1

Σημειώσεις Μαθήματος“Ηλεκτρονική”

Έτος ΙΙΙ, Εξάμηνο Α’Λέκτορας Ε. ΚαραγιάννηΑκ. Έτος 2006-2007

Από τις παραδόσεις του μαθήματος

Περιλαμβάνουν:

Μάθημα 1:Εισαγωγή στα Ψηφιακά ΚυκλώματαΜάθημα 2:Συνδυαστικά Κυκλώματα:

Αθροιστές, Αποκωδικοποιητές, ρ ς ςΠολυπλέκτες, ROM

Μάθημα 3: Ακολουθιακά Κυκλώματα

Eroayuryn oro VnprandKunAtbFqra

HAerrpovrx[l- 'Td[nA6rropog E. Kapqyrdwn

Tr eivor n0An;I.. ulrnOo0pe 6rr a dio6og(5 (Aerroupyei ocv rAetcr6g6ror6nr4g) 6rcv eivcr opOd noAu.rptv4Kdl

I 6ev dyer (Aerrowyei oov cvorxr6g6ror6nr4g) 6rqv eivor cvdorporpcnoAup6vn

2. TTcpar4piore ro ax6Aou0o oxiporo ro ppeire ro 6wcprx6 e(66ou vtca,rrrdr.roopo0E rrlv neprrrOoeulv 6nou or 6uo eioodor x Kor y eivor oe XoUnA66wcprr6 (n. x. 0 Volt) i WnA6 6woprx6 (r.X. 5 Volt)

l&ihpn 1, Fnectgornril f Etoq

Op0d noAurp6vn eivor gro diodog 6rcv ro6uvaprx6 r4E ov66ou eivot pevqAiTepo

qtr6 ro 6uvoprr6 r4g xo966ou

itr eivqr n0An; (AND)

3. H qtrdwnon rou dtiloare yro ro

@6netvoottpguvei pero 6rnAav6 nivorq aAt0eroq

O Oror x=0 Volt rcar y=5 Volt, r6re 4elodog x ppaluruxftfuver Ue rnv 6[o6o xcr6iver F=0 Volto 'Orcv x=)E 5 Volt r6re or 6rio diodol eivorcvorrrorurfiig6veg Kcr ro 6woprr6 nr,rv 5Volt Uerogtperor or4v 6(odo Uerd ard Hiqtrrrtpi rntlot rdong foVur rnC cwicoolg Ro . . .4. [Anopo0pr vd ovopdooqre owh rnor.rycprnon rruAn lOtI (AND) o,po0 n6[odog eivor <cA4g{9 (eivor oe rrynA6dwcgrr6, I roourcr pr <1>) p6vo 6rcv

or drlo eioodor eivor aAn0eig.

M&04pc 1, Fllocrpou$ I- Erog

Tr eivqr n0An; (DDL)5. Eropturg, pzopoqre vo ro0pe 6rr miArteivur tvu 4lei<rpovrx6 x0nfulUq ro onolo 61erpio r| repradrepeg ero6doug rcl glc t[odo.

O Tq duvqflxd rurv ero66uv propei vuildpouy 6to<prr66 rrp6g cn6 6rrc anveyeigrdocrg rrcu o.rvriOug elvcr 0 rqr 5 Volt riO rat 12 Volt. Or 6rio ow66 rrp6govolrd(owos <cQ> (9eu6[s) ti

"!n (olmnC)

cwiororla.o KdOe m)A4 np6ner vc rporpo6orchocar6 gncrqplc! Tlcpcrapiore cnndrogivero 30 ro nodopdxrc 7 xor 14 rwvoAoxAlprlU6vuv.

6. H aryrexprptvn rexvoAoylo uAorol4o6mrAtuv eivcr 4 DDL (Diode - Diode Logic).

O AMeg relvoAoyieg elvor a TTL(Trcnsistor - Tronsistor Logic), n DTL(Diode - Tronsistor Logic) ...

7. Agr,t Aorn6v ot miAeg oxtnrowqr dr.rqdtrd(0 ti 1) eivor cvdyrn vc o(egroOge rqr elrefg6uadrxd!

Mri04pa I, tllerrprovuoi I'Eroq

2

AeKqdrKoi Apr0poi

r Apr0p6E: 342,5

r Eivqr rro eUxoAo voypdgoulte roug olweAecr6gror an6 rn 06on roug votruprepdivouue rnvcnorro0uevn duvaun rou 10.

r lTorog on6 rouEouweAear6,g eivor ro MSB?(Most Significont Bit)

Or derq6rrol oprOpoipnopo0v vo 61ouv rrtgouvreAeorfg rougqr6Aou0oug 10 opr0poOg:0 , 1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9

Auadtroi Apr0poi

r Apr0p6E: 10011,101 r Tunrxd 0a 6npenr vo ypdgerqr:

oxrddo xcr xopiorerpddo ror I dud6o xarpia povddo xqr 6vadeOrepo rcr rov6vor6ropro xor 6vc 6ydoo

Md04pc I, Hlattgovrril I.Eroq

Evag opr0p6g Ue Fdon v unopvo 6yer urE ouweAear6g vopr0po0g, roug ax6Aou0oue:

,1 ,? , " ' v -1

3

oro dMoApr0p6E 1: 10011,1 Apt0yilg ?z

342,5 601= 10 10 10 I 10, l1zy34?z?=t71 ge xparo0pevo 0t7t:2=85 pe Kpqro0pevo 18522=42 pe Kparo0pevo I4?22=21pe tgaro0pevo 0?I:?=tO pe rycroupevo ItO:?=5 pe Kpdro0pevo 0522=2 pe rgaro0uevo 12:2=l ue rgoroOpevo 01:2=O ue rgaro0gevo 10,5x2=11

l . 2 a + 1 . 2 t + 1 . 2 o + l - 2 - l

= 16+ 2+ l+-* , = 19,625

Md04pc 1, I-Decpnrxi I'Eros

M Dpeoow 6AeE or 6uvar6E dr.ndrxig A6[erg (bytes) nrrv 5 dr.ndrxtilvg4giuv (bits).M vpopei o nivarcg oAt0eng rng dAng OR.l-pdyre roug nptilroug 30 ap€po0g pe Fdon rc 12. Xpnorponorfloreypdppcra yrd vo cnerxovioerr rd 3 reAewoio Vnpio.TTorog eivcr o peycAwepog 6uodrx6E opr0p6g pe 15 bits; TTorog eivor o6erodrr6g roodwop6g rou;liercrp6ryrr roug en6pevoug 6r.ndrxo0g oprOpo0g oe 6exc6rro0g:101110, 111001.11 ror 11@0110011.liercrp65e roug en6pevouE cprgpo0g orn dedop6vn Fdon oe6axodrro0s: ?l22l4gy (34201)0, (60)0, xor (189)621.illerqrp6r1,rr roug endpevoug 6ercdrxo0g apr9po0g oe 6uodtxo0g: t321,546,5?.103 rar ?@6.M Dpe0ei n rrpi rng Fdong x cv 2111,,, =1521a).

mi0ngo I, FDactp,ovrril I'Etoq

4

TI0leE AND, OR Ksf \l9T

H n0An AND diveronortAeqrc 1 g6vo 6rav6AeE or eioodor eivqr 1.

H nuAn OR divercnoriAeqrc 1 6rcv piorouAdyrcrov cn6 rrEero6douE eivar 1.

H rruAn NOT diver roo;prAtptlpq rnE ero66ou.

Md04pc t, Hlerrpovtxil I. Erog

TT0leg NAND Ks

.r H nuAn AND 6iver

{ H n0An OR 6iveranor6Aeqra 1 6rov piorouAdlrorov on6 rrgero6douq eivcr t. Apa nP^n r.loR (Ngr AND)61er nivora cA4OercE

Md04pc 1, FD,ectpovrril I' Etoq

5

TT0AeE XAND Ksr XO

H n0An XAND diveronor6Aeqrq I or eioodoreivor idreg.

H n0An XOR 6ivercnoriAeqrq 1 6rqv or 60oeioodor eivor droooperrx6c(oryTAnptrrpar r xi g' uerq(6rouq)

Mti04pc I, H)-errprr:q f Eroa

iArveAos BooleI r l r l Y e t | l

Eivor n dAve0pq ru,vffifo)(uer n cvnperaOerrxnrdr6rnrq Kdr yrq rovreAeorn + Kql $q TovreAeorn'fgluer n erflpeprorrxqrdr6rnrq u,g npog rnvnp6o0eonIoy0er n edFeprqnrirdr6rnra urg mgg rovroMorAaotsouofoyuer n rpooerctptonxfirdr6rnro yrq rov reAeorrl +fo;uer n ?Tpooerorprorrx[t6r6rnrq yrq rov reAearn '

(x+y)=:i 'y'(x'y)'=1'*y'

Mri04pc l, Fllettpovrr{ I' Ezoq

6

Aei[re pe Xpnon nrvdxrlv oAigerag rnv rq(0 nrrv rdpdxdrurrcwortirurv:(o) To 9etfupnua rou De Morgon vro rperg peraDAnr6g:(xyz)'=x'+y'+7'(p) Tov errptprorrr6 v6po: x+yz=(x+y)(x+z)(v) To OetfupnUa rng anoAolgtig: ry+1'z+y7=xy+x'7AnAonorfiorr ng ncpardrur anvcprfroerg Boole oa tvqv eAdyroroop€p6 ncpoy6wuv:(a) ABC+A'B+ABC(F) x'yz+xz(v) x'y*tcy'+ry+x'y'M drarumfuorre rn Aerroupyic rng n0Ane XOR rprtfuv etoddtlv,ogo0 nptfuro Xpnorponorfioere rnv dAveDpo Boole Kdt rov nivcrcoAt0erag qurtig rng miAng

Md04pc t, FD,empovtril f Erog

EpapHoyn@6Aoupe vd KdrdoKer.nooupe x0xAulpa ro onoio gc 6xer 4 ero6doug xct pio6(odo.Ee rdOe pia cn6 rrg ero66oug 9c rono9er4ooupe 6ro161114 evd, arnv 6(o6o

H Aerroupyio rou 0a eivo 4 cr6Aor,€4:Krir0e draruvr(6uevo€ nou np6ner va rprOei oil6 4 rprr6g, (x, y, z, w) 0ae(,erd(erar an6 roug rprrig. Awoi pe rn oetpd roug, ove[dpr4rc perc(0roug otrogaoi(owag vrd rnv r0y4 rou droyrlvr(6prvou, 0o naro0v 6vo6rcx6nrn yro vd rlngioouv NAI i 6ev ga tov ncro0v vrc vd g4gioouv'OXr.O Aafmnpcg 0a ovdper dv ro cnor6Aeqrd rng Vngogopiog aivot apv4nx6rcr o drcyurvr(6pevog 0o evngaptfuvercr or rpdvpdrrr6 1p6vo.

