Aim-

A] TO ~ b u d y a n d vekiCy + b ~ t h+ables o f AND, OR, NOT

and EXOR gates.

~ p p a ~ a + u S- T b ~ i h e bi Bbesd boaad, c o n n e c & i h j wibes ,

xcs .

ThCoby -I ) PND 3ake-

It has N i n p w t ~( N ~ L )a d one ou tpw-h . Digi t41 s$w

aye spplieol o,t t h e i n p u t t ezmins l s maaked A and g.

The a u k p ~ ~ tis ob+q;ned ~t t h e ou -Lpu t *earn;naI mo,a-/

signal. The AND o p e m + i o n

i s de-Fin d 4 n A N D gste is I ;$

and o n b if sll t h e i n p u t s w e I - Mqthems-l-icsliy,

Y = A AND 0 FIND C - . - - AND N A . 6 . C . ..-.. r \ l

= ABc ,--N - ( 1 1

T h e vqwi4bles sae binqaY i . ~ .a c h wmaiqbte cqn Qssurnec

one oF the +LOO p o ~ ~ i ua\ues,0 or 1 .ble

Eq9 (1) is knodn ss &he 800)eanqua+ion 0% \o j i cq ( epuafjo

04 AND ja-te.

Foy an AND o p e a d i o n C h e y t e opens (Y= l ) o n l ~w h e

s l l +he inputs sxe pa-esent. i . e st logic I level. ~ c s\ogicsl equation is .I=8 6 and is bead qs

" 'I e p s \ s A AND B I)

I C N o . 7'432.

i

2) OR j s t e -It has inputs I ~ g e )and one o u t p u t Digi-ba

si3wl~42e o p P ~ i e dst +he i n p u t tearninsls A snd The o u t p u t is o p t s i n e d at the o ~ c t p u t tebmInclI

a n d i t i s slso s d 9 i t q l s i j h q / . The OR ope3af jon

if and, o n 9 if o n e oa moae i n p u h s qse I -

Ms~hems+ieaI ly ,

Y = A OR B of? C - - - - - O R N- A + 8 f C . - - - t- bf -(2)

AII +he vwisbIe~ i ,e, inpwt qnd o u t p u t vaaiables sac

gq t e opens [ Y = I ) w k

o r e inputs ske p'b4senk !.aat logic 1 /eve!

o f 4n OR gate . It csn

" y epusls A OR 8 ".

3) N O T 3 ~ 4 ~ -N o r gs+e is qlso known sS an invea-tea-

I+ h q s one- i n p u t (A) ~ n dohe o u t p u t (YI .

T h e srnclll cibcles in t h e symbol OF NOT gc\+e is

khomn QS bubble,

The symbol F o r NOT g s t e csn be (sl oa (b).

Its l o g i c ~ g u a + i o ~is u-w-i++er, a s

Y: NOT f i +

= ,A

1% i s ;read ss " Y e ~ w l s~ 0 - rA " ob " y e~uqls

complement OF A ". The Nm opeasSion is s l s o beqfebed to 9s an

4 i o n . T h e pesence o f a

i

+ Vcc z

-..

4) ExoR g a t e -

(J) It h a s f . u o of - o w e i n p u C S crnd only one ok+pu+.

(2)~helogicel eguahion .Fa7 E A O R g ~ t ecan be w3i4 ten asT-

Q ) T h i s cixcur'+ Finds sppl icsf ian w h e ~ et u o digiks l signs

mwe. +o be compsaesd.

4 NAND G a t e

Symbol

I I -: -F. D 3p-r-fi;.~t y :-;>

.-. ~ . ~ ~ . ~.. .~ . . . ~ ~ ~~ i- -.-~

I Y

I i ON i I I 1 I I

! ! on' 1 I I I

I! 0 I 0. !

; I I I 1 1 0 (2F ,gi I ! I! i

a Aim- Zrnplem~nLf%l lowiy gaIes ~ s i y NORbasic jahes- N ~ N o , 4 EX@

1 ) AND gate -

The NOT-AND opebstioh is Known as Che HAND

o p e n t i o n . r+ h s s N (N inpu+S snd one .output .

Fijuae" show3 AND gccte fo l lou led by s WoT j s + e .

The ou-kpu-b OF AND 3s-te be Y ' csn be wbi%+en

cLS

Y ' A . H9

rdow, ON+PU+ OF t h e NOT j a 1 e Y can b e w a i ~ i e h

T h e logical opem.f ioo e p r e s e n S e d by eq. (11 is kno

as +he N A N D opeiy&;on - The s~andsad symbol oC 6 h e

ih +he f 9 ~ 3 - e . t(exe, t h e

side of t h e N4ND g a t e i nveas ion OT c0rn~1ernenS.s-l-

Y = A . 8 a n d i s sew4 a9

* y NOT I AAND B)

6 Symbol

N O R ga6e -The NOT-OR operat - ioh i s known a 3 Che NOR opea-a+;

It has N ( N ; 7 / 2 ) i r , pu+ tert-oihsls ~ n dohe 0 u 6 p u C. +ebrninq1 .

The o u t p u t 06 O R y ' C q n be wb;L+en a9

Y ' = A + 8

NOW, the o u t p u * OF +he NOT g a t e y cqn be

This i s the l o j i c q ] ey? Foa N O R ga+e 6: is d ss

" J Y Y ~ I S NOT I AOR 6 ) ." T h e bubble oh ot.6puk side O F +he NOR j d e

NOT o p e b q f ion.

- -

31 EXOR usino bask ystes-r

43 E X - NOR ga-be

.

T ru th T a b l ~

LED S T , L ~ - Y <

i R

. . . . . .

