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Transcript of DSD journal
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 [email protected] 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