ RR1*., (oqic cirtutt.._ A bi€(erence- c A oBoB'.o Bout C Ae t E tsin* RRrur) Ca{\ a\So lae iwrplemer [.\DtQ ".- A 'Pu\\ S u\>tvo' (*o { a^^d t oR t o.?rl^ tuJo lrtot( Subtxacto\s -nte-d tcte' oi t€erqn ce Bout  bieRq',,cqncQ- = Aoeo Bin ta Rout = (Aots)Bin + Es ( Atr t ne) Bi',. + Ae - T.t ARBi*.t Ag nEei*., (... AtBc = (AreXnn.f ) = ARei. + ts(Agn*A) = AE ei* * B( (etil(e;A) (-' Rth= r) = ARBi.+ BBi-q+ BA a Br.,(Atr+e)+ --. ea ('.' AtBc i(A+R)(atc1) = (.'r (-Uit einnq\t r\0' \. f A:AgAlAtAs B = 83 Bt B'. Bo' A+ zk' cornnPtu'rnqrru oB B A-B= eo\nP'oe B +\ = A+ rts C2- c1 co uinrrqvrd 43 Ar- A' Ao --> ,tS qb$rlP' oF R Es E, E, B" -+ t" -ht Cs Ss s2 Sr So Btect< diqqYq.iYl:- 83 B' B, --_-.--*_1]- 4 - bi t poxqrej dffi  toet c diaq \qYY\ '.- 83 43 ) (or - Btnqvq qddqr/ Su\atxo-$ol - Psrs{tut SdsI/$lqttov a' _ --------:----:1J ---------: : Br Ar B, Ar - Bo Bo Sz S, glg:- 4*bit Pqxq\hJ oddev I sorotv..rr.t. bJnef e \^ - Cs\nr\ot(\ input, ie \{ =O (.' Aoo:6 - M:o (.' = AsA" A,Ao t Ra BrR,Bo ciil=o ) = AtB. "'. Li'e ) -r\nts c-ircutt o.C* o.s o.dde\ 3.€ t\\=\ *thqrn o\].ttpr.q - A3A,A,\ t qE,R,Eo * Cin (:' Ast : a ) A3 Ar-A, Ao t EFS,R-" + t ('" M= I =) Qn: = = A-B e-irqr.r\ o..(".t q{ Sub't\qc*ox A3 A1A, glocr d't (+-bf F fu.rallel A &,  oheod co\\!\ Rgle\qto v- f :- *= -rhe Surn qyrd cq\\t outErt\ o€ q\U Srqqe oR n_b.rr Fo.\q.\\e} o.dAer cqv\Yot be Produce6[ Llnbt -tb,e tn\p,r$ Ca\\t occu\S , -illis Lqqds to tirnro dnQ tvr qddl+iovr Fxocess. fhis.tu\o1 ir Knoush q8 t\ cq\\t p\opHq*iqrt d.e\oX," * L Acq ts \).sd tD e-tiv.ntvrote t\,re- "ot\ { cf-e\ * LAC o.&ditton \r(a {roo €*.rvrcNe,,,tr Lt) cqyrt tenercrre 1Or) CL cl c- (!i) cq\\t P\oFqtate C Pt) A2 A, A6 + B2 B, Bo cS S2 S, So ci *t e- HAS q\nd oR gcll* t'':^"ttn Pf cl Sh0\,5f).i Pr = Ai6Bi Grt = Af 'Bi utl*t p 4 crr, Susn 4 ca.tY8 ca$ be QXPIQ SSed qS tsnptqtnqr1t Rab o.dcteV u)e- feguivqd , ti ) A - rok bo.\a\\ qddey {or i\lit\o-0 eci.&irierr Lii ) LoStc cir cut t tD detec+ Sutn ts ${eotey :*ttern q O'r) \ot , r-ii\; \ nnorQ \ - b."t binarll q.&der to a4d (o t ro\  to t\re sNr0 te SLNn ts eq\r$ ts rS Txu\ tq\ole ]P tSdSS["* (ooic --*-* $+rlt p *tec* Slm0 -- s< S. S, So oooo o o o'o I o oo lo o ootl o D t oo o o I Ot o o I to () o[e ts u:hqrr ilp >9. ottl o I O oO o t o ot O to ro I lolf t. I I Oo I I I ol I I lto I \ I rl t t - t.nqe sisnpti(i qilt\gn : - {ox y :_ -s,S. ol {1, oo sSst_ o\ \,sr- t I s=S, to ,'o Y= SBS,+S=S, --* toqic diqqrqto :- 43 At Ar Ao 4 - bit binarX o.d.de\ ctn=o ofp covrX Q.te 4- bit Rtnurg o.d d e.r CtSnorea) ctn =Q * 4 -toit Rt".ort 3.n c\a\\e\t\tey ! Ca c1 c. A = ASATA,Ao - br.t \!r1ur\ \1o' A3 Az A' Ao t I At \ = Ag ArA,Ao t t Cart.f slS sD  ,k 4rbtt Bjr\s$_ DgJEro5$3;er- A = 43A2-Ar Aa Q-bit R!