8.digital electronics handwritten notes, Lecture notes for Digital Electronics

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BEBEL) ’ voCctcGse — f y) = >\ 2 | a a - HAND WRITTEN | E @FLECTRONIC = ENGINEERINI = a =, a: - SUBJECT:- ws. z ‘DIGITAL ELECTRONICS a . (MTAAANANN g g 5 ty 8 8 & 5 aq ie || For Video Lectures www-.satishkashyap.com Not available in NPTEL For Video Lectures www.satishkashyap.. : . ilable in NPTHL Boovean ALGEBRA. “ERPE el aa es =| Boolean Algebra «- es ' © when no. of variable are less. (12/3) __ >~ W ft is _preffered when output is _O- Or + La) 2 WED UE ORs ee ee ee " Se © When no. of variables are 2,3,4.5 _Cupto Ss variable) c) output is O.107, ~~ Tabulation method — — 7 w Itis vsed— When no. of variables dre mare fan Boolean Algebra Ba : ie owe _ T A complement > Ao. A‘ in ee Al en A : = het 5 ont nee AS ce ARROW SARK VAR CTIn. ro. ONet axsiiphloin MFA - eaphon. ~ta) O 4 (et aaa una = ~ 6). 2 pas a3. E sor | Agr ABC + ABG © Cy) = AB +r AB (CtS) 7 ae Ae: (cee =1) | = A(é6+r@e) sae | = A No NAND gate required - as aT a Advantage of Minimizaton :- 3 No. of logic gate + => Speed T = Power dissipaton v => compleaity of cirevit less 4S fanin + (no. of input _v) > Cob? +. + Froblemy Simplify =- «a) AB + ABC + AGCD sov:- | aBCeaB (1+ GO) ABs. = AB ; (GES SD) j = alea+ec) (: &+86 = 8+C) = A(B+G) = AB +AC : @rB) (Ato) 2 —— ‘Sol=- AAtr AC TAB +r BC = Ad ACtrB) + ec = AUt+B4tC) + BC. = Ar - | Transpasition Theorem | | @rey(arey) = arec | ee ee ee ey eo mek pace [_ | FREE online GATE coaching www.egate. ws FREE online IES coaching sil Beas _$$X+y¥) (xz) ©) (AtBtc) (A+ 6+C) CArBtE) Soly taKe AtB = = (x+€) A+ 640)-CrtG) ae + co) (A+ B+c) = x (At Bre) = (Atay (Ar B+c) 7 = A+ 6(6+tC) = A+ B66 +6C = Art BC 1 “@h| (A+B) CATB) (At 8) (AB) Soll (A+B) (A+B) (A+ B) (At GB) (At BB)eCA+B6B } ACA) — = = \ " Ml Fo aietarty ss a = A EERO SSD 3 [a+ ec = (A+ 6) (Are) | Distribution theorem. 3) At AG 24 (A +4) (A+ 8B) = 1(AtrB) = AtB. q)| At AG gr:| @+A)(A+B) . s = 1t(At@) = AtB : ©) ABr AB + AB sot} A (848) + AB = A+AB = +A)(AtBI = A+ 6 Ans, a classmate ; : Fy, id eg bectures AG TREES app asin Not available in NPTEL : SaaS BC AtA) +-AB = 6+aAe = (Bra) (8+8) : (6+- 2 ; is = AtB Ans. a ABG + ABC + ABc ne Sol’-| ABC + ABC + ABC 4ABC (+: AtA=A : = AGB(C+O) + ATA)BC — 7 We = AB+EC : = @(AtC) a AB+ Ac + @cx—— redundant term. Sor: AB + Ac+ Bc (ATA) = AB+tA; + BCA + ABC = AB (f4G) + AC(ItB) = AB+AC ‘ In this case 8C Is Known as redundant term -ie. notused. or not compulsory term. ; —= AB + AC + Bc = AB+ AC , galled consensus theorem or redundancy theomn - = Shortcut method :— ©@) Three variable . .- each variable comes twice. ©) One woriable is comple mented . at) eB The term which is complemented fs token. > > mb | {Plo % OO} 4 + D 5 HS O + + > > [ ° or Video bse. ©) (846) www-.satishkashyap.com Not available in NPTEL (A+B) (Atc) . ~~ (81c) 3S redundant.term. «| (A+B) (G40) (atc) sor fA (8+tC) | @ AG +66 9 - =a Soli} In this case al the variable are complemented only one are oncomplemented. then. : = AB+AG (*: The term whichis Uncomplemeried is_ taken) Minimizatian swe eet complement Expression Truth table www.egate. ws FREE online IES coaching Not available in NPTEL A= Xy then . A+ AB {(AtA) (At8) tet f(Ae@) = A+B Then the valve of 44 (ae?, ¥) 52) is 4Y- 2 Cc) Kr+P2 FREE online GATE coaching For itete tren of Prodvol” Farnighkeshyap.com - Nat Sate NPTEL _| ABc + Aec + ABC a ‘ CG minterm x In sop Form, each product_term—is -known_as- Minterno_or Impucont =| Sop form is used when %/P of togical eapression is £ 1+ A and 0—A) — “ABC — aBcD (means Ex i- Ss — 101 -9 = -1001 For the given truth table . minimize SOP eapyession A 8 AB 0 AB sop form anly 1 taken. A6+ AG B (A+A) 8 =e can written as i- = m(O,2) Y(A,8) = Qves'} Simplified the eapression f° ¥(A, 8) - =m (02,3) co lo im Sol”: logical “Gipression in sop form :- y = AB + AB +AB G (Ata) + AB a+ AB eS (3+A) (6+8) At& A+6_ Wwww.egate. ws FREE online IES coaching a deo Lectures Se ; Foun hshyep com Not available in NPTEL @ (itis a_minimal_form) E form eack term most have all variable. SES Er Sk. _ By AG WAB- - Jt mincterhy’ will ‘contain _@ll_ varia Poet i Je ~ groweahateaal 9SOP “form. ;. MO. Of » min term presenting the logical exprasion © Artec IS. o m@ 4&4 ©) 6 w) 5 @) 7 4 oO m A az+8C = aleeB) (cee) + BC CALA) - 448A) (C4E) + ABC +ABC i O Fez idepsLecpures, ( Product Of Burp hkeshyep.com. Not available in NPTEL (as 84) (A +846) (At B1G) & man term 3 | Pos form are used when 9 is. Oo- A fo So lola eee mae. 92> 901 as ABO: Ques:} For a given th truth table minimize POS e7pression - A 8 0 Qo oa 1 Ow ( Oo \ 2 Ad 8 I ' O- “we take “only that valve “at which (A+B) (At 6) B+ AA = 8 ~yY can be written in PS form Y¥CA,B) = TM (3) and for sop y (A;8) = =m (02) =mlo,2) = TM (1,3) > Siliebhele (4,8,c)= =™ (03,054. 2) There are 3 variable then 8 combination then maa. term are, 2.3,5,6. Zio ae Fisec> aot WT ™ (2,3, 5,6) “Fords ogee" variable, winenmableshyamsitie _MINENBS alain NH prnterms grd 2". eye & ie gon hak, te (8 aokcina tr ——Fetad no. of _min or max terms are 2's 4. “efor M3 ie. (ABO ‘ Tata) nos of Min er_mar_ | ‘terms are zk 3 fr n=2. (A,8 total 16 togcal expression ie. A AB . AB _ AB At8 | | | & |2'\ + |2 |o- >) \> | Dy Dilm |>: ‘ di) >i + | 2, AB ArB Variable maaimum possible logical expression ; a ogical expression = =4 whatis the total no. of agical eapressin. 4 3 (|; ical eapression = ior ibisdiectPotin wwwsatishkashyap.com Not availgbt e3) NPTEL tive logic __- —ive logic : 2 tive logic means higher __2 -Ive- logic means _ figher voltage corresponds to voltage . carresponds to logiowh: eae + 6V logic “O'—»~ ov v logic “1 > +5v Ov logic 0” =e) lad: logic | > —a8N i =0-8V is larger value than — '7y then it ts +\ve logic. tive logic AND —ive logic AND ni oO oO 0 f + ive logic OR A BY 3 | For -ive logic or gate , convert 'to o and oto L. -wWe can say that tive logic AND gale. is equal to -ive logic oR gate and -ive logic AND gate is qual to +ive gic OR gate. ae r° Desh SRE ion _is used. ¥O” “SSA bEPY RE FRE logre _inbt eved _ em NPTEL E —ive logic “to. _tive logic. _ Se Sr a re suet -ar@o hues oe ‘oval is “nothing but _—ive logic. In self. Dual eapression WsaehSAO RBS duos igNosedilablpee OP TEL _ same eapression. n variable —>° Self Dual = sera are n-variables then total no. of _ self dwal eapr- ession. “is motes eg = ie eer pee eee Then: dwoal eapression. A— Sett dual —~A Total self dwal eaprestion A >A are 2. f ub Bo eee — Then 4 dwal expression . AA a B— 6 AA 6-6 za diy For n2=3 3 2 = 16. Then 16 dva) expression. a SS ~,— . A, BB Bio On GpuABEOCECD menos Gera €) | Complement 2- if y = a@c+ ABC + ABC complement is, : ee y = (A +6 +6) (A+6+6) (A+846) | ¢) AND « D i] +A) (6+ 8) +8 +) for Pposform. @ues-} soPeapression for Shaded region. A al 4o AB+ AB +AGB A(616) +AB = (AtA) (At 8) t Video Lectures ~_ a -www.satishkashyap.com Not available in NPTEL AB + AB + AB +AB : oe on BATA >} + B (At A) For -3- variable sop ‘form for shaded portion AES 2 ABC+-AOcr aes + ABC+ABC + ABC _ = BCC(A1A) + AB(GtC) +AC(BtG) Serene’ = ABtBCct CA S i| OR gae follows bath commutative and Associative law. ® a mmotalive law - = BrA a a E E E E . E E E | 1 E 4 ] { : ; #ssociative law :- AtBtC = (At B)+C Enable and Disable — ; ae ee : 3 |. pt” ig changing or we sy ee! i a tH ° ey z 5 kb — a ee | oe ee | a j or Video Lectures wwew-satishkashyap.com Not available in NPTEL t aay 3 Op is fined or not apanqed. yea :_ itis said to be disoble. _ Unused I/p‘s .