Digital Electronics.pdf

EE-23lol Dl GITAL ELECTRONlcS LTp Hcsedits 3 Keoene Books. letroni ce Rp. Jain Desig...

EE-23lol Dl GITAL ELECTRONlcS LTp Hcsedits 3 Keoene Books. letroni ce Rp. Jain Desig M M Mao 23d Tuly, 2o21 UNITL Ele ctrical Sgoals bigitol Ancleg Thie ype of Siqoal bas ontnuo us Hae iscete vaes t ime. vaues wrt ine. Cg are ~ave igod Sinuseid Sigpal Algebeato Dual Powe Suppy nob NecesSaiy elcetodc civult pot component| Cutoft Gatura ion VLS VLS1 cohich bas input veltge [o -sv] avnd ooly oubput votoge.  Numbeg System Hesa deima Deinal Bioy ds Octl Lhc N.S as its base. VSes 2 digits e. md 1. 1tere, he baec of this N.s c 2 4 bits | Nibbe A gèoup of Sinay 5tNibble e digts Byt Deciml Bioavy (o.6]lo.vo]. Decim embex Co.ne] Co.zs]o 2 And  * Binary Codcd Deionel Numbex Systeg [BuD] sy In this stn ach dcciel mber eprrsnted by 4 binang ils. eramplei , L Bes J 740 185 wng Mthd ox BcD (9) (a4).. = Bcs Manciun ox BeD Maci m 255Jj 259 hodes om be ntgatd into the system the hinhest sy stem But Heeadedona aystem  Exces-3 Code Egcess -3 BeD 3) obtain the Code foy gien decim nmbev, 3 is adde cach deCma numbe omd the cqui va lent Snavy calcuat {om tbat Sult [oloo olel] Excess -3 +3 2St5 Tuly, z4 Uosigned omd Signead Binasy Nmbe Kepresenta lior Uhingped Bnany No: enlly the inang qyt the mmgnttude decim t bex *Ggned Snany No; Sinany Cam Cocle epesnt d fom o , -2,-3 -22-olo =[lole J Nete: )4e igo poensn y / 1 3)1-)O 5) oith a be from the neot bighr bit. Ioo1 Oo|1 to the LSB he esult ut. Sy way Gaoagss:ip fo J  Hecoednd Nebe Systemn This number Syslem lgtssta tig from seSb O,), amd F], base i-O this Systonn lb. Syslo lHexa de cima nenbcy cgi (zs.[ J. 35 3 3243 = Sin c base hecadedo nbe is 16 -2 So, any beade dol Can be rcpre sen ted by y binary diai ts |3 6 G  Digit al Lonte ates Thee arc the basic building Slocts fo makinq: igtad elerones Citey S Thee bypee tegie gates namey Basic ogie Jotes [E3*NoT, AN OR, E*-oR gatee Logie NoR gaks ) VP (A) olp (y) Tuth, Table A Y= A It ba ie logie gate eohich bas sángle (nput md a Single output Complinente d The lagi its output,i|y- also ba sc ogie gate ahon {ts inputs HlGH (1). The boaeo Truth Table A Y SuTabe:A BY 1 1 1 loge Jate cohsch HI G4 () owput my f ohen its input is HIGIt(). Loglea pveseni A  -oR qat: also bassc ogie giveo a HigH output when he ae H1h ) nputs. uth Table? A A B A )  Uhivrsal Lonye Thussd Jaks y an qvallable bagtene rge O Any gas xeaused bae loge Crn be by V#ng Unives wgo oks. Jates onsrne Legs io Com pa hon hat the lagie gote. Emples. NAND qate md Nof gate Tis Jate H\GH () autput cahen Los (o). txu h table ? follow: A This qate Lowla) olp hey Ony one (s A 4p l6 osnbos  This ype y gobe 3 distioct olp StateG ire. (lo o][HNaw] and high impednce Stabes. -ieNoT aatt nvert Contl Tesmibal 1 () ACTE Conn tmil)S Nos lbverte -()Same.silp-olp H'gh lmpedomie In Acthue HIGH ineske, shen bhe Con l Tearaio Conoectd with LoGlc fHte- | (H)G), then this Tsta te °peate nomal gate. And hen the