H rdurrep6rnrq rng eilrrponfig eivo 6r o xprrfig x eivor o np6edpog Kdt nryrirpog rou 6;1er Dop0rnra 2. Or ryirpor nrrv dMrlv xptrtilv 61ow Dap0rnrc 1.

gledroorei ror vo uAonorqgeiro r0rArlgo.

Md0rlpc 1, lllecrpovocil I' Erog

7

(E,psptrovfr) Bnpq 1:Karqoreui TTivarq AAneetqgAnproupWir r6oeg cniAeg 6oeg eivo Kor or eioodor.ITpoonagtfu va vpdp 6Aoug roug 6woro0ganvducqro0g rruv ero66uv.KdOe eioodog gopel vandger 6r.ro 6roxprr6g rrp6g 0 vraro'OXf ror l yrc ro NAI (n ouUOurvla UaS).l-rc vq Un Xdorl rcv6vcv o.nrduoqr6 cAM(ur ro LSB avd1, ro a;r6olg en6pevo avd 6rlo, ro en6pevo avd 4 Kdr romSB cvd 8. (geurpfc ordr.nornfg).

M,iQtrc 1, ttlrrpouril l' Etoq

(EpqppoyrD BnFs 1:KqraoKrui TTivqra AAnOasg

Ere6oov n Vireog rou x 6xer pcp0rnta?,noAAarloord(u rnv ryrirpo rou eni 2 (tXer v6npo vrd rrg0errr6g ,yigoug). Ernv npoypcrrr6r4ro eivcr oov vd6Xu 5 rynrpo@poug.

Mdt0ngo 1, tllectporucl I. Etog

o x gtlgloe NAf(x=l), o yOXI(y=O), o z OXI(z=O)

Kcr o w OXI(r-O)Eroug 5 $rtiOoug or 2 elvorOenroi. To onortAeqra

cpvnrrr6 (F=0)

8

(Epqpuov0 Bfrpq 1:Kqraoreui n@eurptirwog 611 6vog AaprnRpag arun6 rdor1, o Aaprnnpcg 0a ovdger rrcrdorcon <1>.To np6pAnua A6er 6rr o Aa1onor6Aeopo rqg ry4gogopicrptner vc 6rop90oouur ro'

Md04pc l, tUenpovxi I'Etog

a I t - Q A ,x Y z U , , F

ryqKs A^nE'srqgrnpag cvdper 6rov DpioKrrolovdger drcv ppe0ei ornv

0

oIIoooo;I

I

I

oo

IoI

;I

I

0oo0

o7II

I

o91

I

0

oI

t

I

I

oI

oI

oI

0

1

o1

I

I

1

I

I

I

oI

oo0

I I o 0 0I I o I 0

I I 1 o oI I I I o

(E,pqppoyn) Bntrq 2zAruloupyio rng

H rpdrrn nepinnrrot 6rou n F eivcr aAr€rig elvcr 6rcv ox g4gloer 'OXr rdr o y Vngloer OXf rar o z g4gloerOXI rar o w Vngioer

'OXI.

An ddtl o rp0roE ourrduooU6g ypdgercr oqrpoArrd:;'ry'o7'ory'

TToporttpnoq 1: A9o0 Vrigroe o x'OXf (x=0), r6rero o.4rnA4prlpcrrr6 rng Vigou rou, ?rporpovrirg eivorx'=1Ilapcripno\?t H miAn KAf elvor dAneng p6vo 6rcv6Aeg or eloodor elvar 1.

Apao nptfurog 6pog rng ouvdprnong F 0d eivor o

x v 2 w F

o 0 o o I

o o o I I

o o I 0 I

0 0 I I I

o I o o I

0 I o I 1

o 1 1 0 1

o I I I 0

I o o o 1

I o o I 0

I o I o ot o t I oI I 0 o 0

I 1 o I oI I 1 o ot I I I o

Me0npc I, Iil.ecrpovrr4 I'Etog

9

1 '

(E.pqppov0 BfrUs 2zAnHroupyic rng owitprnong0

I

2

3

4

5

6

7

8

910

11

t?

13

t4

15

McQpa 1, Hlacrpouril I' Etog

Krl0e arduoqdg rligurv eivar xor picA6En 6ucdmi. Ag rnv per<rrp6wuue ornvcwiorory4 dercdrri rtEn. l-ranopdderypa n A6€n Ollo1e1 efvcr 4awlororxn 66sy

I v z w F

o 0 0 0 I

o o o I I

o o I 0 I

o o I I I

o I 0 o I

0 I o I I

o 1 I o I

o I I I oI 0 o o I

I o o I 0

I 0 I o oI o I I 0I 1 o 0 oI 1 o I 0

I I I o oI I I I o

t '

(E,poppoyn) Bnpq 2zAnlrroupyic rnc ouvqprnong

F = E(0,1,2,3,4,5,6,8)

Md04pc 1, FDenpouxil I. Etoq

10

(Eqqpuov0 Bnpq 3:AnAorroi4orl rn€ ouvdprnongi 6eo6og AAyeppqg Boole

F =2(0,1,2,3,4,5,6,8)

F = xt y'z'w'+xt y'ztw'+x'y'z'w+ x' y'zw'+x'y'zw+ xt ltz'w'+x'yz'ut+ x'1y'zw'+ry'z'w'= x' y' z' w'+x' y' z' (w'+w) + x' y' z(w'+w) + x' 1z' (w'+w) + x' )lzvl+ry' z' w'

= x' y' zt wt+x' y' z'+x' y' zt+x' y' z + x' vz'+x' 1zilltry' z'w'=

= x' y' z' w'+x' y' z'+x' y' (z'+z\ + x' y(z'+mt'\ + ry' z' w' =

= x' y' z' w' + x' y' z' + x' y' + x' y(z' + z\(z' +w' ) + ry' z' w'= x' y' z' w' + x' y' z' + x' y' + x' 1zt + x' 1tw' + xyt z' w' =

= x' y' z' w' + x' z' (y' + y) + x' y' + x' 1/w' 1 ry' z' 'w' =

= x' y' zt w'+ x' zt +x' y'+ x' 1Nt+ry' z' w' =- y' z' w' (x'+x) + x' z'+x' y'+x' yf =

- y' z' w'+x' z'+x' y'+x' 1nv'

AnFroupyiq Xtprn Kornough 4HerqFAnrtfuv O xdprng

cnoreAeircr on6 15xeArd,6oor eivor rqror duvoroiotrvdr.nogoi 4 bitKd€e vpauuiowrrpoourne0erorynerprg6voordr.nog6 vra rtg 2nptilreg UeroDAnr6Erar rdOe oriAnouvxexpru6voor.rvdr.nop6 yrc rrg 2reAewciegUeraDAnr6g

Mti04pc l, llleetpouril I' Etoq

AN

xy00 01 11 10

000 1 3 2

014 5 7 6

111 2 1 3 1 5 1 4

10I I 1 1 1 0

11

Vdft;re I, Hlerrpovtr4 I'Etog

To reAi aurdovTnrpoour?feoel To

anvdr.nqd xyafl=lll0(&ndrx6s ap€u6g)lrou oro 6exc6rr6

qtornpc elrror ro reAit4

(Eqoppoy0 Bnpq 3:AnAoroinon rng ouvAprnong,lA6eodog Xsprn Kornough

F = X(0,1,2,3,4,5,6,8)

Mci04pcr l, FlLecrpovr:q I'Etq

12

(Eqsppovn) BnFq 3:AnAonoi4orl rn€ ouvqprnongl 6eo6og Xtprn Kornough

H oud6o nrry 4 awtilvdoorrrv 6xow 16ro x=Orar 16ro z=O. Agaqvnrrpootrme0et rov 6pox'z'

Awri eivar pic rerpddcdoouv rouqwr?rpoorrnte0e t rov 6poxy'

EvoE dooo6 Ftopel voxpnopoilornOei an6noM6g ouddeg. Apref vopn pelver e.Aeri0epog!

Mti04pcr l, H),ecpovmil I'Etog

(Epqppoy0 Bitrq 3:AnAonoinon rng ou\tAprnongiA6eodog Xaprn Ksrnough

Mri04rc 1, Fil^ercrpovrxil I' Etoq

O xdprngKornought

eivctrutuvdprrt69.

O 6poeaw6g elvaq o

13

(Epapuovi) Bnuq 3:AnAonoi4orl rng ouvdprnonglA60odoE Xqprn Kornough

F = x' y' * X' / + 7q' 7g1' +y' Z' w'

TTopcrrlpo0pe 6n n ouvdprnon enrd6xercl enlnA6ov cnAonoi4o4:F=xY'*x'(z'*ztf!t'z'w'=xY*x'(z'*z)(z'*w'Yy'z'w'

F = X'y' * x' z' + a,' g' +y' Z' W'

Aw6 orviper enetdi 6ev npoo6[qpe rnv ruAtvdprr6rnrd rou Xdprnvfd rnv ouodonoinon rurv 6ptuv O,4,2 xat 6!O Xdprne Kornough diver rn D6Arrorn anAonoinon 6oov ogopd rnv6rgpaon r4g ouvdprnong uE dOpotqro yrvop6vruv.

Mri04pc 1, FlLerpovrxil f Eroq

(Epsppoy0 Bnpa 4:YAonoinon rng ovrtitprnongF = X'y' *X'Z' + 7' g' +y' Z' U'

Mri0r1g.o, 1, F0.empovurft I Erog

14

EpqpUoVn: ErnvVdXvoWe yro olor<Aryruptvc touneprtlowr 3 m)Aeg AND 6i,o ero66ruv (TILSOB)r 1rnitun AND rprtir ero66uv (74L511)r 4 rn)r.eg NOT

(741s04)Kdl

r l mirAn OR rprdrv ero66ov (74L527pe 74L5O4)

Ewoturd 0c lperooro0pe 4 chips, 4 6nr6rneg, xotuirdtd Kdt tvcv lolmrrlpd.