'i' . ..~ .----~ ~

A ! (

I !

; 0 I 0 I 3N i ! I 0F FI0 I ! 0

!

I I 0 !I 0 j

I O F F j

! !

I I ! I 0I.-' I

The ExoR 3qte

in the f ; g ~ a e . by using bssic jaCes

is ew &e shown

4) E X N O R g s t e -

I+ h s s o

o n out.pub s j d e s

T h e boolean

inputs and o n e o ~ ( t p h t . The

s k p b e s e n t s NOT. 0peaa.f- ion.

equa-hion O F Ex N O R 34+e i9

b u b b l e

: x.g + 4 . 8 .

The Ex-NOR gate bJ u s i y basic gaOeS is shown in t h e f iqua-P.

NAND QS b n i v e a ~ s / Q O C

a] I.mplet-nen+o.tian o f AS5 "Sin? 5

A i m -T o imp lemen t +he bssic j s C e s , EXOR snd E X N O R usi

uysiversql g s t e s . .

I] NAND QS uaivek-%I 3st'e-] AND sing NAND

T h e I O J J C ~ I e q ~ s + i o r ,OF A N D j s t e is Y = A . B

he o u - k p y t O F Fibs4 N A N D is shoa-&e$ ss is C h e

input O F & h e second NAND 9~754.

The doub le inversion o n RHS j i v e s +he q u i a e d

expwssior , Cob 4ND. -Y z p x - A.,Q

b l ~ o f u9inj NAND

T h e NOT g s t e has 6nly o n e input snd NAND hss

t w o . ~heaeqobe bhe o h e inpuC is shoakal +o , j ive

C] O R using NAND

The tog i cq l eyusfioh OF O R gs+e is Y = A f 8 . .. - ..

T'kihj double inversion 00 R H S-\I= A t 8 r-A . 8 ( B ~ De Margsnfs ~heobem.)

, . a] l r n p i e r n e r ~ t q ~ ~ ~ r ~ANDOF U S ; P ~ NOF

b] I r np le iw~ r ,+q5 !o t \ o f N O T using KOF-

Th;s i s t h e l o j ~ c s I qu-csfion AND 346e.$07

= A+B ( :~ou ble inve~sion)

T h i s is t h e l a ~ i c s l epuq+;an f a y OR J Q ~ Q .

c] N O T Uihg NOR

give t w o i hph t s

470 abe -y = m

B u t A+/? 5 A

I]E x - O R usin3 NAND :

Boolesn Expb-e3sioo OF E X O R : 3 . AOB = X . B + Qg

Tqking double inveasioh -. .

Y = A 8 t A&

T h i s i~ the a-eywia-ed e x p w e ~ ~ i ~ nEX-OR usin3+%&

N A N D g q t e .

L e t X = E.8 2 = A B

.: y = k + Z

Tsking double invea-sion,

- -

- -

31 E%-Nof? using N A N D :

The Boo lean e r p b e s ~ i o n f o ~ EXNOR ga3e is

y = R O B . = A . B i - P B

L e t ~ . 8= A and 4.8 = Z

Tqking double ioveas i o n

y: x+z-x . 2

This th- is t h e aepuiaed e x p % e s s i o n $03 ONOR

using N A ~ D 9 s t e .

@oatear, exp ress ion fo-a E X N O R-

This Is h e q u i s e d ~ x p b e s s i o n Tor Enr\~oR using

P>oceduwe-

Pawt 4 -I. i n s e r t IC it-, bosad so + h s + no+ch is t o u s a d s IefC.

2. IC 7 4 0 8 is i<ser+ed on b w q d boqbd ,

3. Pin n u m b e r 14 OF TC 7 9 0 8 is connec+ed -ko +Vcc i.e. 5v

snd 7 i s

4. Respect ive j a k e i n p u + s sse g iven qnd O L ( ~ ~ M + ob'cqiq

5. TF nutput i s hicgh , L E D glows.

6. Repea+. s k t p p s Q S a-ep~;aed.

7. A F i e x t h i s i n s e b t L C 7992 , c 7 4 o q ~ n d31C 7+86 on<

by o n e qnd vqaiFy the ' csukh tqbles.

Pawt. €3-

I. cohnec+ X C 7 4 0 8 qnd I C 7 4 0 4 O n bbeacl boabd &o Foam &oc

i h p w % N A N D g ~ % e .Conneck IC 7432 d: Z C 7404 to C'aaro

t i do - i n p u t NOR g s b e 3 using rc 1408, IC7~104, zc 1432

m s k e C ' I ~ C U ~ ~ E X O R and Ex-NOR g ~ & t : e .t o f o r m

2. c o n n e e 4 p i n n u m b e r 7 +o j a - o u n d und pin bumber 14

40 +Vet OF Z C ' s ih the c i a c u i t .

3. Supp\y i n p d and t q k e o u t p u + fbom LED.

4. O b s e w v e h e LED s b s b u s s h e s n d vqti +j

1 . ~ o n n e c b NAND qnd N O R gs+es t o Fobm AND, O R ,

Ex-OR snd E x - N ~ A g a t e s using t h e c'ikcui6 diagmm.

1. O b s e b e khe L E O sbs+us and vsaify + h e kbut-h

+sble s,

~ o n c l u ~ i o n-A] W e hsve studied ~ n dv ~ a i F i e d +a-u*h C ~ b l e sOF A N D ,

O R , NOT qhd EXOR gqtes. we hsve impI@men.f-ed NAND , N O R , €%OR 4 EXNOR

using bssic 2s 6e.s.

c] W e have c 3qte.s. EXOR and E X N

using LI