applied coith agie o (Los) vey higb im pedcmie to the ohee connecte. CwordS, behavs ot connchng the ( A ctive Low inver tex Conwl lermind o In Acive Lo e shen the T i appitd oith b lo), it opeales ike NoT ate, when Conlrol itp Temina Conneced LoGLL HiGH) them thi inty te ofers vey e high inpedcn the ciit Connete  Boolean Algebra the algebra of bioary vasiable. Binony Vas latblee alo knoon as Booem vaiables has only two vaue Boolcm VaHables The Boelen algcbraic be Dpey ationsCon in the ef egieal wth 4 Sign logteal AND an d Cemplem ont opera ben Oxinve hon NoT  bZ024 ENO. 2. oma Vriicaio gsgales Almi shudy truth toble of ba tc m NAND Gate A A 1 NoT aate lc4o AND Gate, A oR B, J  Agt, 2o4 tdnesty Beoleom Alag ba othe othex lheos two mearo leicxpss the elatonsie betee Vaiables digitl ciuit. Thrse are: O Tsuth Table Cx pressinselations, de sigr Cngee bny Les no. Jals amd Compsnents while making digital iruit. This vedueed the Gost the dgital Sy se (crease he operoton, The the digitd ystem he Boclem expwsons the md he miiimiation Vaiabls shal be Booem ex resSon done by theos The tod cirut be aSsemble based he he logicad epresion vosables. Anslhe ehrique cshich (s miimie the boojed vo iables from the ogical Serne onpotont Booleom rel tions: ) A+o = A () A +\ Lao (ii ) AtA = A (v) = 1 A4 = A ANO Laws = (ii) A.A A = A Doube toverhon Negabon La A =O, A 3n, Lhen À=O lenutaive B.A Assoda ive G) (AtB)+c= A+CBtc) At Btc () (A-B).c - A.(3.c) = A Bc Dislbulie bawsi G) A(Btc) (Gi) A + B.c (ANB). (A*C) Absorphon la wsi G) A A. B A (G) A(A+)- A  A+B () A(48) = A () (A4 B). (A+6 )= A () (A4 e). (Ã+B) AB+ Ac (AAB) (Ate) CBt e)= (A+B) (+c) (  Aigst, 2074 De Thus doy is Mosan'e Thiorenn irst thcosenn states bat " compliment of ogial ( eapal the Complemments".e. A LHS: NoR Bybed AND Seond theore? 1t staes that camplemmt of a produet C the tornplements" e. A': LHS R.HS : NAND ante a Bubbled oR qa te calle intre chongbi li el:. 'that Booleom veaton, Can deive aano they Boeem veata : by Complainenting any rreoing inthe enpresspn.  A tO A dualeaton e) be A.\=A is U becle ne saten, A (Bte) Ne, by pplyng dulhy heorem ge: A+(3. e) (A+e), (A+c) Passleen velakons: cponding Simputiel yAB+AR No ) Ainput Cne wlth the Yowput the f a we. y (A +). (A+ B) he 145 August, zon4 bdnesty Prove tbat eqvt AND- oR crt, NAN -NAN Lhat ) 4 Thettare, A AND -oR Gcaú t (A. B)(d) (+B) (E +5) =Aete.D hat, NeRRnout ienrt oR-A'Nn cruit.  Combino 5ooa Digital Gruste Noki fam-in of a og'e Ehe mae num gaks Lhat Co be Conoeete ayic gabes, of lage Jate: Ehe mamr logie gabes hat om be conneted Voes of logte pes,f Digital uits Cam bina ie neal gito ( isui t y pe Ehis of ital dru t, the output 9ute qt atiy deponts ony momemt enHrey depende the prrtent inputi Con tHons at thatmement de qn Such cruyts aarAND, oR amd NoT operaions ded. E romple; Malbpexer ( MU%), Dem Bplexe (DMw) Adder, Sublvaeler Code Convrte, paihy cheeker, ALU, ete. this cuit, at my monen t the out put otates depends the