— In oR gate , usused t/p_ is connected down.” Connect to one of the used I/p. If it is ECt then unused t/p canbe open or 4loated - In OR gate, Best way of connecting the unused Typ iS A +o connect to logic ‘0’. joe aO — - ete : § . Aoblerp- In the CKt Shown infg. in TTL, ANO,OR INVERTER OKE tor the given I/p OjP is. www.egate. ws ~-==For Video-Lectures—— ———wwwesatishkashyap.com Not available in NPTEL For ECl AND , oR, SNVERTER - _ mined é Not available in NPTEL Fay Xige° Leckyres,_ (gubbied SSL acon A : — a = “> AG Arce oe eee are Cy _ 0 disabr ( natchanging if one Y/p is zero ) cS = | NAND gate follou commutotive law bot not follow “asscciative kk ita ABG ee — AG 7 B = e Sp e= ae ee ABTS wa c + The. only. two ote. ’ not follow associobve law .e = universal, NOR gate. : Sieve ns) Le _gate NAND or Unused yp in NAND gate can be connected similar to unused Vp in AND gate = — — oe | aan NOR GATE 7- (Bubbled AND) 2] OR gate folloned by NOT gate. rad dik wks =e www*satishkashyap.com Se when ‘both ep ts is tow the oye is . (So) 1< drsable- ome as OR te. th are same . ga > and disable — bo a i: enavle commuotative law and not follow — asc ative law. ve. m AtB = Qt+A © ArBtc = AtB C er pr PT | | jmjlar to + unused tp in NOR a@te con we connectecl similar . a als SS oR gote - i oro i oR gate oR gate is also called as inclusive a g | ! . “ = _ 6 : ave af = A : E ; =F > when] a=8 , Wp is low te ©: = 7 u - 7 = aay 0) | > phen AFB, Ap is High ‘te. logic Yr. online GATE coaching : 1 www.egate. ws FREE online VES aia ___ www, satishkashyap.com——————Not-available-in. NPTEL O— Coffer ; 4.-» inverter It ig also catled controlled inverter. Note A ®, Ae A®A a A® O A® Tf A@®B=C then, G) A®C = 8B ©) B®C = 4 A®BBAC = O Then we say. odd no-of same Typ gives same O/p and even no. same @t/p gives 8Zé 4 |. Since, A®A =O A® ADA =A A® A® ABA = O and soon --- as Q/p. B .. 4m is odd Oo , if is even. Froblem:- The ckt Shown in fig. contains cascading of 70 EX0R gate. Kx & te 1p then Ye is. {2s —s. | 8@ 8@8e---- n = — @) oO = : ) ae = ) > Pee )> (6) > oy WC) .X - 1 Qk ap of even €xor gate have same OP. Ans, : : z : a o. WWW.CP ALS. WS online coaching or VideoLectyres Tndernat Oigrans -of “ERSRTYAREP SO ExOR gate follow both commutative and _- associative—law. =| ExoR gate is feltow available — with two Isp's only.- ) > > VV | Truth table :— A 8 c Y (A@86 @c) oO o o oO — oO Oo 1 1 a o 1 oO { ‘ = oO t 1 oO se i ao o zapnl) ° t oO Tae 1 ° Co ! { 4 The Wr of EXOR gale is 1. wWhen no. GA is at the -lip is odd no. Z 5 fi logical expression -— : : : Y = AG@c + ASG. £€ ABC + ABC oe = oo! + O19 + 100, + f11 —> add no. af t's. / 7 . La =m C€ 1.2,4.7) The reduced form of thys eapression _'S, AS ©@@c = : clascrnte pacef_[ [ ] FREE online GATE coaching www.egate. ws FREE online IES coaching Forder Leqhares x NOR - = a www-.satishkashyap.com : Noteavailable in NPTEL pe. = whenever the “ey same YP _1S High. xX ' o Oo 4 SOP expression = AB + AB” POS expression - (At+6)(A+8) EXOR'- AB+AB EXNOR: AB+tAB (AtB) (A+ 6) . (A+B) (AtB) When A=B_, then o/p iS Higb - 4 therefore coincedence logic cht and_ also called as equivalent + detector. as = when A#B the YP is low. = Enable and Disable :- : : > ____ For Video Lectures — www -satishkashyap.com _ Not available in NPTEL A _ MO AOAGAS LL - and 39 on: : eeceo Ss ==-- nn = 4 if N= even 8 4+ ne odd. exoR and eExNoR is not always © complement , it ts comple- ont when the no. -of Ip is even. and if ypis then BOR and EXNOR are same. gf Ae 8@-c = AO BOC > Dme. A®@Beaecmp = AOD BOGOD > complement : a = Find eapressign Of AO BOG. AoBeo c (AG+AB) OC (Aart AB)G + C6+aAB)C (AB . AB C + (ABt AB)C since, "i ALLL LL A A % ABEAES = (AOG)= AB = AB+ABGB (Ae+aB)G + (AB +A8) C Aee +Aec + ABC + ABC \ = A@ BE C- = Ei \ " E online GATE coaching www.egate. ws FREE online IES. coaching! 1 www:satishkashyap.com-— > ot-available-in NPTE A@BO@c (5) AO BOC AGB 9G (0) A B+B6 + AC - “ for EXOR > O/p is | When odd no. of ('S atlip . Inthis case., : Y= A@B@cC = A@BOC Ans, EXOR and ExNOR are -never always complemented , Lt Is | complement only When even variable 9ccurs. ‘ 7 Tip EXNOR gate iS even no. ot 1s detector when _no. of T/P'S are even. exnoR gate is odd no.a{ VS detector when no. of T/p’s au ma CLT) FREE onlirle GATE coaching www.egate. ws FREE online IES coaching Acekaat ee e 6 8 AB, SE ee com Not available in NPTEL sae | (Ss 28) @ aa j= @BsRe) AB 4 (AB+AB) AB 2a ag (Aa8) +48 (At6) + (AB AB)AB aa «Re + [(A+8(Ar8)] 46 AB +AG + [AGyAB TAB aé 248 + AB AMG Ale #6) +7 AB (aA (Ar8). ie: ‘Bubbled oR P= ated ano www.egate. ws FREE online IES coaching For Video Lectures www.satishkashyap.com NAND aS Universal = Wy) NOT 3— erento A 3 1 gate requived —E{ o me . . q “Yy): . For Video Lectures ww wwsatishka ap. Not available in NPTEL For Video Lectures i = avail able in NPTEL Logic qate NOT |- AND oR ExOR EXNOR — he min ‘ne D e to implement—XyZ- The min no. of two Ijp NAN gat required. Totah no. of NAND gate i i +r NAND te 0 implement xy +wZz, the min no. of 2 inpu ge : required : } j 4 i | 4. rd th nd 3 cancelled utr Sy yt inverter cancelled 2 and Now the total no- af NAND ® gate is_ = — —~ 2+ Bubbled oR (= -NAND Two level AND -OR = Two level NAND i - nn 4 EE online Gf g PWWEDAte: FREE online #86tdaching a For Video Lectures . * www.satishkashyap.com DATE t | | ee ee “qm implement sop form, — only NAND gale alone. F =| 7 implement Pas_form, only «Nor gate alone. ins it @tB)(CtD), then min nd. OJ cate. WI Twoleve) NOR-NOR_- ee OR--AND = _ NOR-NOR ee ae 1 cceicteoeieeerere eel 7 jackie ble in NPTE Digital circuits: combination ckt Sequential c okt at_%P is only depend => psasenn yey, Fasent eae esent T/p. Previous °/p ‘la No feedback = feedback. >. No" memory: = Memory. > @@8. Hdl Adder (Ha) 4 €q- FlipFlop (FF) FA —Mbx Register Counter . DEMUX E online GATE coaching www.egate. ws FREE online IES coaching For Video Lectures www-.satis| _COMBINATIONAL CTRGOPP. one (TESTE | Procedure to Design :- ©) Identity vp and YP. Ge t) Construct __ twth table a write logical expression tm _ sop oa Minimize logical eapression if possible Implement _logia—_ circuits. POS form. AD) HALF ADDER CHA) bala aaa AO logical eapression— AB +t AB AB. Fo} Video Lectures” www.satishkashyap.com Ei { II | Née abailhbid in NPTEL HA using —NAND qate > =p as) R = [ : {-- - AD B_s_30M, E | = ——— no. of gate - § cIe——._ 4B = carry } HA USINg _NOR gate :— _A®6B = sum - 3No. of NOR gate f nee = 2 eA =e (8)} HALF SUBTRACTOR :- : rw La Daas ne = HS = mm BARROW Wd Toth table - ’ iu - A 6 |. Diff Barrouds ; ; a oO a ° - oO 1 ' ' I ° a °o ' ' ° ° tio logical _expression :- bigerence” = | AB + AG gARROH® = AB dy - Tmplemeni +- SSS Lhe ali hk Garou: = www.egate. ws — = Www satishkashy ap.com ———— “Not available in NP] es AO > NOR @ate =5 3 (@m mux) MUX Sc - nh 1 OR Gate- : i (2x4) pecoder 2. DECOPER *— _ AGt AB _- Barro =" Aes 2 2 = pression 40° pifperence expr hae or ene Se s vsing NOR coe 4 video-be z ‘www.satishkashy ap. SENS ae FULL ADDER 1— ee ee o A SUM : FULL ADDER a) = , CARRY. wo truth table - { Aq 65 5 [-) =sum CARRY } o oo°o oO ° ca o oi} 1 ae o.1 0 ' oO Oe is at 0 t = 0 © | ° 1o ! oO | (aC - oO ! E-rA 1 | aw logical enpression %- SUM = ABC + ABG + ABG + ABC - A®B@G a Sm Cases) -CARRY = ABC + ABC + ABC + ABC = A®B+BC+AC. 3he truth table cf carry Shows the majority oj Ss function. = Em (35,6) a SAS Bee tea — | ere 4 a HT co i ; YI | 3 In full adder each logic gate hove propogation delay of ta to provid sum oar carr o/p, it requires to 2tpqg delay. & FREE pnline GATE coaching wWww.ega bo snag “Rag RRE Ere = = ABC + =A ee - iT aaee B+AB) AB( CxS) + cA 2 AB + -G-fASS) : 1 - = Important ques > : — i) logizal eapression for SuM= AG B@c .CARRY= AB+t8C+ = = ab No. of HA and or qgote = 2HA, 1 ORS = a Mir. no-of NAND es i ai) eon A ee ke) w3- of MUX - = = - 3. of DEGODER = ¢ 1, (3x8) Decoder and 2-0R 9 www.egate. ws For Video Lectures www-satishkeshoat bs L_] ela Lashed hal w Implementation of Full adder usiING NAND = Ag: (cVWHs) [ t = AB + CLABB) iv [ Y usi NOR Gate - dv Implementation 9f Full adder using since’ A® BOC = A@BOC. The the ckt ig Same only NAND is replaced by NOR. Gmc (AS (arB) (c+ AOB) AC + AASB +AAG+ Bc + BAB +BAS AC + ABt BG+48B c (AtB) + AB online GATE coaching BC + CA e _ ae www.satishkashyap.com me For Video Lectures www-.satishkashyap.com PARALLEL ADDER =~ : Not available in NPTEL There are three type_ of adler 1. Serio) ocdler (we write with sequenhal okt) Poralle) — adder. took. ahead carry adder = 0s Cy) ig used 10 add gro. = In serial adder only one Full adder (FA) _ of bits. t_is slowest adder. _ " foraliel adder + y | For 4 bit adder ? | = 3FA and 1 HA required . or 4FA ‘srequired. | Poraliet adder ‘s used to add grove of bits >| To add two N bit no. Half adder. oF, = N Full adder or, it requires. (N-!) Full adder (2N-1) Half adder and W-) oR gates required. Diagrom of Farallel adder ed “Video Lectures , faraliel Gdder ss asa oad RTS carry | Natefeilable in NPTEL _Propogation delby from Vp array to Wp array . Hence R @ also Known as Ripple carry adder . S- Tn paralle) adder each —FA_ will peenies “R-logic gate eoPAL In ™ tt parallel adder provide’ total delay of - [seta = 27 ta | LOOK AHEAD CARRY CIRCUIT :— adder 1S carry propogation delay present speed of operation — reduced - Fropogatan Generation At @® Br Ac @- Bi BR @ Co -_ACe+ HO aac So Deal FREE online GATE coaching www.egate. ws FREE online IES coaching Lok. ——www.satishkashyap-com Not available in NPTEL So = OG — “ i POC, Si S3 =~ OC; nerator _eapressior Ciey = PCR RG look ahead carry gener AP >, Cr = %Cot+Go / Coe EC aG = BCR Cot Gabe ort Sr Pc eG, ay G3 = BC, +G. = PLP3Co + P2PiGot AG,-* GL C. = C3 tGz = PRP PP, Cot PaPrPGo+t PaMGit 3G,+ Ga ANDO Gate inside 1424+ 3+ = no._of _ANO cate = oLnsth > | Teta) no. o no. of OR Gate = Nn. Total Propogation _ ‘dela = 2tpo This _is faster than _ Pe ralle) adder. Diff Se =a saa ) Drf{-(A-B-c) SARROW - oO oO 1 ' eapre SsI0n -— Sm (1,2,4.7)- = A® Bec BARROW = A@c + ABG + ABc +ABG = Be 4 A (6c18C) ; = ec + A (B8@C), add ABC two More -- A®BlG +c) +(Ata)Bct CA(6tB) AGr ActrBc.. Sm C172.3,7) = FREE online GATE coaching www.egate. ws FREE online IES coaching Lic tang 2 ce r_Video Lectures ; = Not-available in NPTEL Barraw eapressian :— ' A@c +t ABC + ABC Ft ABC AB(Ctc) + Cc(AG+ AB) AG + c (AOB) €S3) AGB = AB +C( 8) = BARROW. >| Full subtractor unll be imple mented with 2-HS ard + oR Gate. AB Tmportant_&ues-— no. of NAND goie = 3 no. of NOR gate = Ss Onfeence = AGBEc Garrow = AB+AC+ BC oO, AG+ CCAOB) loqcal_eapression for logical eapression for no. esi MUA 1 no. of Oecoder :- 1 (3x8) Decoder and z2aR gote => pa __Not-available in NPTEL- Truth 408 lw Imple mentaton — gc ae a PA 4 For-Video-Lectures——= - MAP 3 ce 3| Ht 's used When %p is 9 1, and X (dant cae 2) In K-mMaAP gray code representation (Ss used >| K-map 'S_qrophicol representahion > Gray code vepresentation changed ©y only one > each successlv bit. SB LsB wo variable * Twa variable ) For Three variable =~ For Video Lectures www-.satishkashyap.com Not available in NPT |For Video Lectures—________- www: satishkashyap.com Not available in NPTEL For Video Lectures www-.satishkashyap.com DATE & forhvabloiclinsberks | our «variable = — oe en —— = os So at as ; oO 8 1g | once reed f 3 og =| Minim ze. al 4A. = HM 2,3) x a:-| I (+ is put due to Sor fovm) | 5 eee eee ee | Ry|Vided MeAruftds - = ™™ (0, Iwwwasdtisitkashyap.com Not available in NPTEL =| In_ sor form i ath are \'s means. 9/p y All are don't care “means ~ dont core. Three “variable - :- (A,B,C) Z = m(U3,5,7) = eI =m (3-67) 3 we toke 8c then itis redundant term and it must be removed - wake) “H pany ac = araaey = ACT AB -For-Video Lectures www-.satishkashyap:com Not available in NPTEL Propedure = | teed —— @ e actets Qvads PANS smgie term Preantty @emve redundant . = pen) 70) ees ia ¢ AB +Gc+ AB Ae 23AB + AC sarl K-mop provide Minimize eapressian bot not necce ye.ie to Sol” alsa- FABC) = Srml2. 51+ Sd (36) | 2 | | : Ml =m(ai,6.1) +¢ dl 3D ideo Lectures www-.satishkashyap.com Care | Not Waithbid ds NPTEL | 6c a we CD = m(0O, 1.6,7) =e ( 3,4,5) “Variable .— 4(A18,6.D> oz = 19 (OPiS; Sok 2 Sai Se co f{(A,B,6D) ¢ (AB€,D) “= m(G, 2,8,10,1G) + = ACS,1S) classmate For Video Lectures www.satishkashyap.com , Problem — 26 - page -13 R + Pa + RS RS RS_ Rs es For idee Lectures _ — www.satishkashyap.com i ot Not available in NPTEL al yp Truth fable iS t= ao ; ’ oat ue .