\Ao\{ 'rc\w\he \y \y A-t = A3A"A,Ao* oool = 43 A- A r Ao+ 2's 6t'nP' o€ ooo I \t o( Oool t = Ag A. A r Ao + r'S CoYnP. I., \\lot \t7 = A:A.A,Aot I * +'A Bino.rg ttu\tip\ie\ : - (i) zx :- B.nqr h ttu\(Ptte\ '-- R = B,'Bo fl- A,B. 2-bit 6irorU Y)o.'s. BxA + B, B6 --) Mu\hptiLa\d fexa = Slrrrop(e rnut+ip[i cq$ion\ I xAr Ao ---> t'tu\ti n\iet l AoB, AoBo l Pqttio-! preluc*S A,B r A,Bo i l _> I c3 C2 Ql CD Producr Ao A.r  \ Bt\q\t B =' Bs B, B, Bo 4 * b'tt v\(e. 3 -bit K,nutX (0.' A =AlA,Ao BXA *---) Mutttp\icqltd Bs BL B , ,Bo t"ruttip\\Q\ X A> Ar Ao -) AoB, A;c, i AoBo _1.:: :, r---- TAs. A,Bt A,B, \ I A,\, I Pq\ticri p\odrl.u( , l J I i*-: I i I ArB" \ {s= A"q- A,B, ! ca cl G --> trroduq csk ,i.t ' ilr, Ao A, 4- btt' B?nrrX Coqt Ss 5- Sr A -btt Bilrro\\ s3 sr- Sl g.ostlDofc\to\ --- tritiEot to:nnEfolo\) : - \ J * A corrrnPoto'\o{ fs SP ec\cL0 CoSn\ira.q*i Or,..s., ctt cuit siqr"od - cl.e Pri nnar i\r6 to eov\npq\e \-tr\g re\o.*ivq rnncrgn\tudc-r C>e tuco R\naf X nurunhe,cs. {A tt tecdrles tLDo Y\ - b'\t nuvnhets t 4 B aye ?nFut q.n d pxo &urel 3 oulPu-t\ R:8. A(8, A=ts U$i3g gbit coloParcrtol bqic _\: gqtsr a - bit coN\NFA\o.Jro\ connpo,.xal 2, z - teit bllnorrX \u\ba\s. Btoct< Aiosvoro'. -_-r fifr:ol SD r ol. 2- bit CetmPa\1tStt A=R AzK AB AB) > €.nn ( q ,8, 9 r 12 it:' t't) (A (B) t{- vrqo sirnnot\R\cotro$ '-' -- (A=R) : 2m(o'S'\o'tS) oo (A = e) 5 E, AbE,Go n h,floR, Ro * ol A1A6f318o + ,A,FoR,Eo rl = fuE" ( A,R, + A ,n) + aoq(h,B,. n,n,) : C 'q,E,+ A,R,) (A-6Ro+ A.RJ, to (A:B)= (Auos"[A,OB) E>v tA >B) l- trD( ( A{8,):- tf LA>e) : 2m ( \' 8 lQ,lz t3 'rt) ' (A ol I o D \o I o O (l o I I Oo \ o ol o I lo O I \t I I Sr.rrn: Znn(\,r,gr$) c-urqrX = am (r" :,s,6) = 4urr(j,s, 6,+) Fu\\ c.ddex qs\\^g Decodqn q exey\^a, SqteJ :^ A \ ts Y = awr Ct ,r, \,1 ) C 3:B Y d,o-co&n. Y ) cq\ru(J.-- LuA O,f ,A,c. ) Y Y lri ;El. s S.rnp(Qsner1.1 \{^{ {til\otoiuS b.o tzaU eXpressigrai ,^s.l*B &codor. -- *c F,cX,Y22) = 'I\M(o,3,9) F,-C)t, y, z)= TrF^ Cz,s).b9,. x Y 3lt Z Aeco&n $vqm -t-t^q o.bove eirruit :.iTM trl = to,3,,u) F2 : Tft"\ (r, s). W* BCb to : + - Soqrnent.- uec,odev :- 'K + o 1_1_l " l_l-d o. tgr + - seqrn ewr Ai.ptog -a rhete o{q tl-oo tgPes o{ + * Setv\nqw/t dftp(oUs. 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