past oudpub moment as the Inpu t Presnt qt Ehat  To de tgn OR, eRNoT oprraHons, *eaied, Memey etc Ke pre simtaion of Logieal,unction 3 K Sunn of Produe k Sop 7Thene are 4-posssle AND iyna)s eohich are in Cornplennte d amd ncom plemente AB ÀB, AB nd AB. These be ocpreSem te d A A B tuundamnentol oduct (|) The truth table each fmdamentad product fo the input produing utput Con be repocsented the table as shosn below? Fundomneatel produet AB 1 AB  bhe to As input vGsbks as: as the fmdamnenta) podusgng 41GH C) Emplei heo  August, 2o4 3Vaiable Tuth Table A Tundonent Phoduct A B A Bc ohich qives A sc S,. A Bc  Augus, 2024 Kaxraugio Map vismal dioplouy f fmdaental producs Sn piodct (so) soien. The Ahree im por temt Lypcs k- M ef nomely 2- vaable k- Map k- Map b s Vaable md Too Vaable k Map A Tuso ieiable k-Map ony Vaiable complemente d uncompimente d forms as shown in tg1. Com convert my gite 2- brulh table vaiables inte k-Map gihen belouo: Cont he TT ino its Map: iA AB t Ab A Three Vas abe je- Mop: 1t ontains ony in its vasables 3 bomplemente d amd uncomplemented foms shon. cmy iven k- Ma as below: A B AB AG  A Conrs | TT into Ie- Map: 1 1 3 1 olo Posble oay 1f 4-vaable Mapi Lt cantains.ony ovarrinibs c AB 11 1  \e- Map nothing but Pir of ppeoing be howontay adyaent each the the Simplified k-Mer p fron the iven = A (B ta) Noti A ei mine ody Vanable 220e As t Ruads: tour othey adjacent ithes hoijontaly in the. K-Map A qel Can varsab leg at a Hme l0. wte the Simpifed sof fox the Ma Taking palrs! 1 AB C AB S lege gahe is op of Ls that adjacen t each othe veically hoitgon aly 4he le Mep Sinee, Vai ables Ca be  wte he Sop S- Mop Soh A fay: ÀB D AB 1 AS ORling Lhe Mapi at the 0 AB AD AS A Be Singr t ABc C AD B Po ABc A AD  ugust,2074 Thnseay Podsct of SUm CPos)Me bho in th me thd he fmkmcntad Gum that prodvces con forthe Hons {n Ihe trth a ble ldenHfed, Then, by Aing hese SumS, Jet ihe the Pos aHonfo tabe. The wepen ing aie be bult by oR-AN civult twvalent dua Noß -NoR e he PoS the amd, 'also dvao ihe ruut. Sob (A+GHc)(AS+E)(B+e) 1 tmdmenbal 1 his. in to Comerwnd mabe NAND-NND e mplemenlny ceit barnemenlng Non qals md  Nole:)se He cuit howlng less no. f chenge AND gates NeR NoR And A Hvaable TT has be into k-Map Drauo Ne R dte gats. the Sim 4 fedroagie cvit rna The complenen e wfll be 0 c) As À B AB 1 AS A9 + Ac t A D..NAD i4NoT Con de eeit A  yqans Guywg a 1  Combinakcnal Ciruwts Mullkple xer: may. Mux combina Hoño digtad oheh has rmany in puts but has ony output t com be presen ted by ehei ollo coing diagrom,..ontel igoals / Siganl As sho in y Can tromsmit any one of the data bowards Ehe utput (olr) Une Desig MUX Baie Logic 4ates G'en No. A D A No. of conn ilps D A -o Then AN aate ilpo ae bal Ao A 1  2024 MalkplereY kandy ( Sinc e 8= 23 No. f A ony the vpper AnD Do 1 oill be aeHve he AN gat oill be disabled C Da shen ABc )o) A De D No. of ips conbrol 4.". No. of piols MUx bas and One olp. Since it ha 4 lonsol t(p ignal, This Mux is as Gel