& pone oe . (Tee _methool for wnting “athe _enpression {VO _ ~__Tuth table) _ | pop \ | | a} z 3 Rero—+ AB#! ABxO + ABC = °° Le | } ; \ ' | ‘ =. AB+ ABC ~ B(A + AC) @(Aic) SS ar Ln. } i For Video Lectures Many T/p and one Vp I & Se contrah It ig combinationa& circuits Depending on contpl ar select Up ne select T/p to the It is then alsa Many to one cKt OF, serial scKt Loq : ™m ; of dota l/r where m= na no. of select i/p MULTIPLE Wk. satishkaslpapicbm| |{_[_ J{ 1sp ,ane at the f/P 1s universal Notlavditable in NPTEL transtera colle as pata selector, logic cKt or , parallel 10 : coontrol c/p) (symbol of U8) For Video [,ecturps, an ae www-.satishkashyap.com __Not avajlable in NPTEL_ jee Teuth abt : ~ at ——_—__——_ ee jae togical-enpression Y= SIE, + St, Implementahon :-— _ OR gate. y=-%5, eb lagical expressian -- So For Video‘Lectures S, www.satishkashyap.com Not available in NPTEL ‘ Implementation of higher order MUx With lower oarder’%- x Implement ust ; if 5 2 (B) Implement 8.1 MORK using 271 Mux. 8°44 G2 a 2 2 z 4G&+2+1 =7 no. of Mux = To: In 8:1, MG-Of 221 Mux= 7 ss Par | ¥ Se For Video Lectures RiGee pet www.satishkashyapcom - rx 2) ie * 2S eaux os = RAT AeUX S2e MeReucse! PSS ext MUx 2Sext FoR 4 + SIUC OS 44D - | Therefore fOr Mux the o_o sux required mux ror GA NUL i. = = —_———_ ser Not available in NPTEL C®@) “ARO + AB he MUX (2:1) 13 required — for AND Gote DATE For Video Lectures ——~www.satishkashyap.com. m x > | 2. MAOXK required for NAN DS gate sao —— bs 4 ( peaux (2:1) required for GOR gate. EXNGR ~~ ExoR, ANd gote required 2Kni ~MO¥ - = 6 = a ee ILL tL i For Video eS 3 - Nox oepniesstiphivashypp.com nite ssi Not available in NPTEL — 3 wun required @A) AOR sm ott AB BARROW. — AB = t mux. o— = Y= KB- o- J =e e 2 MUK required and. — For Video Lectures Hazard is occvrs due to ‘propagation delay gf the logic cht > This is _ unwanted ohange at the 9/p. ckt Dbetermine 2/p Waveform when x there is propagaton delay of AND gate - Por VidéOLettures www.satishkashyap.com Not available in NPTE Hazard d =a dynamic e Te Essential \ 3 occur in multleve) occurs’ in cKkt Sequentia L .cut 4 in ambinahonal cireuit 2 Awd by adding Static o "edundant term ‘oro => OR-AND crrauit 2 Dy POS Form % ovoid stotic and Oy nore Hazard ave added in combinational okt Essential Hazard :- These Hazards can bt feels essential a | aerate PAGE T. FREE online GATE coaching www.egate. ws FREE online IE! abana For Video Lectures www.setishkeshy ap eolnl | | Not metas ih NPTEL Memornes - cm 1 i 2 | f imary C71 ) pecondary 1 1 a 1 ROM 5 Semi random Serial access tmemors rite ) Read only Al disk 27 moqnetic tape ) Random access| = Randomadess _ cD 3 Magnetic bubb » Voltaile » Non volatdile ‘ DVb » Ferrite core 5 Temporary ) Permanent HD 7 ecDdD datr data (chorged couph g10s/ Sysk ™m program device) Ferrite care > DRO — Discrictive read ony out RAM (Random access memory) . tach memory vocation 'f m obits ore stored then memary capacity C27 xm) with n-bit address - man. no. of memory tamtion reqair 1s er: memor Se address line = dota lines. 4 — static _ eee A 4 Stored Like www.egate. ws FREE on! aching _|_For Video Lectures _______www.satishkashy.ap.com————= ae Memorres — ~~ Not available jn-N RAM i t j Semi random. 3... Read jwnte = Read only 3 All disk } 2 fore) }2_Noltaile = Non volataile =) Ovo os hears : Lin Rondom access | 3 Random acess b Temporary. |3 fermanent HD data data 6i0s/ Sys tem program Ferrite core — DRO —> Discrichive RAM (Random access memory) = le Each memory beation if m bits ave stored capacity (2°x m) With n-bit address - man. no. of memory is areeeene Eos memory . =. gt 5 2a Sea Serial access Sh) 2 mognetic tape 3 Magnetic bubb > Ferrite core > ¢ecD (charged caupk then _memary tomtion requir 12— address line &— data lines. - Static Stored tike FF or Video Lectures www. satishkashyap.cc com" _DEMUK ( DE ‘muLTI PLEXER) 2 = " Siegle- “ie and “Many o/D. 5 ben is combinationad_—ext_which have one I/p and may 0/p cdepe on Sseleci Ip. transfered to anq - of the o/p 1 to many ct ,_ vets 3 Also known as or, dato distributor. bs a = - z ° Y, vi T Twth table :- — Expression :— Suey oO Yo SSE ot |) SSE 1 ae, i implementation !=_ s ha B 114 DEMUX 2- For Video Lectures www.satishkashy ap.com oo x m tower order: Maghe r oder DEMUX ‘fro XS pDeEMDv*X a wig CEM 2 ee (x4, DEMUX 2" ee ee { X#4D EM OX uy 16+! Ane 1A 8 DEMOX m2S6& DENMDX ses Bie 2's DEMOX ai FREE online IES poaski Sales PSOE 7 o EPIC ne aE Py SPSL 4 ae ~ Not available in NPTEL >| is used +40 convert binary data to ather code “Loinaky to eg. Binary to octat (3%) sie ecp to Decimal (4x10) . CD a) Bina ry to Heszadecimal BCD to seven segment 2 tay decoder is minimum possible decoder. 2x4 Decoder .— Truth table EAB ¥3 O xx ' a0 1ot 1a rit yo & presson -- a ABE AGE ABE i ) pace {TT | www.egate. ws FREE online IES pa ak | For Video Lectures www-.satishkashyap.com GATE { | nu available in NPT: b cong gr — @ Teemtement Hey adder using 2A beaxter. - Sa) Gz —_———e SUM « CAREY = AR 1. axe decade and tar « : ea ssp colted @s sas 7 & ease eno sume 2M (12,6,7) © aa F 2 vee - CARRY = online GATE eee t www.egate. ws FREE online TES gga¢ frq | For Video Lectures www-.satishkashyap.com Not available in NPTEL Implementation of Higher order decoder vsing lower order 4XIG “ = (Since CS IK1G > a Ie Gotu 16nl mh | A 6 FREE online GATE coaching www-egate.ws FREE online TES coaching For Video Lectures www-.satishkashyap.com ONTE LN bt available in NPTEL ~ Yo a cians at SKB — J ccahesnmealiomnnl mahi Lh | ! fei ae FREE online IES coaching NOU 5 www-.satishkashyap.com Not available in NPTEL Encoder is the combinational ckt which have many many Op 's used to convert other code to Binary octal to Binary Decima) to eco Hewaclecimal to Binary Octal to Binary Encoder ¢ Bx3 OOTAL to BINARY 4 In norma) encoder one oft the Yp Binary available at the figh and correspon oP In priovity enooder no. of no corresponding Truth toble jp ts Bigh only highest priority Binary ig available at the Up Sie Were sates oO Or =O oO oO Oo oa oO oOo Oo =O Oo 0 Oo Oo Oo oO | ’ For Video Lecturgs, nression oe 7 www.satishkashyap.com i __—Notavuitablein NPTEL atca: SS =a “Ye = = y+ Tyot te es Ye = Te aI, +Te¢g +r, Ye =} Ty +Ist tT +1, = pecoder contains AND Gate- = pemox contains AND a@ate 23 ENCODER contoins oR e@ote. —=__ Far Video Lectures FLIP- F LORww.satishkashyapson{ |” | +4) This basic memory element. It can store » bit. FF hove two o/p which have complemented to each © her Jt have two stable state hence It is known as aistable multi vibrator. GONT &NT i— Oo. SK latch = NAND oe ; NOR ~ ckts Truth table Characteristic table characteristic equation _ Excitation toble - conversion trom oneto another simple cKt. ‘ ———— latch the problem is, it have only one - a using Not gate NAND ar NOR e instead of I/p then we USE ‘not gate. : FF is not only used for storing ‘bit but it alo vseh coy = divider . we : ea we ss Se tog bal pe 3 | For-Video- Lectures eee www .salishkashyap.com SR _ latch using NAND - a — Invaibd . (@=@=!) 