Av {rcv pc(rr{ n napdytrryi cwo0 rou rurAdlparoE gc pnopo0oaFe rrd roxcnooxeucooupe oe 6vo oAoxA4prr.rp6vo (chip)

,T,

* yrv6wcv ov eiyope arn drdOeoti uaE p6vo oAoxA4pruptvc tql-tsO0?

M,iOqF" l, lDectpovrril I. Etoq

rart

tdtt

ra.t

to

rar

tlltr

ratt

rlltl

7.,I{'6'

nl|'

ta.!,

rattlr

M,ihpc 1, Hler<tgouril I Etos,

15

@

Knoerg1. No uAonorn0o0v or n0AeE NOT, AND, OR, NOR, XAND xor XOR pt Xpnon

nuA0v NAND2. No uAonotn0ei n or.rvdprnon F=Z(4,5,6,7,1?,13,14,15) pe 6rr n0Aeg

enrOqreire.3. Nc uAonorngei n ouvdprnon F=E(0,1,8 ,9,1?,13) Ue Xpnon rou 74L500.4. Nc oledrccrei g4grox6 x0xArr.rpc rprtfuv eto66uv x. y, Kdt z, Kol picg e(66ou

F. H 6Eo6og eivcr I 6rav rar p6vo 6rcv ro orivoAo rurv ero66uv 6;1er reprrr4oortltia, dnAodi 6rcv ro nAh0og rrlv eto66urv Ut npi 1 eivor neptrr6.

5. No uAonorn9el n or.rvdprnon F=x'yz'*x'y'z+xy'z+ryz ue rn Fon0erd rurvoAorA4prrrp6vruv 55f nou nopouord(owdr ornv err6vo. Yno06roupe 6rl roroAtildro nou ouv66rrdr n eioodog x, 6rapp6erot on6 pe0pa rot eivotppaluxurAupivo Ue ro xaAtildro r4g ero66ou z. To raAtir6lo nou ouv66erclpr rnv eioodo y eivcr xopp6vo. Er4v 6[o6o F ixoupe or.ry66oet 6vovlraprnfuo. @o eivar cvol.rptvog i oDncn6g;

6. Eledrdore 6va a.ry6r.norrx6 x0xAurpc 1re Tper€ ero66oug X,y, z Kdt rpttgc{ddov€ A, 8, C Orav 4 AeA&( nK( rK erdfui eivat O, J, 2 I 3, 4trntrxtUnrrng tt0tuu twtt tatt itt parchtntp?rr?tg tttbtou.'Orav rtnpt rng ero66ou eivct 4, 5, 6 n 7, n rrun rng e(66ou eivct xard 6va

Mrig4pc I, Fllexrpovrxil f Eroq

7. Na DpeOei n 6(o6og ru.rv qr6Aou0uv xurAurpdruv dv or eioodot eivct x xct y

8. Ee 6vo o.rpDo0Ato ofroA6vnong uiog npoun0ercE undp;ouv 3 xprrtc. OtVirpor roug 6yow drogoperrrd Dopn: Tou xprrfi A 6xet Ddpog 3, rou B 6xelFdpog 2 xat rou l- 6xet DdpoE 1. Kc0ivoE an6 roug rptr6g 6xel 6vov6tox6rrn rou rov xAeiver yrq vd g4gioe r NAf xqr rov cvoivet Vtd vc ryngioetONI. Ee nepinrron toogrngicg ro cnor6Aeqrc aivcr OXI. Na oxedtdotrt ror0rAulpc nou 6ei1va dv ro onortAeopd rng g4gogopicg eivcl NAI f1 OXr.Exere or4 drdgeoi oag 6non oAorArprlp6va 06Aere.

Mri04ptc 1, FDempovmil I'Etog

16

AornoerE9. Nc uAonornOei n ouvdprnon F=2(O,1,2,3,4,5) pr rov eAdyroro opr0p6

nuAtlv.10.l-ro ro or6Aor€o r0rArlpc pe

ero66oug x,y,va Dpegow or 6{o6or A xar B.

11. Eledrdore ouvdrrorrr6 r0rArlpo pe rpag ero66oug xo 1.rio 6(odo. H6[odog roo0ror pe Aovrx6-1,6rcv n dtndrri rrpi rng ero6dou eivarprrp6rep4 rou 3. l-ro xd9e dM4 nepinruron, n 6[o6o9 roo0rcr pe Ao$x6-0.

t2. Mia ouvdprnon nAeroryngi aq, rraporv eror or 6vo otryducorr 16 x0xAurpa, 6rovn 6[o6oE eivcr io4 pe 1, cv or percpA4r6g e roddou ilow neproo6repc I cn'611 0. AMrOg n 6to6oE eivar 0. Eledrdcre pro anvdpr4o4 nAerogngloqrprdrv ero66uv

13. AnAonoreiore 14 ouvdprnon Boole F, pq(i ue ng or.r€hxeg cdrorpopiog doe (i) d9poropo yrvopdvuv ror (ii) yrv6;revo aOporopdrrv(c) F(x,y,z,w)= E(0, 1, ?,3,7,8,1O), d(x,y,z,w) = E(5,6, I 1, 15)(p) F(A, B,C, D)= f (3,4, 1 3, 1 5), d(A, B,C, D) = Z(1,?,5,6,8,1O,12,14)

MtiQpa 1, Fllocpovtr4 f Eroq

Aornoefg (rup6veE)14. Na q(edramei 6vo ouvducmrr6r0rArrryo ilou vd noMcnAaord(er dr,ro6ucdrro0g cprgpo0g rrr.rv 60o bit oxdOe 6vog: ctrdo xcr brbo, xor ncpdyerro yrv6pev6 roug cacactco nou eivcr6vag 6uadrr6E cpr0p6g reoodpurv bit.A0onO g6yrorog cpr9p6g nou pnopei vor.mdp[er rr,rg nqpdvowqg eivqr ocpr0p6g 3(ro) = 1112y'OAor or dworoiorvducolroi nou pnopei vc tmdp[owyrd ro 6erodrx6 o0crnlro, eivcr orar6Aou0or 10 or.rvduaopoi: 0x0=0,0x1=0, Ox?=O,0x3=0, 1x1=1, lx2=2,1x3=3, ?x?=4, 2x3=6, 3x3=9.Biuq 1: A4proupyoope rov nivcxc

aog, Ur ro yvrucn6 rp6no: yro 4tmdpyow 16 drorpoperrroi

ar to br bo ca c2 cr co

0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0

0 0 1 0 0 0 0 0

0 0 1 1 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 1

0 1 1 0 0 0 1 0

0 1 1 1 0 0 I 1

1 0 0 0 0 0 0 0,| 0 0 1 0 0 I 0

1 0 1 0 0 1 0 0

1 0 1 I 0 1 1 0

1 0 0 0 0 0 0

0 1 0 0 I 1

I 0 0 1 1 0

1 1 1 1 0 0

M&04p.cr 1, File:ctqovffi I- Etoq

17

Aornoerg (rupiveg)(Ew61erc AoxnonE 14)Britro 2: Avqppi(oupe ng (ruvcprf,oerg Vrq rc cs, c2, c1, cs, or onoiegvpdgowor rlg dOporqra 6o,uy, ornv or6Aou04 popg{:

c t = E ( t S ) = a , a o b r b o

cz = Z ( to ' t t , t + )c t = 2 (o , l , o , t t , t l , t + )

Bipo 3: AnAonon0pe ,,. 6nr"i$J;li.'8'r*rn, Kornough eivcr n nroevderxvu6pevn u69o6og cnAonoinong. Anproqvo0pe 3 Xdpree, yrq nge(66oug c2, c1, co Kdr ncipvoupe rc croreA6q.nrc:

cz=at4bo+araobr=arbr(bo+ao)=arbr(boao) co = dobo

c, = ororobr+ araobo + arbibo + aobrbo =

= o obrb, + oo) + a rbo(o o* D, ) = o obr(q 4) + a rbr(a obr) =

= (ao4)@ b,q)4: YAonoro0pe ro x0xAurpc Ue n0Aee AND rcr XOR

Mri04pc l, Hlotrpovrril f Etoq

Aoxhorfg (rup6veg)

15. Eva Aoyrr6 r0rAulgc uAonorei rnv rqpdKdru ouvdprnon BooleF=A'D+ACD'. Exer cnoder;Oei 6rr o o.rvdr.nqr6g ero66uv A=C=l 6evpnopei vc anppei nor6. Bpeire pro anAo0orepn €rgpaon vla rnv FXrnor pono rtirwog n g rardMnAe g ou€hre g odragopiag.Arlon:

F - A'D+ AD'- A(DD

Mti04g.c 1, Hlettpovrril I. Etoq

18

Euvdusormt KurcAtfuHaro :A0gotor6g, AroKtudl ronot4r6g,TToAunAixrtg, ROn

HAexrpovrt<4t-'Td(nA6nropog E. Kopoyrdvvn

Adderflp6deon AexadrxdrvAprOptirvD 3 o . r y 5 = 8o tor,nt l=2r 3 o u v 9 = L ?ITp6o0eon AuodrrdrvApr0gtirvc 1 o r . r y 0 = 1a 0 o u v l = 1u l o u v 1 = 1 0

r l-rq rnv np6o€eon ryngirlu,Ocnqrro0wat 2 eioodor rqtQ6[o6or (pia yrc ro A0porqroxcr lric yrc ro Kporoupevo)

i Enop6vrl E, o HA 61er 60oero6douE xo dOo e[66oug

AOporcnfiE (Full Adder)Tr 0q yiver crrnv nepinnuonnoAug{gruv cpr0ptilv?D 32 or.rrt 59 =91

l 15 ouv 2l =36

o H np6deorl yiverarrcrcr6pugo, op1 i(owcg cn6ra LSB xcr npod6rowag roK ornv en6pevn rcrar6pugnnp6o€eo4

ITp6o0eon AuqdrrdrvAprOgdrv

Mri04pc 1, ilettpovtril I-Etoq

x v z K A

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 ,a 1 0

1 0 0 0 1

I 0 1 1 0

1 1 0 1 0

1 1 1 1 1

x v 2 K A

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 I 0

1 1 0 1 0

1 1 1 1 1

K-xy+xz+yz

A->Q,2,4,7)--tr@ y@ z

2

A0porsrfrg (Fulf Adder)

K - *' y, * xy' z + ryz'+xyz = (" A y), + rcy

x v z K A

0 0 0 0 00 0 1 0 1

0 1 0 0 1

0 1 1 1 01 0 0 0 1

1 0 1 1 01 1 0 1 01 1 1 1 1

a

Ausdm6g A0poforng g bits)

Mci0qpc 1, Filerrp,ouril I' Eroq

3

) H cnerr6vron pe 8 rynrpia rou cp€poit 12 oro duodrr6 o0ornpa eivar000001100

To +9 cnerxovi(erot Ue ro bit npoo{1rou 0 ornv cprorep6repn 06oncroAou0o0pevo cr6 ro 6uadrr6 tood0vcpo tov t?.F Av rar uraipyer p6vo 6vog rp6nog vq dfietKovlooqre ro 9 tmdplow 3durgopenxoi rp6nor vo dnaKovloou;re ro -9

O Anerxdvron rpoonlrcqttvou p6rpou: 1@001100O Anerr6uon rpoonpoop6vou oupnA4ptirporog u,E lrpog 1: 11111@11O Arerr6vron npoonlrcop6vou o,4rnA4ptilpdrog rrrg tlpoq 2: 1111101@

FE4perdrvouge 6rr ro or.rpnAnpurpq urg trpog 2 ev6q, dr.ndrroO ap€po0npoxOrret an6 ro o.4rnA4prrrpd urg lgog I (owlrogunlwcg ro O pe I rorro I pe 0) npodtrowdg gia povddo oro anpnAiprlUa ug npog 1.

