Date.
Page No.
UNIT&
Quis!4Lhat isomeaut
ya
keeleala unetien wuithet
NAND Qmd NOR atu ae tuinolal gt
otea
pues
baplemect the NOT
NOT Qate
A-A
NAND
=A
x/+y)+X(z'+Z)
|
1tA 1 and AtA'-l ,ublng boolaaua ideutites)
Date.
Paqe No.
frs 4 state the linitatous.
kasuaugl,
beelean
ltconse tisáactial
isjt uanaklt.
blncealey
dabs,
to
hander
it
Lahcablessalakng
baelea
Qutl:5ate the asociatie hsopoty
AND
-
A.8).C = A(8.C
his huepeziti smean that you Langa
the harenthesiu uehen uslag AND Ok
Aus:6 tat the
camatatiue quapasty
beelan Algcba
o
Date.
Page No.
As 60
Cemuetatiue
Bepetty fer AND:
A.B= 6A
9) omntatiine brkerity fer oR!
AtB= Bt A
his feperty mmeams that yo
can
AND o bRspe'atious, the sesuutt usil
QuesT dtato the distibutise jetahesty fot
Bocleau Algcba
1)DAtibitine peßety AND er ORi
A(6t) =(p:8) +A. C)
BueAND
At(6.c) =(A +8). (A4)
RulelAt8 = A.B
his los lndicates that tho comhleneit
heó
diuidual conpleet
Date.
Paqe No.
Rulo.
AB
AtB
his ple indicotes tat the complePt
the
hrctiuidual onpleneil
HIÇA. Bt ist e
statemect"the octht of a got s
AIGul ds true Yor AND gate adi
A
B
1
1
1
1
1
tlera, the ethct is LoW)enly skeu
the iahut ake HIÇH (1)
dus l2. kogic gat! ae the electrouic cineuits
aa'aigal ayatea
aeLod
Date.
Page No.
Ques I3
dns/3.
ighgates asce called as the
niuonsol
gatls hllat ae ito aduaitages?
ALminOdal gate is a gatewhick can loe
'Bosleam fumetiea
inpleuantud
y
ang
ethot mee to LSe
he NAND and NoR gatesauuiuorsll gate.
Theise akilty to inplemedt olay
legical fnstion enolles dinlifed cireki
atsiqusahace and cast fgicteuky asdfult
tolenaice
Qucs 14 deshat is kannaugk Map ?
Cát s4 kaswnagh Map Sefera te a pictonial
amethedthat
a utilised to mnimise
LALanloud Bosleaa exhsestious utheut
Lsag the Bosleam algelsa thuekens
alosg sth the equateu mamiheulations.
onninnae Maious
LexshaoslonA that haue
to4 uanaleles using
Quss Is. dhous that (x4 y 4xy)x+Yyk'yo.
dhus f6.xty' Xy)(x+y)(x'y)
,
A.A=A amd
A. nl=0
Xty' txyt xy'ty
9) (X'y)
Data.
Page No.
Kxly +xx'y
x'ky txxy t y'el
Oyt oyt 0.y fo.yl + o. x'
tlence, L-Hs
Rt8.
Aues7 Snyhlewent DR gate wsing NAND gab
A"AA
A.B
B.B =8
Qus
nplemet AND gate using NoR gak
AND gata
wing NOR yatei
A
A +&
Date.
Paqe No.
A
1
A
So, Aseer i".
dectionb.
fuess thesing theerus
Boolean alqelna dinhiy
AABC A8'c 't
t
AtABCt AB' c't Bc ABc)
A+A8't ABC+ A6c)
A+ABc'
t
At AB+ AB'c
AB1)D
5A/1 +A8) +AB'e
’Al+8'c'y
AC1) = A.
Ques 23. Realize follosing
exhsasaiouu usith the kals o
NAND gate
ds.a) 4=A8tCD»
A TL AB
BD
B
’AB+Cb.
BD
A&CtA
BDtAD+
1
1
AB1)
AB
AB
CD CD
CD CD
15.im13,4.6l,
13, 1,9,
fla,
map
K
AB
AB+
BA
B ABt
A
AB B. ABA6AB
B.AB
A"AB.
A
AAR
AB) A'B+
4= b)
No. Page
Date.
Date.
Page No.