1 Oo - Frevious-state (no change) latch it both gates are enabled %/e remains some previous state and boathare disable then /p yvemoins same invailid state - SR tatch using NOR gate: —— *> @AND enable isi 4 disable isd and, irttOR- E= O D a eC a position aL 5 i invalid (€=@- Reset 1 — Set invailid. —» vnused 2 Twth table is same as for NAND SR FF. www.egate. ws pRRE! For Video Lectures... eae oar rcene Cesare .com. Not available in NP’ Charactenstc _ table :— AP: - ee : | Co@ine oO Qn \ oO OQ invailid Citi ha 0a 3 Since S=1, R=!. the O/p is iovailid becavse s-R=1 not : satisfy the above condition. i invailid- state Present when JK Flip Flop 3— ectures Cw satishkashyap.com— = Lt JL erlrrditabte de MPTEL Ansi a Hold oO Reset Set Gp Togqle- J-K FF using NAND gate om Si cu ed Seed aon SH =e using © nor gate FREE online GATE coaching www.egate. ws FREE o pline TES ‘oaching | For-Video-Lectures: =www.satishkashyap-com JK FF character’sho table >— EE online GATE coaching www.egate. ws FREE online IES coaching called transparent ‘atc! Excitation table :- An Qos a oO ° ’ 1 Oo =For Video Lectures www. satishkashyap.com T flip-Rop = Chowocienstc table >- @n Qnst 0 For-Video Lectures __www.satishkashyap.com— __Important S=—= awit eee a. oe 0. See tae Qn => AN tables-are inside 3 FF _ therelore it is also called as - SK FE Universal dlip Jlop. Excitahon table -— a rP Ane a i { Oo cc oO oO Oo 1 O° x U oO FF > Flip Flop - one bit storing element Qn = S+RQn > SR = Set Reset Q@ne1 = J@,+¥K4@n F JI* = name of person who give the IC Aner = oD => PD = Delay dement Qui = Te@An a T = Toggle Toggle mode of JK -— All 7 diagram is fn Toggle mode 7 Level trigger a al In tevel trigger ckt , O/p may changes many time: in single_clock in_ single pUIse. br Video Lectures www.satishkashyap.com Not available i in NPTEL Race Around _ _conditior} ye ED OccuIS in 3K flip-flop (Draw back) “1 tow = taonsec teeg = nse. then:,- Teprovide nbit data serially out it requires (n-1) clack pulse. Ty (6)} SIPoO (Sera in parallel) ovt) :- pe io at 9 i > In sipo register to provide nbit data seriolfy in it requires nclock pulse and provide parallel oe it requires O chk pulse required. : It is used to seria) to parallel converter a 3 sTPO is used to convert Temponal code to Spacial code . es Blow to fabt converter. serial. t= - Parallel = Spacial code. The ckt shown in the fig. tf 4O6it SIPO register Which in inital, toaded with 1010. Tt sare three chk pulses applied then the. data tf the system is. 2 j = fe @ 1010 ees tot CG BECL —e}—__2 6 6. 0-—____—_ For Video Lectures www.satishkashyap.com " Not available in NPTEL si a‘ ; ISO is also used to convert Spacial! code to 'termporias OD code —PIPO_LFarallel in parallel out) :- is used as storage register - “Parallel in it requires 1 olock pulse. _ parallel out it requires 0 clock pulse Important :— S Each shift left register operation provide multiplicatiar by 2. , = nm shift aan operation PAarmed then data is moli plied bee 2" Each shift right. operation perjormed them data is divide by 2- fa If 1 shit right operation performed the cota divided by 2” eres u iL online GATE coaching www.egate. ws FREE chlite IES goaching wv res Oo Lectures . - www.satishkashyap.com === xt] COUNTER s :- Cin) Gounters are basically ~ wed .to caunt no of _ clack pulse applied. it can also be _osed__ —f ee reer. Geet, =e Hee measure mans regen _meaurement , Range measurement, pulse width. Pulse. ie. hi i counter UL — 16X_ Pulse widlth = Total wrath. Also used for @avefarm __generator. with nm -ff , mar. possible stage in the comter 1S or, nN = &,N- where N= no. of Stage n> no. of FF.- \ clock pulse applied counters of two +type:- — Synohronaus All FF are apalied = same clack , : iH is faster Fiaed count sequecé ie. ve ar down. www-.satishkashyap.com “Not available in NPTEL modvlug of counter Le if Mop 5s counter 5 staqe Mop n counter = n Stage C3) ‘or Video Lectures => No. of stage use in counter “mean acre Tes A decadde “counter 16 applied “with frequency of 10MHs then O/P drequency _ fout =_ aie = 1OMHZ _ INH, , 10 1a let Modm and mopn are cascaded MoD Mn counter. fe ie fear a content +— Basic * Ripple counter Non binary ripple counter Ring counter Johnson counter Synchronous series carry Synchronous” parallel carry | Synchrawnovs counter design Qrel Ana Ripple _counfer = Itis.a F nchrowaus “counter. Different: FF used different clock pulse. Toggle mode. =n — Only one FE i& apphed with external elk. and ather oe eI ase {t's @re clk is from | previous ff ofp. ether & ao Q). the €F applied with| entemat otk will acts as 188 then (fF gm will act an [ForSiisat esgic i ¢ | sé e} &xplanabon :— 2 The cat shawn in fig. @o toggle “ter “every clk pub 3 @n charge When 4, change from 1-0. fe. @Q, changes when 4, changes from 1-—o = Truth table :— lasl_| a 0} =|'0} =| O] =| 0} ~-lagla Oo 0 ! ' Oo Oo 1 ! oO => Its atso called mops ripple counter. Tiening Ofaqpam 2 ose ee Te CLK o 1 aris 3 — & = 6 = & — ies ed rig | ed bad ol cn aad rant ay For Video Lectures www-.satishkashyap.com Not available in NPTEL 3 In" bit ripple counter propogation delay of each ff Is tray. then time period of -CLK is, Vern = tpeayy Sa ae ee one cek ty a) -ive_ edge trigger — @-as cloak -—» | up counter wife u me up counter vib Ee ive ’ » : j down counter . +iIVE 7 : down coagntex 3-Bit Ripple counter ( Qown counter) := Explanaton :- = The ckt shown. in 49. Go toggles “for every clock pulse - a toggles When 8&9 _ changes om @Q to 4. 3 4, toggles when 4 changes q ato 4. Twth table § For-Video Lectures wwwisatishkashyap.com — a ans ; Ts is called ripple counter. because _ ne wu ch : a e is_the Ye of previous FF “output. _ this ts qust Like ripple . then called Ripple oo counter. the Oe is (000) and clock ts applied 1 then unwanted dr decading error. | also called trangent state . _Dscadiing errors a1 transient state preserd_'r._ ripple counter _dwe to propogation delay . avoid decoding error __ strobe signal is used. strobe signal is zero for Oto and after thot a i é neat clock. then all the Op. is zero cor transient time -therefore due to strobe signal remove decodi error . ae a | a q . . q E : . . E E E . Ee E E E q : : . ] = — In ripple esunter . ™an- possible state Ripple counter If” ore for SFF Gp is ue FREE online GATE Saecine www.egate. ws FREE online coaching - DATE ‘or Video Lectures www.satishkashyap.com | [nu avhileble & NPTEL =| Clear and preset drze Known as Asynchronous 1;p Shia 6 Oar > 1O,T ave Synchronous je . ‘a is 2) | Clear :— ___ Clear ‘3 use to rest our 44.07 counter | Preset:- preset is use to set our FF or counter, —— ee = eel . =e i+ = - = ol —f— I : —Ciz___ CY SO, F0 eHfeF — c =O. F (sree = =jA+_+f-ig-20710. pea ha (| _Non Binary Ripple counter :— { @|—@cb— counter :— (Oeccee counter) Q o ° -|-| | oO} o/o/2 -| 9/0 Oo} -| 0 aay np] Ot = 9 0 o ol -| -| Oto] 2} 9} 9] 219 Gqiqi qi +] - classeute Re race [TT J 830.41 Bo FREE online GATE coaching www.egate. ws FREE online IES cand au Lo ah or Video Lectures www.satishkashyap.com ~~ Not available in NPTEL Cg) af we ose” only & and a, ,we also use the as __ |ctear exe. eS eee re i Es ee ee a ee ws ae cua — ce ; ay i | a > AU BCD counter is Deavede counter _but__ reverse __is rot trve. @co counter ts Asymmetric ap time Diagram . a > frequency of 860 counter is t/q _ 3 > low for 8 clock and high for 2 clock in a, duty cYcle tis 20%. Tae aR eeep com Not available in NPTEL (Sy nctOVie’ S - L ; | TD [> The last ff ofp is connected to first 4f° £7p Erplanation = + only one FF O/p iS high and rerraining FR are) locas 4 states are there. (ie. for nFE there > In &4bit ring counter is m States)_ Truth table :- CLK oO ' a tive edge o ive edge . the =? In sypchronaus qaounter the Oo/jp remains same_ jip Th Diagram ‘— Gp ime oe g sk et classmate EE online GATE coaghing www.egate. ws FREE online IES coaching ee rT Fo Video Li CHUTES » > we Sate iy ap.com Not available in NPTEL * . ; t, ‘en 20) x waveform — ts 360/, ; ; j i } 4 ts Phase shift of generated Apphodtion. i i 3 _vuseal i'n Stepper motor - contro) . a in Analog te Digitat convertor No. of unused state in_ ting” counter gate are requirect . decode no logic the 37p of Se last o/p can not be cannected in gr Video ectures oO www-.satishkashyap.com (dD) mson Counter t- Not available in NPTEL Z : ar C2) > Symm etre, o/p wovetarm. =) 8 Stages are there for 4 bit counter > phase shift 360 - 90 ¢ 7 3 Tt its pst like SISO reqister Truth Table *. chk 0 ' 2 3 y S —z = & a Total no. of used state . 