Mti04pc t, llloctpovxil I. Etog

. Agcipeorl AuadtKrirvAprOptirvB 0 - 0 = 0o 0 - 1= 1 Ue 6overx6 !o 1 - 0 = 1o 1 - 1 = 0

. Ernv qgaipeon 0-16aver(6psorr pia duddo Vrovq yiver n qgqipeon, 6nurEqro 6eKqdrr6 o0ornpo6cver(6paore pid derdda yravq yiver agqipeon (operurrtog x eivcr prrp6repoEon6 rov qgarper6o y)

r Enopivrr.rg, o HA iler 6uoero6doug rqr dOo e[66ouE

Mti04pc 1, filactpovxil I. Eroq

x v K A

o 0 0 o0 I I t

I 0 0 I

I I o o

4

I

. O TrAnpnS qgqrpirng eivql6vo ouvduoolx6 x0xAtr.lgonou rKTrAei rnv qgoipeon

uero[u duo Bits noipvovrogun6g4 6rr pnopei 4 Ary6repoonudvnK[ Dq0ui6a vo 61erdqverorei pio lrovddo

. To x0xArlpo 61er rperEero6doug xqr dOo e(6doug.Or rperg eioodor x, y Kdr zo4rpoAi(ouv ro perult6o, Tovogarperio Kdr rorponyouurvo Kpcro0pevoovriororlq. Or 6(o6or A xqtK orUpoAi(ouv rn drqgopdKqr ro xporo0pevo ef6doucwicrrorlo.

K- ( *@y lz+x ' yA :x@y@z

- 1 1 0 I t O O

Md04pc 1, H),orrpovtrl f Etoq

x v z K A

0 0 0 0 0

0 0 1 1 1

0 1 0 1 1

0 1 1 1 0

1 0 0 0 1

1 0 1 0 0

1 1 0 0 0

1 1 1 1 1

lAuadrx6g A0poorftE - Agorpirng

Kr Ar A2

Mri04pcr I, Hlenrpovrril I- Etoq

5

Aersdrr6g A0pororng BCD. @ewporige rnv np6deon 2 dexadrrdrv Unoluv oe BCD uq(f ue nr0cv6 rparoriuevo cn6

npgrivorfievn Dagui6q. To doporqc ruv Vhqlrrry 6ev pop-eiva [cnepvdir ro 19 (pc(l pe rori9or6 xporo0pevo e[66ou)

r O 6r.ndlx6c cOpororne oxnuari(er ro ri€poloua duodtxd rol nqpdyer 6va qnor6Aeoud tTourqrlvercr on6 0 p6Xpr 19. Awbi or duadrroi cpr9poi o.rppoAi(owol ge K, Zs,Z4,Zz,Zr.Ta &rdrxd a0ooioucra.6nuc euoovi(owcr orrc e[66ouc ev6c dr.ndrxor.r qOoororh 4 bitsgcivowcr or4V 1n drnAr1 Hnapdaraof,rouE oe iOdrra BeD otiiverar or4 2n'orffr4.O agpororhe BCD (nx ro TTL chip 82583) mooelvc Kdrdrn(etxtorefue rpiq chips. Atrc chipMSl'6uadt{oug a9ioror6g xor 6vri chip SS[-na,r nepr6ler nC rpete miAe€'yrc rn'Aoyrri616p0rcnVdlvanpe vo ppo0pe rov rw6vo percrpon{g r4g lnc ornAne or.n?'t.c 'Orov ro 6tndrx6 dOpoqa elwr <= rou lOOl 6ev lperd(eror percnponrio Orqy ro 6uo6m6d0poopq sivot > tou 10Ol npfmr vq nposr€0€i o 6uodrx6g opr0p6g 0110 : 6ro yro vq

yiver 4 percnpornlXped(Eror 6r6p&pn rouAdxurov 6rov ro 6ndx6 60poppq €ter K=1. Yndptouv dMor 6 ouvduoouoiatT6 1010 udror 1111 nou rohd(owor 6r6p0oon. Aurol 6rouv l-orn 06cn Z. fla vq rou( tertrtoiool,uecn6 roug 6rcilSrxo0g t00O

'ih 10Ol xoOoil(oupe enrrMori 6l eire io 4 eittrc 22 nptnfl i'ri-eiiror l.

'

Oror C=l_nptr_er vo npoo0€ooupe 6 oro 6uq6x6 6poropo xqr vq Abooupe rpo'ro0pwo e(66ou orrlven6Uanl Fc€Ui6o

C-K+ZrZo+2822

O oOpotqrrie BCD (ax ro TTL chip 82583) wopei w Kqrqo(anorrl ue rola chips. Ar.ro chip iiSIdlndrro0g o0poror&E xo 6vq chip'SSl roti'iepi61er nC rper6 mlAeg Vro rh rroyrrh Urdp0ruon

Mti04pc I, tD'enpourxil I'Etog

AOporsrngAr.ndrx6 AOporqro A0poqrc BCD Aexcdrr6g

K l Z r Z 2 Z t C 1 4 2 2 Z l

o 0 0 0 0

0 0 0 0 I

0 0 0 1 0

o 0 0 I I

0 0 t 0 0

0 0 r 0 I

0 0 1 I 0

0 0 I I I

0 1 0 0 0

0 r 0 0 I

0 0 0 0 0 0

0 0 0 0 l I

0 0 0 1 0 ?

0 0 0 t 1 3

0 0 1 0 0 4

0 0 1 0 1 5

0 0 1 I 0 6

0 0 1 1 | 7

0 1 0 0 0 8

0 r 0 0 1 9

0 t 0 1 0

0 1 0 I I

0 l I 0 0

0 1 I 0 I

0 1 I I 0

0 1 1 1 1

r 0 0 0 0

1 0 0 0 l

1 0 0 1 0

l 0 0 0 0 1 0

t 0 0 0 t 1 1

t 0 0 1 0 t 2

t 0 0 1 1 1 3

1 0 1 0 0 1 4

1 0 1 0 1 1 5

1 0 1 1 0 1 6

1 0 1 1 t t 7

r t 0 0 0 1 8

t o o I 1 I I O O I

Mdftpc I, Fllempov*l I' Erog

6

AOpororie Ilpoo€er6og 1 flpoo€er6og 2

Md04pc 1, HLecrpovrril I- Etog

EuVrpmng Mey60ougEvcE trnoAoyror4g xdver np6o€eoq, oiyrprorl xcr geragopd6edop6vrlv. EvcE o;yrprr{E Uey60ouE eivor 6vq ouvduqorrn6r0xAurpc ?Tou ouvKpiver 60o cpr0pouE A xqr B rqr ppiorer roolerrrd roug peV60n. To anor6Aeopc rng ouvxptonE divercr peTpag duadrx6E peropA4r6E nou deixvouv qv A=8, A<B xar A>BEorur A=AsAzA,Ao rct B=BsBzBrBo.o Or 6uo oprOpoi eivor ioor cv Fl qAnOigo Eivcr A>B N FzoAn0igo Eivor A<B cv F3 oAnOiE

4 - x3xzxrxo

Fz : ArE, + xrArB', * xrxrArBr+ x3x2xrfiBo

Fz = 48, + \A'282 + \xzArBr + x3x2xr[Bo

Mti04pc I, FD,ertpovxil I'Etoq

xr=48,+48,

7

l t , F

KUJOtKegr O r0drrog BCD (Binory Coded

Decimol) eivcr grc dpeoncwroror;1id rou dexadrxoOVngiou ue ro 6ucdrx6 rourood0vopo. To prip4 arovrdrdrro aw6 eivor 8,4,?,1c O 6erodrr6g cp€g6g 516 oro

6rlodrx6 ouornpa eivor o10000001@. Erov xtildrxa BCDeivor o 010100010110!

a Ordv divowe qprego0g rrg6e6optvq orov unoAoyorti, cwolroplcrawo elre cno 6uadrr6or.rornpq elre oro dercdrx6,udorrr rdnorou 6uqdrxo0 x0drro.

. Evag dercdrr6g xtfudrrog nouXpnorpolTor n9nxe or raAro0grmoAovror6g eivor o <exc6s-3>. Aev 6xer Ddpn rqrnporirnrer c?r6 rov BCD penp6deon 3. EivcrowooutmAnpuuarrr6e.