Rues a4 Realixe XOR amd XNoR gatis
eith the
Ö) xOR LsgNAND gatai
A.AB
A
A AB . B A
B. AB
AAB. B. A8
A ABt B. A8
AR
AB
AB
A: AB
ADR
AB
A OB
BoAB
Ao AB. B.AB= AAB
AB+B A = AfB
AB =
A OB
+ B. AB
nAtBt8(A16
Date.
Page No.
Qasoue that A8C + A8c)-+A Be t ABC *
Ad 5 L-H-S= AB c+ A8c'+ A8'C+A BC
>ABC+ ABc) +(A80+ AB')+(ABCIAB
AB(Ctc)+ AC (B+B) + Ac[AtA
AB+ Ac +BC= RHS
Lag|m(56,14, 1o,l 3,14, 15)
(
AB
AB
DI ’BD+BC+ADtAl
D
-F.
Date.
Page No.
Qucs97.Mtunction
MÃ mMAL. And jhlemeat the
fi=sm(o,l,4, 6,l, 9,1) +8 (2,7,i3)
AB
AB
X
AB
(o,,0,)-
BC,lo,4,2,6)’ Absl9,n) A8D
BC tAD+AB D
A
D
A
abd
(A¥X)(xt
(hux
(ZXFhtX
=0tX=Ghh)
tX
X
ON
Data
Page No.
X-
4=AB +a'B'
A
B
As AB
y= AB tAB
B-AB
tB'D) +AC
6D
ACt
B'BBD >A8+A8tA
Ct
A'B'c)
AB
DAB
A+A
boeliau conhlament
of
the Qbtai
Qucsto
No. Page
Date.
tion
minie
the
mathsd
oupit eslinatpnal
dlinglb
Cluskey
ActBC
radutiou
GenneMo
taular
the laung
3.3. Qua
exhucsi
+Bcen Amifeol
=TM(8lj9,47.
(ujA,6,c)
BC
A
BC
AB18C4BC
A
BC
BC BC
A
BC
No. Page
Date.
Date.
Page No.
f=sm(ol, 5,7, 0lb,l 4,15)%
Reprassataticn
Muinted
B
Minteui
CD
Lo
15
Mite
Min tos
ABcD
1
1
O 1
101o
3
O11 1
15
&kteh 37 - 2cel coubinatibni
1111
Date.
Conbinatious
A BC D
Page No.
(o,1)
100O
0 01
(5)
(8,1»)
1 0
5,7
5)
-111
(14,15)
1 11
PRIME LMPLICANT"
Brime Imabli. 61 5 7 8 o
(o,1)
I4 5
XX
(o,D)
(,5)
X
XX
#(8,10)
(5,7)
(7I5)
X
X
X
(6,lo, 14, 15)
(O,19) ’ABD
(14,15)- A8C
5,7) ’ ABD
Hence, k ABDtA8CtABC+ ABD
Date.
Page No.
Qucs 33| Minimie the
nkloneit the niimisnetion
NAND gala.
8.GD) = hm9,2,0,9lo, 13, l3,14)
AB
AB
D
A8
AB
D, 2,0, 1o) ’ BD
(12,8, 14,lo)-’ AD
Date.
Page lio.
Quy 34
ABCD
hns 34 Mites
1
4
6
13
15
Mitesus
D
9
3
6
3
13
4
15
A BCD
Data.
Paqe No.
Ateps
cell nofaseutationi
Conbination
(),3)
(,9)
(46)
(89)
1 00
O1 1
10 1
,)o
(9,1D)
(9,13)
10 1
(ti, 15)
(13,15)
1
1 1
1 1
1
eb4:-4cell combination
Oembinatior
(3,9, 1)
(9.,13,15)
BCD
1
-1
6
1315
3,9,0)( x
x
(x)x
(46) *
X
Date.
Page No.
(3,9,1) - &D
9U,13)5)’ AD
(u 6) > ABD
(09) ->ABE
Date.
Page No.
is enousu as Loncidence
-gatea
detcto
Aslo X-NOR gat is aeuen as lo Iucidnes
the Anbut
dame.
Questllhot is asscne Iinplicaa ?
Knmap
e called
Qus-19 etate Duality thaoso
dns14. his thecebu stat
sne buflicatl
thot the dual o
aitenclauginý the lagical ANDeheaatoh