35 Total no. of unused state = 2a: azite-= 8 Stote_o > Vie 5 Also called Twisted, @bunter , Mobies counter OF, creeping * counter or, Walking eounter or, switch tail counter - Eo Videoectures @, @, eywesatishkashyap.com : Dee in NPTEL o oO 0 oo @O ~ Qs Qo : qd Doo a; 6, c a 2 t oO _o — qa_o @:131©0 Gp vt oGyi1 eee >| In Johnson aounter to decode ‘each stote one two | xp AND / NOR gate used. | | Disadvantage: = lock out may occur (When counter ehter into vnuse state) a In synchronous counter _propegation delay of each counter iS teary . then. [Tes = tase] FRE] onling GATE ‘coaching www.egate. ws FRE! onlin TES coaching www. satishkashy ap, bok | (_| 3 carry counter s— For Video Lectures _S4nchronous Series i oo a ae & ~Gick = = Explanation = = series _ Synchronous - tn this counter ein a toggles | when Goethe Qi _ toggles when Qu = a3 will _toggles When This oXt_may be down counter when & @o-! 9 is Te te Truth table + = } GOL. toggles dor every clock pulse and Clock ig applied - and elock at ard) olockt applied +) Inde pees in NPTEL IZ. Y UuP_counter dy “applied = conne ctecl > To provide down counter used A Up ‘to TE coaching www.egate. ws HREE online G, "provide “nent stage For Video Lectures www-.satishkashyap.com Not available in NPTEL 2) titaws » 12$$) (124 eounter + ®)) Synchronous parallel carry pe a D f--l i TY a > Faster than series carry counter Disadvantage is increased I/p pin af AND Gate ‘ Torx > teder + tran | Son — paraliek earry counter. for faster logic . Ripple counter To prove down counter used @ %p to provide “neat stage > Faster than series carry counter . 3 D&advantage is _increased We _ pin of AND Gate: cu > tedre + trapwo — Fo Video Lectures www-.satishkashy ap. Bum | E43 | = { Not eee cen NPTEL | Sypobro | nova counter des ign | dor | the Jive! n seers e~ ~ Gay) ' Foblerh:- Design @ BAynchwwcounter {or the count quem ising -rive edge tiger 0 -¥F. - CO—— bees : afd) : . O->3— 1-* 2-0 - Procedure :— Ww) Iderbfy no. of FF and ae anA %/p. | Constuct state table. logicag expression fer I/p_ Minimize. Implement the clr. ub state table '- fesent state Neat s tate Q@ Qo Ai4Qoe oo 1 a T \ 1 o-) 10 ' ' 0 Ome iad logical eapresslon ,— D; = Qi Go Tt @,2o =o Do = one + @:4o a Im ple mention classmate | For Video Lectures besiqn aoe a ees __www.satishkashyap.com: = Not availablein NPTEE— o- 3-81 - 2-0" _ USieey SE SES Various codes. : = 2 _ Data representation... > unsigned = a signed 3 signed “maqnitude ts vs as Number system and codes “= : =e “Weigh ted — qv “Unaeignted, > fositional-weighted 3 No weighted cg. Binary , octal eg. gray code , Excess -3 ax Decimal , Headecimal ‘ 2 Anumber system with base or radia r contains different digit and they are trom (Q— 1). eg. Go'),. yr = Base or radian. Base Different dAIt- 2 o1 8 Oviatt 10 One Sig. O, --- SAB (oe 5 ..A.6,c.D.€.F REE online GATE coaching www.egate. ws online Foulit eel RSH Sion (Various WOmber woe son .. Not available in NIPINBIL, ' ij Decimal w= cthers: KS ) Qe)- TS into any other base r 5 divite > % oonrvert decima) na integer port molttiply freohonal part with r. e £ ak c= convert’ (25.625) ,, Citoot- 101), : amuerde nn (25:695)" C= a O-625x8 = |= When we go from higher to lower fase the no. | jncreased. Conver+ (28-625), — (- Sic 6 [25 Ss dterr GAS AIG ideo Lectures DATE | | Convert www. pees com. (27-4 Yin piles (Gare Yu 4 1z 7 z fe -3 LK afr ae } OLR, be o-! Jt Nbi-abbilablelin NPTEL OG AG = BG OuxG = TSE (123.128 ), * Others to. Decimal ‘- Oa %aKs- Wy = To convert any other base ¥ to decimal _muttiply | “20ch _digit with easitional we ighted then _add. ; aes then, =a (—)vo, = Xr + Kar Te kg xt Nitin ie Convert (10101 -t1),_ oe tx2"4 0K 2° + 1x27 4 » — ole S48 t tt —-8 ot = copvert (567-4)6 2 (Jig sx18' + 7x8° +4ax8! LOAD ek: = 220+S6+4 s s 4-S 7-5 Jay convert (ST-4)ig = C dig Skl6@e7 +.&. = 87+0-25 = (87:25 )ig convert (GAD), eae Ce re Nx 1674 AFA IO x1IG t IS Z256K11 + 160473 @ For Video Leattrset GS)e swwwssatishkashyap.com Not available in NPTEL peaeciai nee Be Sy SY6" Sx Bas C39 & 8 Octad to Binary & Binary to Octal ; Pp each no is represent by its 3 bit binary formate. i | convert (37-45), = C2 (orn. ‘oo tot), Binary to octal convert (10110. 11), (o10 110 - flo), @é-6)y convert (259A), = (—)2 (e010 0101 1001 #010) r DATE Foy Video Lectures www.satishkashyap.com ot ‘available in NPTEE™— iw _ARITHME TIC OPERATION 7 ait a —~ 133) (A) Binary Addition , subhaction , Multiplication +— 1rorreoao +O Fr Oy Go Sob. s Lt oO te ee ee 0.0 ae ONO ab nana aos = : _ z a Sp NONE es Se 2 GB) Molt'ply : ? vo.1 b) hte i 1 === 1Q@10 7 [ivectoanty a _O 00D == 4.) ee ee sh of (8) Gclal. Addition , subtraction ir Y Ot0= 0 TAL eee als ont °o Et =O) are 7W7= Bs a a Len. . (#7 = 10 seer . te, 742 = 10 Sumof 2 octakno1- a 243 ap 56.7. eA ED et ES 4SS 1032 Subhract = (nee ona S564 = eee ERE online GA oaching www.egate. Ws_ FREE online IES coaching chreematec. pase © hk Not available in NPTEL AtA = (2o)ig 1+ B= c ADD muse Video Lecture Siar Satie kes hy enc nn (cose ee esaam (D} Complements :— ae v= > (Y-1)’s complement = | : v's complement ARS) 2 4. Octa es Binary =>! S is —— ELE Decimal se 9’s | Heaq eee 10s : 16's. (v-1ys_ complement -— > Sobtroct from man. no. t0 the gen ™. [aces comp. of ( !'010) =z Css =; TOTO O-101 ba determine (¥-1)’s @mpliment svbtract given no. fom mom. no. possible In the given base. (mar: no. } te 2a) a e§. 1S complement of lool is, Sol.- piapde =Toiror OTOO0TO determine 7's complement of octal no. 5674 Tet —S6 7% = zZ7 03 = Determine 935 compliment aj Decimal 2679 sal 99 99. = eee aaa axel __@:| Det. F's comp. of Hem. 2689. al inal FFEF ae FRE www.egate. ws =A www-satishkashyap.com bare [ Nbt af filaple } [NPTEL [| T'S Complement — To deter mine a r’s ‘camplemen? firgt wrte Crea je compicment then edd 1 at LSB. (at right most) 2°S complement . oF 10100. Determine 2's camplement at 1O110 re complement = °1001.00 «fl 0100 —ro-}- Ans Complement of ~- octal leds FG ~ of. Video Lectures —www-satishkashyap-com—— CODES a cD. code «— Weighted code. 4 vit Gode_ | 8421 code. i Each decimal digit with represented with _& bit Decimal Bco Excess -3 code . 