O xtildrxoq, ?4?l 6Xet Ddpn2,4,2,1xor eivcrduro(rulrr^4pu.r;rorr r6E (rrq rpogro 9)a O 6erodrx6g 238 ncprordverot

orov rtfudrxa242lvtg001000111110 . To oryrAnpu4ldrou u,g rTpog 9, o76ttcprcrdvercr orov i6ro xtirdtraus U011100O0O1(cwrrcrdorqon 1Ue 0)

O rtildrroq,S4-2-t 6Xet Fdpn8,4,-?,-t xor eivcrduro(rupnA4pugcrrx6gO rtildrrag Biguinory 6Xer Ddpn5,0,4,3,2,1,0 rct eivcr x0drrcg7 bits fiou rrTrrp6ret ovixveuonogcApdrurv. Kd0e deradtx6Vngio xudrxonoreirar pe 5pndevrrd xat 2 dooougronoOernp6vouq oe 06oetg uecwioror;1c Ddpn

Md04pc I, Hlenpovrxil I- Etoq

AeKodrKoi r<tfudrKrg

Md0rlpa 1, Hl,extpovrri I''Etoq

I

AuodrKoi Kti,ldu<eq

. H dr.ndrr{ zfipogoplo lnopei vc perodoOel pe iltdppar4Aernxoruwrcrd p6oc (oripUcra, HM r0pcro). lG0e efrrrreprx6g06pupog aou ero6p;rrdr or 6vc r6roro U6o UeraFdMet rrg rrp6grdnorurv bits an6 0 oc 1 rot on6 1oe 0. l-to r4v avl;veuolrtrorurv ogcApdrulv propel vd Xpnotponorn0el 6rrog xrirdrrcgqvlXveuons ogaAptnw (error detection code), 6nug.r Xp4orponofnot bit rorrglog, ro onolo clwt tvu emnAtov bit fiou pd(or4e oro

Unuluctc tro Oare vq rdvcr ro ourpfir6 ilfi0og ruv doalv dprro rl neprrr6. Frqnqpdlcrvyq se tcprrrrl roorrglc. ro prlvqr 10ll eq rodrronor40ef aro 10110

: O rdldrrqg 6r!y o orclog tyel ro nAeovtrr4;.n 6rr or cpr€pl percpd/vlowor rcrdtvq p6uo bit rd0e gopd nou oufdvow xord tw. Or dexcdrxol qprOUof qrov nildrxq6nqy elwr ncrd oerpd:

o@o,q[,mlr,0010.0110,011 1,0101,0100,110o,110r,1 11r.I 110, 1010,1o11, l(x)t,r0oo

bl-ewflrpra dpnagroonpidg 3 bits

- t - a

\-\.''-l \ tz'

1)J-EAevrrig dprrogtooiluidg 4 bits

Md04pa I, FDecrqovrri I- €,roe

AAgcprepnn Koi Kdrdr req

IIoMig epoppoveg rurv HN dnatro0v rn Xpnon 6e6optvuv noucror€Ao0wcr Kqr ort6 ypdppqrq. Eva o0voAo cAgcpr0p4rrx0vXqpqKrnpurv eivcr 6vc otivoAo orotxefurv ro oroio reprAolrpdver ro 10dexqdrxd Vngiq, ra vpdgporq rou oApaptrou Kqt'erdrro0g XdpaKrrtpe€.Aur6 ro o0voAo nepr6ler neptoo6repd ar6 64 ororyeia. ApaXpefq(6pdore duqdrx6 xtfudrxa wv 7 bits.O np6rurog (stondord) 6uodrx6g xtildrxaq $o roug aAgopt0pnrrro0gXopoKrtipre eivqr o xtbdrxoq ASCII (Americon Stondord Code forfnformotion fnterchonge). l-ro rcpddetypa ro A (Acnvrx6)fidprordverqr urg 100O0O1. Ernv EMddq XpnopoTroro0pe ro np6runoEAOT -928 eyxexprp6vo on6 rnv fSO 6nov ro A (Aonvrx6)ncprordveror urE 101(8) Kqt ro A (eM4vrr6) ug 3011ay

Mti04pc l, Hlattpovrril I'Etog

I

Merqrporn Ku,6rrti,rv

EvoE tJrrdrpontaE x0drro (code converter) eivct6vc runAulpa fiou rdver 6uo oumhpcro oupprpact6,or6pn xor 6rov Xpnotponoro0v drc9operrr6 r0drroMerorponn an6 rov r<tfudrxo BCD orov xtfudrxoexcess-3:

Mti04pc 1, Hlenpovrr4 I. Etog

AnoKurdf Konof nTnE

pogoprdlv_orco orgpoAi(ovrartKeg. trvcgn bits eivarioer ewg 2nela TngnAnpogopiqE.

E"o$ onoxuldrxoror4rdg eivcr 6voowouqoTrKo KUKArrruq ltouperorp6ner r16r.nd-r4 nA4pogopic nvpaUg.iry ero6dou. oe gy9 2^povqorKeg Ypoppeg e<ooou.Evag onoruQrxoggr4rng o116 n - or- m'lpqFu6g (m.Zn) 6;er rovqx6Aoueo nivqxq oAngerqq.

DoDrD2D3D4D5D6

MriQpcr 1, Hie*rpovrr4 I'Etoq

x v z Do Dr D2 D3 D1 D5 D6 q'

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 1 0 0 0 0

o o 0 0 1 0 0 0

o 0 0 0 0 1 0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 1

10

BCD - to Seven - SegmentDecoderEvcg cnoxurdrxonorqrfig BCD rdrdrxo oe enrdxol.rpdrro eivcr 6vo ouvduqmr16 r0xAurpd ?rou661ercr 6vo 6ercdrr6 ryngio oe rtildrr<o BCD(I)

Eledrriore ro x0rAurpc rou dtToKrrdrronotnrnXpnorporordrwag rov eAd;lcro apr0p6 nuAd.rvNAND(z). Or 6[r dxpnorgorToinror anvducopoi 9c

ulg anor6Aeopq vd Unv mdpxer 6vder[4.

Md0rlpa 1, Fllecpovrr4 I' 'Etog

enrAoyti rtrrv Koppdrr&v ev6g evdeirr4 nouXpnorponoreircr yrd vc 6ei[er ro 6excdrx6 ry4gio oepro rurorfl onrrrd popgn.Or enrd 6[odor rouono xu.rdr rono r nri (a,b,c d,e,f g) evepyono ro0v rq

Ta op€pnnrd orippoAa aou droA6vorye vto rlcaupaort|ooupe rq dercdutd qrngk gafvowcr oro

11

x Y z w o b c d c t I

0 0 0 o 0 0 0 o 0 0 I

0 0 0 I I 0 0 I I I I

0 0 I o 0 0 I o 0 1 0

0 0 I I o o 0 0 I I 0

0 I o 0 1 o o I I o o0 I o 1 0 1 o o I o oo I I o o 1 0 o 0 o o0 I I I 0 o o I I 1 I

1 o o o o o o o 0 0 0

1 0 0 I 0 0 o 0 I 0 0

I 0 I 0 I I 1 0 0 I 0

I o 1 I I I o o I 1 0

I I 0 0 I o 1 I 1 o 0

I I o I 0 I I o 1 o oI I I o 1 I I 0 0 o oI I I I I 1 I 1 I 1 I

Mti04pc l, Hkztpovtnl I'Erog

Il r t O

,ArtOfiAtKTeg

Anorurdrronor4rfiE an6 2-oe-4ypdppeg pe pfc eioodo enirpeg4g.'OAeg or 6lo6or eivar 16rcv E=1.'OrovE=0 ro x0xArrrgo Aerroupyei u.rgcnoxtudrxonor4r[g pe

D3

Or neptoo6Trpor epnoprroiororuldr ronor4r6g rcrqoreud(owor peNAND. Ot rr.eptoo6rtpolcnorurdrxonor4rtg nou eivor 6ro06orpor oechips neprAappdvouv pic I neproo6repegero66oug'Enoble" vro vd eAtvxoupe rnAerroupyia rou ruxA0porog

M&O4pc 1, Hlettpovuril I'T,toq

A B Do Dl D2 D3

1 X X 1 1 1 1

0 0 0 1 1 1

0 1 1 0 1 1

1 0 1 1 0 1

1 1 1 1 1 0

12

AnonAirreE

O anonhtrr4g eivcr 6vo r0xArlpd Trou d6lerornArlpogopleg an6 Ura anAri VpaUUi Kcr ng peraDrFd(eroe pio an6 rrg 2n ypayytg e€,66ouOr Aerroupyieg rou cnorurdrronornri Kdr rouanonAixr4 Aoppdvowcr on6 ro idro x0rArrrpo yraw6ror 6vog cnoruldrxonor4r{g pe afoodo enirpeg4govopd(erc r otrvti9u g cnorurd r xono r nrig/cnorAt rr ng

M,ihpc 1, llloctpovrril I. Etog

Kul6fKorornr6gKuldrronornrig cn6 orradrr6 oe 6uradtr6

Evcg xrldrxonornrig 6yer2n (it Ary6repeg) VpaUU6Eero66ou Kdr n ypopp6ge(66ou. Or ypopp6g e[6dounopdyouv ro dr,rodrx6rtirdrro flou owrcrorlei angUeroDAnr6E ero66ou

x=D+*Dr*Du*D,

!=Dz*Dr*Du*D. ,z=Dr*Dr*Dr*D,

No oxedraarei

Do Dl D2 D3 D1 D5 D6 D' x v z

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0

o 0 0 0 0 1 0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 t

0 0 0

0 0 1

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0 r l

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13

H Idiq rnqTToAunAe[iqq

sl so F

0 0 lo

0 1 l1

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1 ,l l3

Mri0aprc t, lllectpovuil f Etog

fioAtrnAirrng

fToAwAe(io (rnultiplexing) eivor 4peropipcon ev6g ueydAou aprOpo0nArlpogoprdru p6oc an6 6voprrp6repo cprOpd ypauutilvEvcE noAunA6rr4g entAiyer6tn6rxig nAnporeopieg on6 noMtEvpotrU6E ero66ou Kdr ngrqreu00ver orn uia povqdrrhvpaupi e[66ou. H enrAovi rne piag

F vpapUig ero6dou Yiveral ;16ol rr,uv' VpoUUtirv enrAoytigO noArmA6rr4g i74er 2n vpcUUigero6dou, n VpopUdg enrAovig xar I

sl so F

0 0 lo

0 1 l1

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M,iht "

t, Fll^ecrpovrrfi I. Ezoq

14

TToAunAeIis

. H opxrxri rd6a 6ev iXer aMd6er. AnAd, or r4Aegurv4rpreg cvrrxqrccndOnxcv fir6yewtrpreg rtrpdyu,vr KOv noAgtfuv!

. Eqnu 611 6xouue 30 ouvdpopnr6s ev6e rnAeguvrxo0 x6vrpou. O noAtmA6rrngnou 0c xpnoruonorhoouue np6ner va 6rc96rer rould;lorov 30 ero6douE Kqleno[ivurg 5 vpouU6g enrAoyfE, or oroieg lcpi(ow orov noAunA6rrn 32erooooug.