9900 O01 Ff ooo! oreco 0010 OF Oy Oolf o (ee 9100 Osta vt oro} 1oaoo GAS 'Qooaq%» GIy (oO Eo 1ooo POSEN TOO, T1090 O}] M}N] a} @) >] ®] »/=/0 10to tol 'T00"F“invailid 8CD code ar. don*t care —++84- tlle tbo — ps During Arithbemetic eperatboan ft _ tnvalial - Bob present the add 0110 to oot correct result. ; A combinahsnral ckt & applied with Goit 86D cade which S represenicd 2d OD, Oo, , We is ¥., ¥-h Te eo is divisible y 3. then togioal SxPrssii_ 5 : rol tt : For-Video-Lectures= D 000 0 yd, D0, + SBeOrO Ped, Og Dy) + DD, Bg +-D,D, Dy Ds Dud, D, > O.Ds + D D2 Dg it D0, d, For write cD code each digit (decima) is write wepera in 8CD. se (S34), = (o10100" 0100 ) og Excess -3 code :— Excess -3 code = 8CD +3 Unweighted code Lbit code. Decimal Excess -3- code, oO oot! ~ 0100 Olof o110 Olney 1000 100| Talo Torr 1100 WO] mM} YI] OO! w| ©] bo] w= EDU i E onlin | LW ar |Svite yi = 1 = ee err —Noravaiteblein NPTEL = Sol- becima) 2 42 ) a: 4k 7 —@000 i 0001 LO LS ) ©1006 e110 a I — a 16100 o1d ) hole teers ae 3. Binary to Gray code «.— A Binary to Gray a >| Unweighted code - => Successive no. is ditter by 1 bit- 3| Alsa called unit distance code. 3| Also cyclic code, Reflective code. and Minimum error code. : Eo 63 B.2 6, Bo Gs Gi GiGo | Gs Ca ~ Soe ana ee = =a 8, eace| | f } FREH online GATE coaching 7 3 : FREE alia coaching * DATE For Video Lectures www.satishkashyap.com Data Representation :- Data _representahon —— t 7 Magni tod ¢ ; cugelamant | P { — 1 unsig gned saned s Qrs = . : ive A “ — +ive +ive ,-~ive TNS sive +IVE_-ve eee 7 > jone entra bit __3 sign é tl Ssiqn — MSB «logic —0 —» +ive -{ — =we. 1 o1lg ee 1001 (oan*twrite) In_ all tepresentahon ‘ive na. are represented in simibi ff To represent —ive ro in sign. “magnitude sign bit ahange. In_''s _ comple ment represen¥ o =we mo. first write positive no and gGmeapecteot tort. complement first write to it. represent in tw 2's complement tor lols dec umal = vwolwe . + a ; j LAASHREVAT ‘or Video Lectures www.satishkashyap.com ; ot available in EL Gr| lo find s-4 7 S-+ (-G) o1o01 +S+¢ 4) : O101 e 1100 1100 JG) x O00) if any cory present it complement to eatend no. of bit copy mse Sos SS -(oniiae > "loot —> —@o1e1) - -7 ULMGoW =s" — (O00 TH) ar A Binary Sign aq 1 “0000 Oe ute OE + 000) wat ' 20 to +2 2 O-G! bi} t3 “g Oo 180 +h 4 Ono 7s 7S OLE AO. we GLb 1000 ao O01 FREE online GATE coaching www.egate. ws ____ FREE online IES coaching For Video Lectures www.satishkashyap.com : CJ a (thot hbaithbil idabre » bit — range of Signed mag » "Ss complemen: -7 -» +7 2S Complement —S > +7 | ; es a = rae) - and. 1°.complement :—| _ bit — complemen) :- —_o ee J rea, Sty using 2's ‘complement - o101 t 7 — ——— | °100 poo iT a : Overflaw may ' occur When same (two beasse sign no. are added in signed representation, becavse for «4 bit we can only represent. ! in ea eet) ie es eee) let x and yare si9n bit of two no. and z is resviton| sigp. m0. then conditon jor overflow is . By condition ot overflow is ~ classmate ee FREE online GATE coaching www.egate. ws FREE ae y isl lesa FREE online GATE coaching www.egate. ws FREE online IES coaching Vidbediephures synchronous, Baer Ge OB a a aot ee NPTEL __0224523@—= 4-720. = sce 1,6 is unused used lock out condition Le io 6 oO > To avoid lock out change unused states into one oft used states in state toble ‘toi ufo ovffa 17) over lapping | doit 3 4 state yequires > QFF. reyaired . Fyore “8heaty 2 Seneitieelyercon onre NE PSHE EEE] State Machines _ — aoa y = Mealy = ye sependon present state _4y,) 3 9% depent_ Design easy - 5 (ce | 3 Design campler . > less no: Of State. A fd ° For-Video-Lectures_ Wwww.s. atishkashy‘ ation LFA Net Iwalatie in NPTEL nter_ type Acc 3 Retype ABE _© faralle) comparator type dua) slope Integrating ty pe. converter (DAG) -— © Resolution / Step size. Q) Analog Yp_vottage. @) Ves @) 7. Resolution _ S) Error Accuracy 1] Resolution / Step size !- Tt change fn aralag vattage corresponding _ ane tse increment in the I7p. Kesdution _ Vy ar Where Vy reference voltage corresponding to Logic 4 - n= = no. of its. 2.| Anal op vottage += Resolution * Pecimal equivalent af binary dai In a 4bit CAC reference voltoge sv. } binary cdatg too: is applied then analog voltage 8 . Resolutio n Nanalog Wee Yideo Lectures = Wwww.satishkashyap.com ~~ Not ppeeniee inh Foul sagle, _vottage is the maa. op vattage _ of DAG . : gg RR ee ee Resnivu bon 2- 1 ES Resolution = — 100 . > engr acceptable in Avc’ser Cac ts equal +0 resxotion or step size. 3) Analos to _ Digital converter 2 | Characteristics of ADsG’s :— | ae joo se | Resolution = rronge ( are E -Vmin - i 1S fesalution a sati Sa ap.com + Not available in NPTEL R ae lodder hPa. ACs. is Ve fr Resalution oa Qn sie —— ey) i OTN ony. are error ot 256 _ 2001 %¢ 7 7 Frake “SNS __ Digital to Analog aircuits — _ weighted. Resistor. DAC 2— Geib :- SB) Yr more current leSs_corrent VY os Ve 2R Vr 4&R My a SR i I3t Iz +2I,t+To nm weighted resistor DAC the accuvacy less dve = use of different resistance. For Video-Eectures www.satishkashyap.conVATE | | | [NPE ayailablejin NPTEL K-2R ladd er — Norma ladder > Inver tect ladder . Non inverti ng Toverting. R-2R ladder : _Adzecent to = AB Resolubon * Oecirnal equiva lemt of Binary ory dota. Ft Nr = GC as = 2 by tN 120 62 b es SBN aS) Doe 622 Sopar toby 2 j For Video Lectures z= Resat oni Sy ShEVRRRE ga irot available in NPTE Inverted ladder DAC circuit 3 - = Sass A anda’ both are Ground then § (logicat or virtval ground and ground ) the switch is at same potential then charging and diecharg ing OC} switth eroblen removed in prevfous cKt- www.satishkashyap.com == Not available in NPTEL Seed ee ee eee 2 5E [8b + bbs + 2bi bo ( race (| |} ttl isl tin cal iv —- |} + —} Fb Digitod o/p. > | im _conter type ADC a comparator is used to _compare— J/p anal voltage with reference vo provided by Dac feedback - A counter is used to cont 10.of olock pulses app When analog ltage (va) is greater thah pDAc vattegd then -Yp is 3. then counter count and — -analos voltage (Ve) is tess than’ _ reference valtage (DAC voltage) then Yp is 0 and counter shops counti and _tgive the _ comparative dogital ap. Mian- no. of clock pulses required dor N bit conversion ts Bee < - Ton, ra Maa. canversion time = (2°-') Tex. 44 ey ~ For Video Lectures = — ee = “Not-available in NPTEL (8} Faralle) comparator type i- Sal Fea SRE 5-7 car =a = BE ar resistor required , 2° nN __ prion’ encoder . “alleck Flash _A®c (fastest AG). 