' Eorur 6rr or4v npdrrn vpqupn enrAoy{q, rnv.5o rorogero0gg pia yewirptqrerpcvuvrrtilv naAutirv ouxv6rnroc lO-GHz (T=lOOps). l-ra 50 ps n yevvnrptodlver 0 Ko! vrc ro en6pevo 50 ps diver 1.... Ern 6e0repn vpouun'entAovnE Ilv 5rDri(ouue yewnrpro ouxv6rnrqiS GHz, or4v 52 2.56H2,.... ornv Ss3l?.5 MHi.lkrd rn drdpxero ruv 50 nptlnlrv ps wopei vo grAdet o or.rvdpounrng t, rardrq 50 en6uevq, o otrydpognrhe ft... o ouvdpounrne In 0q fqvqurAnoer uer6 qn616 nepr66ouE rng npdrrnq veWnrprqq,dnrcdn Ueid dn6 1550ns=1,6psO ouvdpognriE h ornv npavgcrrr6r4rc Urlger vr-o 5O ns xd€e 1,6 ms,npoxqr6vou vq Ur-Aioouv Kqr or ur6Aornor 31ouvdpopnr6g,6gurg efvqlxorovo4r6e an6 rnv dMn drpn rne ypqpuic arerdt n ergdrvnon or6Fn xcr ev6gypdpgoroE drqpxei neptoo6tepo an6 10@@ us!

Mri04pcr 1, FD,ettpovtrl I- Etoq

YAonoinon ouvduqonKnq AoyrKnq peTro^unAexregI

A -->0,2,4,7)

u Edv or 60o 6pol oe piq srfiAn 66v eivur u6oo oe x0rAo r6reDd(ouue 0 ornv owiqrorxn eioodo rou noAurA6rrn

o Edv,or 60o 6gor-eivcr U6oq oe.r0xAo r6re pd(oupe I or4vqvTloTorxn aoooo Tou flo^uft €KTnEdv o xdru 6pog 6yer onperuOel oAM 61r o erdral, r6reDd(ouUe x ornv owiororl4 eioodo rou noArmA6xrnEdv o nri'ur,r 6poc 6xer onleruOcl qAr\d 6xr o xd.ru, r6reFri(ouUe x' ornv owlqrorxn eioodo rou noAr.mA6rrn

Mti04pc l, Fne<tpovrril f Etog

15

9t

tooole rrXro.olr,rp u ersr 'trol[dp,rno t nrrroprp f,rft9gnhtffi,Sl?lgillgH!; 'rfu 5norlolgnno Snirt (WO.U 5tu Sgrlorr.irfiodAodr) ortnolriordnrpv o-Lidr orou,pi

3rl Ay 'noggor3 Ar.nrlryqDr3n u ArnI ArDdg Ad|I Adry9 Dnorodgp or t3^f9 ]ogo]? 3gP)noggla SgrlrlodA lt.ro ;oronodrla oa;adoul 5alouo 5rr 9lu olrl aggu U'WOU

Ur [rno eb Srngrhrxlrgoro Sralgy lgxrrrdo0org 79 nnoX@-un tou noggJa 5?rlrlDdg nnoXtlpur u9 r0a;odtro grny 'o!d rgpx tr s+!q g ^t|rr 5r3;?v ZE IUD tDr,3Y3rorD

nol ogpaol orrl or;s (+lq ggZ ^rnr WOd 5m rpv rore6pdArdal) gxzt WOd DIW'dO 5av4tr tu tDx tuxu l,trUtouoxtgmvor,D

M^? gw rDrr3v3rouy '5nog9Jc tu rox Snoggote u taXg uxuz WOd DIW

(WOd) o^gw 5UomnApay uill4nyy

5or.g,1 tptmodualg't rrll4?n

5*e'oraa;oAs^#'i'tf ib'-#'diiX"'98]r1ilgif-#i.3lri?$"fi rt'.illill ^,nr )gnoDng^no 3gp,)'no99l3 )?nnDd tu rDv no99or3 )?nnDo u l3x9 wou H<orlngd

'WOU 5Ur <grlotrprlrlpdAodurrl n4orord€Dx D^ aqodonrl UO A.pvnrr Amr A,nggol3 Arnr rox l,uUroloxrgmvouD

nor ̂m9913 A.ru OlDr3n )r3o99^no ro'orr{r orQ! oro Dg?n do )3Y0x5rr rpv frlilouoxrg.n)rollD Aol rDv rrapqfduyrd3r no.u UJorprg Drrl rD !3 WOU H r

'Xg 5ay4u tox [utrtouovtgorxouDnong arl lrgl,ronoyn on lrdourl urlmyx4x gvuoDnglno aroul,tgotoug r

(WOd) o^gw SUornaApay Urffnyy

ouvduoon KoO KuKA0porog

4 n0Aeg OR (rurv E erooduv on6rrE onoieg Xpnoruon-oro0pe rrg 2 i

Mti04ptc 1, Hloctpovtr4 I- Erog

ur ROM A2 A, Ao B5 84 B3 g2 B, Bo dercdr169

0 0 o o 0 0 0 0 0 o0 0 I 0 0 0 0 0 1 I

0 1 0 o 0 0 1 0 0 4

0 I I 0 0 I 0 0 1 9

I 0 0 0 I 0 0 0 0 t6

1 o I o 1 I 0 0 I 25

I 1 o t 0 0 1 0 0 36

I I I I I 0 0 0 I 49

A1 Ar ,\ Fr F2 Fr F

o 0 o 0 o 0 o

0 o o o o o

o I o o o o t

0 I 0 o ! o

I o o o o

I o 0 I o

I t o o o

I I t 0 0

oKnonAiv era r n ouvdpr no4 F= xy'w' *xzw +xy' z'w*xYz'*y' z' w * xz' w'A) Atirore r4v onAo0arepn popgn r4g ouvdprnong oe dgporopc yrvop6vrlv.B) Ern o.rv61erc uAonotnme rnv pr roug ax6Aou0oug rp6noug:

o) Me n0Aeg NAND p6vob) Me n0Aeg NOR p6voc) Me 6vav noAr"mA6xr4 8-oe-1 rcr dv Xpetdorein0An NOTd) lJte r4v eAdlrorn dwori ROl,l

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F = xy'rxzlr) + yzt w'+x' zt w

r = (* + z'\1t' + z' +w\x + y + r)/;l+ y' + z + w')

M&0r1pc 1, Hl.ottpovuril I''Etoq

ail

xy 00 01 1 1 1 0

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17

a

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,

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F =(** t'Yry'+z'+w\x+ y +*)/g'+y'+z +I

f

I

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rofr 8xlIz IIIUX1311r516T7

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18

A roAot€rard Kurddlpsrs

HAexrpovrnfll- 'Td[nAtr<ropoq E. Kopoyrdwn

Ewd uaan Ka Kct AroAor€rsrdKutcAtbpsrs

O 4gra€porori€, o nArtpng o0pororng, o ngtdgdrp6r4g, o nArlp4g ogorp6rqg, oducdt x6g c0pormfig-cgorptr4g, o dnoKurdr xonor 4r[9, o xrl6rxonor4r{9, onoAtmA6rrng, o cnonA6rr4g, 4 ROii, ... flrcv 6Aa xurA0gcrc o.lvdr.norrxd(combinotioncl): H 6(,o6oe I or 6[o6or e(,aprdrwor cnorAercnrrd xcr p6voqn6 rov anvducop6 rurv nptilv rulv ero66urv rng i6rog onyuig.Tl ovogd(oqle oroAor€ia? Tr ovopd(a4re orrypri xot rr ovogi(or+le rpo4Vorilcvn Xpouri firwri?Tr clvur trvripn?

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\II , l * } * .q r l - l , { .

a

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perd crn6 5:1, R=O

perd qn6 5=0, R=l

H r<ardqraot 5=R=0 ttphtet vaaro?G0v€ro eg6ov or 6(o6ot Q rqt

Q eivur q+mAnpqrcrrtg

R-S Ffip-Flop(Aev )pnofponoreiro)

tyBsOrdre ffiQ=l

a s R Q(t+1)o 0 o 0o a D0o I b I

o { 1) cnpoodr6pror4I 0 0 I

I I 0I I d 1

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2

a

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Mri0apc 3, lDecre,oruci f Etos

s R Q(t+1)0 o Q(t)o I oI 0 1

t I )

Q(r-1) Q(r) s R0 0 0 x0 I I 0I 0 0 tI I X o

JK Flip-Flop

Q(r-1) Q(t) J K0 0 0 X0 1 1 X1 0 X 1I 1 X 0

'Orcv orag6po;lcr or4vzponw0pevn rcrdorqot 0qvpdpu Q xcr 6xr Q(t-l)

Q(IFQ'J K *Q J K+QJ' K+QJ K

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To nprino 4Aerrpovrr6 flip-flop cvcroArlg0nKr ro 1919 qn6 roug WilliomEccles xqr F. W. Jordon. Ovoudornre r6re Ecclcs-Jordon trigger circuifxqr qroreloirwcv qrd 6rrc evepyd croryelc. To 6rrcuc flip-flop ro nripe on6rov fio nou napdyowcv or lyeio ordedeu6vo us rnv 6[o6o ev6g cn6 roug6r.ro ou(ewU6voug euo;1w66, rcrd 14 drdprerc r4g drodrrcoiag o<avdafuopo0oro r0xArqr.

Mri04pc 3, Fllectpovwil I' Etog

4

Flip-Flop

Mcifupc 3, Hl,octpovtr4 I- Etog

Q(r-1) T Q(t)0 0 00 I I0 0 t0 I 0

lowrd &6nq,+rQ(r-1) Q(r) T

0 0 0

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Mti04pc 3, tll.ecpovrril I' Eroq

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5

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(r)

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A B x A B vx=O x=1 x=O l= l

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O - / 1 { 01 l o 0 0 I o I 0

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q" i6o1o jgll-lg

Mti04pc 3, Hi,attpovtr4 I'Etog

iEt r otroe r C-K orqor-doe uv

@A (t)=4'11- 1)B(t-1)x+A(t- 1)B'(f - 1)x+A(t- 1)B(t- l)x

A(t)=A'Bx+AB'x+ABx

B(t)=A't'1+4'$21

Y=A'B>&AB'X'+ABX'

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Eio6oc

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(r)

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6

EXediqon prJ-K ffip-flops

A (t)= A'Bx+A B'x+A Bx= A'(Bx

B(t)= A'B'x+A' Bx= B'(A'xFB(A'x)

y= A' Bx' + AB'x'+A BX'=A' Bx'+Ax'=/(A'B+A)=x'(A+B)

MdQpc 3, lllocrpovrxl f Etos

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(?)