3 Bit parolle) comparator :— EI) chock required - f | No clock pulse is tequired. E36 a] therefore itis fastest. ADc among alt. “Man no. of clock pulse required for 9 bit conversion ig Which is Inside PIPO. Na > es Wie > Vas 6v PV ARRAGE™ op analog | esi Se eee OYE Sk ASH le [2% S vas We y, Va S 8Vy¥g Vas 2Veg counter ls used to set the base ckt is used to reset (Vac v,) In SAR Type aoc , counter will present: to ring successivel set the base. Contal ckt is used to reset ,previousl Set bit Whe See. ee in _S8AR_ Type Avc , © Clock pulse reg ‘red fox nit; fae || SAR iS mostly used in Orgital cht to Provide infe ce with microproae ssar. ___Far-Video-Lectures—————__www.satishkashyap.com—————= avll stops. tet oN is count When counter stops: vals ork oy (-T)_ rat ty ee Ne (Cai) Ro Re VaT = Vy (R-T,) Nao Tas SVN Tie) > Na +2 ext AoC capacitor. (Therefore this a more accurag “mana- no. p sige iieeit a digital voltmeter. Lie wMe eee ae ' pace TT TI online GATE coaching www.egate. ws FREE online IES coaching For Video Lectures . www.satishkashyap.com | yet frase in NPTEL § Eh) j [jC classmate FREE online GATE coaching www.egate. ws FREE online IES coaching www.satishkashyap.com (Diade AND Gate) _ | Vo = A+B COrod OR Gate) Fox] idoolisctares = www-.satishkashyap.com "Not available in NPTEL Mee. = 1 9 AMS oo Ona 1 ° 1 wat oO New a ded | = | when logic gate opis 4. (. OFF) it will-act a» current source. = | when logic gate Pp ig O (Tr. ON) it will act as cprrent sink. 3| Th wtaff and saturation region transistor will act as suiiteh,. i Je Je ____ Region ! R6 86 estoy | 4 ee rr FREE online GATE coaching www.egate. ws” FREE online IES coaching For os ishos of (vow. Be jae Cia _Not available in NPTEL. ans =4 aaa = Prapogation delay :- Up) cs wt s measured ™m nsec. Ou OFF a : > _fapogation ty is always measured from 5077. \alve aN to OFF time is more compare to OFF dve to saturation or storatge time - aT . Soap Lectiates www-.satishkashyap.com Not available in NPTEL aon av ¥ ae It is : ig , > on bx 3S Mar, no of logia qote that can be given by © logic gate . . Four = 400140 _ =e . SOMA, Tor =—l6mA Ty 0G 400 find dan out fanovt = — - " ee 4O fooovt, = yanout = Itis the mon. noise voltage that can be added to the logic family which will not affect the %p. | ’ Vou > Van > Ver > Vou wwwagatishkas! ap.com nit ROOD Sed MS e overall noise margin = (NM, NMi) min. 2 i moc asenanort nb aS as = (ED x J @) RTL (Register Transistor lagic ) family :— Basic gate -NOR gate. sons 1 mw: S00 PI O2NV logic family ip We resistance removed _ then resullor is OCTL. 6 tog = 4ONSec | Disadvantaq 6 +4 Corrent Hogging , Az OFF OFF OFF ON =e duetocurrent Regging In Dect. logic . Ff tr. switch different characten'shcs are use the Tt having lower Vpesar then first om and it willna allow other Tr to on.- this phenomeron is KnawWn-as cuore Hoqging. Inteqrated Inzection logic Cxr?uU) t- It's injecting the current into Base 2| when A is high the cwrrent Hows through the base of Tr ! Tr. mt be ON. [7 covers jess Space — = a, a se Video Lectures www.satishkashyap.com-———Not available in NPTE q So sek Se Noe. “guriant Ho99!79 . 3 There is no prablem oft = FON = 0-1PT- = OTP S.- all it Occupies tesS area hence i It is mostly used in MSI ond LSI Also called MTL (Merged logic fomily) dve to integration sof Transistor - - Fbr Video Lettpagele Tv nsistowwtospiisiidshyesl yor Not available in NPTEL A} AND Gate followed by Nor gate. >| z0K vesister used only for -digcharqing the qunction capacite -_ce. The capacitance. which. is discharge. is Transition cap. Ce. Tre lat ig called. Basie ore qate. In this any one of the tp is low. or @22 the I/p are low: , Dy @ng@ Or Dg will become forward bias where as Dand 02 will become Yeverse bias due to tt T 7 ts off and Bikes ise rk when all the tp's are high then. Daand Dg become reverse bias ond Dpand Di will become forward bras and Ti ts on ~and OP is low. = The basic gate ig NAND gate. ted = _30nS. Gigs = 8 Mw. FOM = 240 PT NMOS “OciSve Fanoutt = 3 Tt provdes wired AND operahon. Ee To increase fo"? aoF = we intradvee Trin ALES place oF Diode. Sk” Yesistor vsed yes eae, eo oe STANDARD codiese EEF} FRE onl ER E coaching wwwleds 5 FREE online IES coaching 4 DN __fbr Video Lectures — www.satishkashyap.com = } High Threshold logre (HTL) family :- 4, = : oe eee Diode is Used inplace oa O2 4- 5V (Highest noise margin) 3 Since in DTL atl diode and Transistor 1s —ive temp coefficient Bb loge O= 2V = er C= 8-25 c. logic _ = 12V. > tai= gons => fis, = SS™mw FOM = 4950 PFJ x 5000 PI = Fanout. = 8 ; a Basic _gate = NAND_ gate. ~ ja Noise margin = 4v-Sv- | For Figse EetiBRsistor Transistew-saénpleashy 4 piconh'y 37) Not available in NPTEL Multiemitter transistor. B Ay Ta Tz te A c Cc A c Cc Oo A Cue R S °o 1 Ss s s ce Il Ss 3| The ckt Shown in tig. IS standard TTL logic family. if basically have _ three stoge- : @ Moltremitter t/p stage wb) Phase splitter. uw ‘Totem pole oo, active pullup. o/p stage - active = - use of Tr Ty Pullup = Tr (1%) conneck to Vee.. Opgerahon z— An one of 7p stow. or alt vps are low- then Ee = unchon 1S FB. (Je =. F8). and callector. bose (Cde= = ig R@ . . is in active mode. due to this Tr. 2 ond i. ave, Ofes. Cilp wroff..region) where as VN in ts SAT Hence G/p 1s 4. When all the p's are high then Ve €€6 Junct”) = Fh is 88 ond 3.(ee Jonct" yr SES (The O ' . : mode a operation ‘3 _Keverse active . PAGE Ps FREE onliedaS AEB aching www.egate. ws FREE online IES coaching www-.satishkashyap.com in satoratren For Video Lectures ar ral TA Hence > are cutoff Gi el es — Ive YR DATEL dan o\ ig zero Yeu Acs ) Gs ae -_— e * = i vattage 1 | ON. Tr Ty When 73 4 3\| Advantage of Totem pole :- power: dissipation . speed of operotian . — in wired ogra open collector, FREE online IES coaching www.egate. ws IE Video Lectures , ripple or of operal In TT Clamping transiatoer clam ping There @) (b) (ec) (dd) 40 JL resis Re MeeeTe eee een ter || | \| Not rele in NPTEL itor used w collector 19) O/Pp Slatqe bo vedlice noise qaneralion to in pe high frequency mon , if any Iyp is open «tt behavas a® logic | diodes ‘are connected in 2/p stage doving high jrequency of operation j D. removes ringing oF high frequency operathtar are litferent type of TTL” standard TTL High speck low power Saho tt hy rTtl For Video Lectures wwwsatishkashyap: : | H@h speed TT :- s + In Standad TTL Logic family it Resistor wolpe Teduce then toot reduces and | Negative spikes donot Offect the +transistory dwe to -e power Supply . ECL uses -ive power supply. Cue fo. this any spikes or negative witage nor affect operator. fect eles Rais. - SS™w FomM = SSP IJ Fanoot = 25 M i= O3v Nigecrate: | For Video Lectures www-.satishkashy ap.comare jae] [NE a4 filatfle th PTH logic =. AV. { Fete 169 : ' = —_— = vottage “Supply —e megahi a B v a = S If any Sp is open then itis logia O°. DATE www.satishkashyap.com Not available in NPTEL channe) =— logic 0" =| logic . L. channe} Mos logic 0 logic 1 variable vegistor hence in mos veg: resistor we use MOSFET | Since FET Is voltoge cirevit in place ¢f NMOS NoT Gote em FRE} ons HERTE SSaching : www.egate. ws FREE online IES coaching FREE online GATE coaching www.egate. ws FREE online IES coaching FREE online GATE coaching www.egate. ws FREE online IES coaching For Video Lectures www.satishkashyap.com Not available in NPTEL GMOS NO : Vo nmos power “ dissipahon = 0. Ol1mw 7O msec Dynomc PD During transition from o7! fap For Video Lectures www.satishkashyap.com c | | | [ hid availablein NPTEL GMOS NAND Gates — ie Gag) 8 { V oO oO OW On OFF OFF oO 1} ON OFF OFF OW OPE ! OFF on ON on OW ° OPF OFE For Video Lectures pee eer re u dl —_hheotlavdifable ir] NATE Tyvansmission Gate control _A =O » 1 o { aT Y High impedence =< oO Symbol _ of Transmission gate Total no. of transistor mae AEA SGN CMOS mOnoslable multvibrator :—