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A B I A B '1,

0 0 0 0 0 0

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I I I 1 0 0

7

D ffip-flopsAwro lo [rdvpqrn

l(armdatqry rne UqdvaaelO. lt qtef,rccef

TordnrrqntrrDflipflope

Biuq 1. 4116 14 XqpoKrnprorrri etioruon rou D flip-flop (drogdvero 6), noparnpril 6rr n6to6og elvcr ndwo 6,rr eivqr ro D!Btiuo 2. Anuroupnl rov nivoxcKancordoewv (drcrgdven 11)Biua 3. EEcvdw rrg elroriroergxcrqqrdoeurv rcr e[66ou

A(f)=A'81+AB'x+ABx==A'Bx+AB'x+ABx+ABx==$1+lp1(l+$)

B(t)=A'B'x+ A'Bx=A'x

y=x'(A+B)

Bripd 4. AnAonort! rrg elroloerg xcroordorurv Kdt rnv 6[odo Ue xdprn Kormugh i UedAveDpq Br,ole, cdrcaoprirwqg yrq r4v reArx{ cnAonor4lr6vn HoppliBiUo 5.YAonortil ro r0rAugc

Md04g.c 3, Fllecrpov*l I- Erog

I| - o - - r - - . - - - - - ai...Kqf Tf Kgv$ To KuK^urpa quTo;

'Orqv n eioodog eivor 0, xor or dOo fcpnrlpes el6dou eivor oDncnoi (t-1), dev 0q

cvdrpw ro16. Av elvqr o 6vcg on6 roug 6ri'o i rqr or 6rio, cvcgrtvor (t-1), 9q opiioowpe rov en6gevo noAg6 poloyro0 (t).'Orcv n eloodog yiver 1 rqr efvqr rcr or 6{pfcpnr{peg opncnol (t-1), r6re Ue rov en6pevo nctr6 poloyro0 (t) eq cvdpw xcr ordrlo, pe rov en6pevo (t+1) o A 0a ncpa;refver cvoplr6vog, o B 0a oprioet, ur roven6pevo (t+2) a rcrdoroon go rcpclreiver i6ro erl c6prcro (t+n), u6xpt n eloodog voVlver 1. H 6to6og rou xuxfii{rcrog eivor 1 p6vo 6rov n cn6 ororodinore dMny+darao4 exr6g rng 00, ro x0xArr4ra percpoiver or4v rcrdorcon 0O.

Mdftpc 3, Hl,ocpovrril I' Etoq

eioo6og

8

tI ...Kqr KdrtofgE oKiVflE...

4n Aornon: Av 61rl €vo J-K flip-flop rar 4 eioodo€ J eivor ndwo o4rnA4prlgorrx{rng K, rr npox0nrer?ilOE yivercr vd percrp6rrul vpttvopo ro x0rAtuud rng drorpdverog 15 oe roodrryopoxOxtuuuq xpnoruorortirwcg J-K f lip-f lops?5n Aornon: M 6o0ei n aroAou0ic e[66wv vrq 10 ncAp0g poAoyro0, ov 4 aplrxtixordorco4 efvor 10 ror 4 efoodog eivcr x=0 vrc 4 naApo0g poAoyro0, x=l$q rougen6pevoug 4 noApo0g xor x=0 vrq roug reAewoloug 2 noApo0g poAoyrou. To flip-flopsm.rpodoroirwor ;rc qovnrr xo0c roApo06 poAoyro0.6a Aqrnon: Eexrvrirwog an6 r4v xordordon 00 oro d:dvpagpa rcroordoeu,v rncdrcrpdverog 10, roOopfcne rrE peropdoerg ru,rv rorcordoeu.rv Kdr rnv qroAouefq ef66tlvnou 0o nopqlOei drcv grc aroAou0lo ero6duv rn6 poppfig 01011011101110 egopgooreicr4v elo6o.7 Aonnqn: Bpeire rnv qroAou0io e(66tuv nou d4groupyeiror qn6 ro x0rArr4ro nou 6yerrov nivqrq xctoordoeurv flou nopouord(erdr orn drcAdvero 11, pe oroAou0lq ero66u,rv01110010011 xor opxi(owog cn6 r4v xcrdorcoq 11.8n Aqrnsn: Eorrl 6vq D flip-flop qro onoio n eioodoe D eivar n 66o6oe prog miAngXOR 600 ero66rlv. Or 6uo eloodor rng XOR eivcl ro T ncr ro Q 6nou ro Q eivor 4arodoE rou D flip-flop. Anodeifre 6rr ow6 ro rOrAurgo roodwqreiue 6vo T flip-flop.

Mdfupc 3, Flleztpovuri f Erog

I

Aor<norl (E0yxpovog Auadrr6giAeronrfic)

Mti04pc 3, FUecrpovrxi t- Etog

l.fo oxedraqrel Fsrpnrig a,ou 6ror rcO va perpder G1-2-3+'l-2-3... Fe r<dOe rdltdpoloyro0. Oror rcl n arcAor€lo u6rpnor1g vc onrorpdgero. H tfodog 0a efrrcr 1

Ir6rp4: O 6erodrr6g aprep6C 3,oro 6r.radrr6 o,rarnpa vpdgerot 11. Eroptrug,

Trp.far.(r-1)

:'ITe.K6T.(r)

E€oUoc

A B x A B Y TA TB

0 0 0 0 1 0 0 1

0 0 1 1 1 0 1 1

0 1 0 1 0 0 1 1

0 I I 0 0 1 0 1

1 0 0 1 1 0 0 1

I 0 I 0 1 0 1 1

I 1 0 0 0 1 1 1

1 I 1 1 0 0 0 1

. E(rod.roerg 6r6yepo4g ero6duv flip-flops

TFZ(1,2,5,6f A'B'x+A'Bx'+ABl+ABt'=B'x+Bx'=BOxTo=1 Y=A'Bx+ABx'=B(A@x)

Ir{tiQpc 3, fDecrpovxil f Etoq

10

' ! - t ^ a' zt Yxpova Kqt Aot YxpovqAroAou0rsrt Vngrsrd Kur<AtfuHqrq

Or gerp4r6g rou undp;ow ocv chips MSf ovirow oe 60o rcornyopleg:o Eroug pcrpnrtg ptmiC (ripple counters), or oxpig ruv el6durv rurv flip-flops ;qo4orper.row

rlg nnvlg rnno66rnong drtrturv flip-flops. AnAa6n or eioodor CP 6irrlv rulv flip-flops (exr6grou nptilrou) 6ev rnrpo6orotrwar o16 roug ncA$oug rou poAoyro0 qAld 4fi6 rtg orptE ruvrqoroyopgtilv rou Dvolvow on6 dAla flip-flops.

o Eroug o0vxeorcts perpnrG3 (synhronons counters) dAeE or eioodor rcn CP dArlv rtlv flip-flop rpogo6oro0wor cn6 roug lbroug nolgo0g poAoyro0. H qlravi rordoroo4g xd€eolyrergrptvou flip-flop e[qprfror on6 r4v nopo0oo rqrdorqon rurv 6Muv f lip-flop.

Evqg 6exadrr6g ;rerp4rtig rcfpver grc oroAou0lq 10 rqrqcrdotu,v Kdr tavcwpl(eroro 0 perd ro 9. Evcg r6roto6 perpnrri€ npttet vc 6yer rourrvfultorov 4 flip-flopscrgo0 r6oc bits perd(owqr vq rnv cvofiopdorqot ruv 10 dexqdrrrilv rynoJuv. HoroAou€lq rury xcrqordoerrrv ev66 6eradrxo0 perpnrrl xa0opl(ero cn6 ro duadrr6x0drxo fiou xpnoponoro0pe yrq rnv avanogdaraon ruv Vngluv rou 6erodtxo0orriucrog. Edv xp4oponoro0ge rov BCD n arolouolc eivct 6porc pe erelv4 rulv6uq6rnirv perp4rdlv, p6vo nou uerd rnv xandoroon 1001nder arnv 0OO0.H oxediaon ev6g gerp4rrt prnnE rou dev qxoAouOei rn duqdrrrl oerpd elvct duoroA46ouAerd. Or rumrtg u60o6or loyrroO o(edrqopo0 pnopo0v vo xpnoptpw p6vo ooyevrx6g odnv6g. l-ro rrcvonor4txdreArr6 aror6Aeqrc xperd(eror egeuperrx6rnrcxcr gowcoic.

Md04pcr 3, Fllo<tpovrr4 I- Etoq

I

lEuvXpovo€ lAerpnrng BCD

@o oxedrdor.rge 6vo r0xAoua nou peropolvet o aot 0000 ornv 0001, or4v 0O10,cr4v 0O11,0100,0101,0110,0111, 1000, 1001,0000... Kdr n oroAor€la;rercpdoeuvenorqr(updveror. H rdge gerdpaon qn6 r4v gio rcndorcoq qrnv dMn 0c ylvercr Ue xd€erra{r6 ev66 xewprxo0 poAoyro0.

BfiJo 1. E;edrd(owe ro drdvpoppq rctcordoeuv

Mrifupc t Fl).ecpovrril t'Etoq

11

Aerqdrr6s f,Aerpnrns BCD (@Bitrq 2. O cprQr6g ruv flip-flops nou 0a xpnoponorttoor.ire elvor 4.

&oud(oqre cLrd: A, B, f, A.Anogcof(oqre $q rov nnto ruv flip-flops rrou 0c xpnoUororflor4re.E6tir, ed xpottouoilorrior4re J-K flip-flops.

Erc ouplpovo oroAor€rord rurAriryaro 6lo rc flip-flops mryodoroirwor(rpogodorouwor ri o<cv6cAf(owor) Ue rov 16lo noAU6 poAovto0.

To x0r<,Arrard uq6 6xer 4 ef66oug no xqrlo efo6o. l-ro vq elpoore ogrpelg, n uovodrri efodogTou KuKAri4rcnog clvcr ro port6r Kdr ro rpogo6orrx6 evtil o116 et66oug rptnet pe xd0e ficfir6

rou poAoyro0 vq eppqvf(owqr ue 14 oerpd or qx6Aoueeg rrp6q: 0000,0001,0010, .....

Md04pc 3, Hlecrpovrx4 I. Eroq

TTivarac Kqr E€pdtserc Kqrdorqong (rllerpnriC BCD)

Bripd 3. Anproupyoqre rov rriVCKq KATCOTAO8IIIVBrirra 4. Kcrocrprirvoqre n€ e(fOtOefgKqTAOTqOnf npooncOrirwog x@e eflorc4 ncpo0orgxordorco4g va rn g6poqre or4 popgri:

Q(t)=Q (t- 1 )s+Q(t- 1 )K'rou elvcr n xdpoKrrtprorrr{ e|forlot vrd ro J-K flip-flop

B l-'+BA+B'l-A= B'(f AFB(; A)

/

l-(t)=f (1,2,5,6)=A'l-'A+l-A'= l-'(A'AFf (A)

,8)=A=tr't1tr11Y Trg rcrcordoag fiou 6ev 9c ot4lpowrre Oeupliooue ug odrdrDope€xmaordoerc

Mri04pc 3, Filerpovtxil I'Etoq

l(ordqrcotr-1

Kcrdoraont

A B r A A B r A

0 0 0 0 0 0 0 1

0 0 0 1 0 0 1 0

0 0 1 0 0 0 1 1

0 0 1 1 0 1 0 0

0 1 0 0 0 1 0 1

0 1 0 1 0 1 1 0

0 1 1 0 0 1 1 1

0 1 1 'l 1 0 0 0

1 0 0 0 1 0 0 1

1 0 0 1 0 0 0 0

12

Merpnrng BCDAnAonolnot rou A(t)

O ouyxpovog Uerpnrng BCDJe=Bl-A, K,r={, Js=lq=f[, Jr=A'A, G=A, J6=(o=!Bipa 5: Eledrd(or4re ro x0rAr4ro

13

No oxedrqorei 6voE perpnrnq BCDEvoE d/uAog rp6noE vo 6ouA6qroupe efvcr vo or.4rzrA4p0oor4re rov rponvo0pevo nivoxqxcrdorcoqE ue ordAeE nou cvc96powdr on€ ero6douE rrlv flip-flop. Tnv nA4porgopio yrorrg ero66oug ru,v Flip-Flop pnopoOpe vd rnv ndpouge cn6 rouE nivareE 616yepo4E rulvflip-flop, eg6oov yvupi(ou1re r4v nopo0oo r<or npo4yo0pevn xardoroon xdOe Flip-flop.O ox6Aor€o6 nivoxog ezrpeporlvst rrtv zpo4yo0pevn o<ediaon (AnUloupyorye 8 Xapre1Karmugh yc cnlonofqo4 rov ouvoprfloewv ero66rrrv ruv flip-flops)

Md.fupc 3, ll),exrpovrril I"'Ero_c

Kcrdoroont-1

nago,toaKordoroon

t Eioodor rurv f lip-f lops

A B r A A B f A JA KA JB KB Jr Kr JA KA

0 0 0 0 0 0 0 1 0 X 0 X 0 X 1 X

0 0 0 1 0 0 1 0 0 x 0 X 1 X X 1

0 0 1 0 0 0 1 1 0 X 0 X X 0 1 X

0 0 1 1 0 1 0 0 0 X 1 X X 1 X 1

0 1 0 0 0 1 0 1 0 X X 0 0 X 1 x0 1 0 1 0 1 1 0 0 X X 0 1 x X 1

0 1 1 0 0 1 1 1 0 X X 0 X 0 1 X

0 1 1 1 1 0 0 0 1 X X 1 X 1 X 1

1 0 0 0 1 0 0 1 X 0 0 X 0 X 1 X

1 0 0 1 0 0 0 0 X 1 0 x 0 X X 1

Q(t-1) Q(r) J K

0 0 0 X0 1 1 X1 0 X 1

1 1 X 0

Nq oxedrqoreiuerpnrng BCD

evqq ouYxpovoque Tflip-flopsKcrdorco4

r-1

napotoaKardoroon

tEioodor rrlv

f lip-f lops

A B r A A B r A To T" T. T^0 0 0 0 0 0 0 1 0 0 0 1

0 0 0 1 0 0 I 0 0 0 1 1

0 0 1 0 0 0 I 1 0 0 0 1

0 0 1 1 0 1 0 0 0 1 1 1

0 1 0 0 0 1 0 1 0 0 0 1

0 1 0 1 0 1 1 0 0 0 1 'l

0 1 1 0 0 1 1 1 0 0 0 1

0 1 1 1 1 0 0 0 1 1 1 1

1 0 0 0 1 0 0 1 0 0 0 1

1 0 0 1 0 0 0 0 1 0 0 1

Mcifupa, 3, Hi,exrpovtri I-'Erog

14

tlAerpnrhg Prntg BCD

An6 ro ddypcglrc ;1oouqrc0napor4po0pe 6rr. To Qo owrorptgeror oe r@eroAp6 poAoyro0 (elvcr opv4rrxdorpomrpo66rnro). To Qlonrorp6geror xd0e gopdltou ro Qsntgrer anr6 ro 1 oro 0 pern ora€ixn 6rr Qr=Q.'Orcv Qr=t,ro Qr g6ver p46evrqr6vo.. To Qz owrorptgeror xdOe gopdnou ro Ql rder qzd ro l oro O.. To Qs nopop6ver pndevrqrtro 6otOpo ro Qz /i ro Ql elvor 0.Awrorp6gerqt 6ror QeQr=l Kdr roQe n6grer an6 ro l oro 0.

Mndevl(erar pe rnv erdpevnrop6poro perdDoott rou Qs.

'Oror ro CP n69rer qr6 1oe 0, to flip-flopyfverot 1or J=1, Undevl(erat qv K=1,owrcrp6gercr ov J=K=l ror ;r6ver ouerdDtuFoav J=K=O

Mri04pc 3, Hlectpovm4 | Etoq

15

tlAerpnrtg Prnng BCD

perp4rfg (perp4rfig Ulcg derddcg)

ao Qr

ilerp4rfig dOo 6erd6uv (uerpder qn6 ro 0 6o9 ro 99)

Md04pc 3, Hl*rpovrxil I'Erog

15o r.spddefvpoMtq ypqryii 6e6op6ruv 66xerqr oerprcxd 6e6oU6va oe poppri Vnplulv (bifs), crppovrou6va

ue 6vq pofdT CP.l(maoreudore ro drdypoppo xqrcordoeurv rou xur<Arirycrog fiouovclvtlpl(er rrg crolor€leg ero66ou 1001xqr 101. Ee nepinrwol rou ro x0xArluqcvqruwploer plc cn6 ng nponvo0Feveg crolor€lcg rptner va 6lver 1oe pro vpqrtiel66ou. @erlpelore 6rr ro x0xlrqra fexrvder cn6 pfc dpxtKfi rcrdoraol A rcr 6rr ovquxver€el ororcUtinore an6 rrg 6r}o oroAor€leg enov6plercl oe qurt. Ylonorfcre ror0rArqrq xpnopononilwcg 6vo T flip-flop, 1J-K flip-flop, 6vqv cnorudrnonornrt rarmiAeg OR.

A0sn: l(croor6oeq: A = To r0rArrlrq 6ev 6xer drqDdoer xqv6vq bitB = To r0rAulro 6xer draFdoer 6vo 1l- : To r0rArr4n 6xer draFdoer rnv cxolou€lc 10A = To x0xr\ouq 6xer droDdos rnv qrolou0lo 100

rlt

M,i0rtpc 3, tllottpovxil I'Etoq

16

15o nqpAderypcA = 0 OB = 0 1l - = 1 0A = 1 1

MtiQpc 3, Hlo<tqouri f Erog

15o rqpAderypc

Mti04pc 3, fDacrpovrril I. Etoq

17

15. YAonor{ore ro qxoAor€rqx6 r0rArulro rou reptvpdgeror cn6ro 6dypq4rq K(rqordoarv, xpnoponordrwcg tvq D flip-flop,6vq J-K flip-flop, oxorurdrxonornri xar rniAeg NOR.ITpoodroplore ro eidog rou crroKurdrxorror4rfi nou 0qyperccreire. Tr ed oWDel or ro olurnuc Fpe9el oe rcrdqrcolzou 6ev npooEropf(eror cn6 ro drdypqrgc;

17. Eyedrdore 6vo perp4rt pe rnv en6pev4 enorolqrpor6uevn duqdrrri aroAor€lo:O,l,2,3,4,5,6.Xpnoporor/iore J-K flip-flops. Trg qxpnoponol4reg rcrocdoerg,Oeuprloreng @v odrdgopeg rcroordoerg.

18. Eledrdorc 6vq uerpnrrl pn 6uqdrxrig croAouOlog: 0,1,3,5 ,7 ye T f lip-f lops.

19. Exedrdcre 6vo rplprrro 6r.radrr<6 perp4rri pmis.

20. Exedrdqre 6vq rplprnro 6r.rqdrx6 oly;povo uerpnri;re flip-flops runou D.

21. Eyedrdcre 6vo rerpdprnro 6u,adrx6 pcrpnr/ipmig pe owicrpogn oerpd utrpnorg (bimry

Md04pc 3, Hlotrpovtxl I. Etoq

??.Eva oroAou0rqr6 r0xAr4ro txer 3 flip-flops A,B,f xor plo eloodo x.ITeprypdgerqron6 rrg or6Aor€eg aroprfioerg ero66ou nuv flip-flopsD^= (B l-'+B' l-)x+(B l-+B' l-')x'De=ADr=B(q) Kcraorpd,orr rov nlvqxq rctqordoeulv rou xuxr\ri4rcrog(p) Exedrdarc 2 drcygdupora rcroordoeury: 'Evd yro r0 ror 6vc uq x=1.

23. O n,ipnS dpororie rou ot(tlporog 6yer 6rrc e{ureprx6g ero66oug x Kdt y, n 6e rplrnelood6g rou z 6pyerqr qn6 r4v elodo ev6S flip-flop rOrrou D. H 6fo6og rpcror4r6vouperog6percr oro flip-flop ge rov xdOe fiqAu6 rou poAoyro0. H efrlreprxri 6(o6og 5 6lverro dOporqro rurv x, y l(n z. Bpelre tov nlvcro Kor ro drdvpauuo rcroordoeuv owo0 rouqxolor€rqxo0 xurfuirycrog.

Md04pc 3, Filertrpovrri1 I' Etoq

18