Page 226 - FUNDAMENTALS OF COMPUTER

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226 Fundamentals of Computers NPP

The desired solution is: AV… gabrH¥$V ì`§OH$ {ZåZmZwgma hmoJm:
Y = A
(b) The given expression: (b) {X`m J`m ì`§OH$ h¡:

F = (A+ B+ C ) (A. + B + C ) (A. + B + C )
Karnaugh map contains three zeros corre- Cnamoº$ ì`§OH$ _| VrZ 0 d nm±M 1 hm|Jo Ÿ& {ZåZmZwgma
sponding to three maxterms. Five ones will be K-_on VWm J«wn ~Z|Jo:
there:
A B C 00 01 11 10

0 0 1 0 0

1 1 1 1 1

As the diagram shows there is one quad EH$ ŠdmS> VWm EH$ noAa Amodabon H$a aho h¢Ÿ& gab
overlapping with one pair. The simplified ex- ì`§OH$ BZ XmoZm| Ho$ H$maU àmßV nXm| H$m Vm{H©$H$ `moJ
pression would be the sum of terms obtained
from pair and the quad. The pair gives .B C be- hmoJmŸ& noAa go h_| C.B àmßV hmoJm Š`m|{H$ A n[ad{V©V hmo
cause A changes, when we move from top to ahm h¡ VWm BC = 01 h¡Ÿ& ŠdmS> go h_| A {_boJm Š`m|{H$
bottom. The quad will give A only because B ~mE§ go XmE§ OmZo na B d C XmoZm| n[ad{V©V hmo aho h¢ d A
and C both change while moving left to right.
= 1 na pñWa h¡ & AV… gab ì`§OH$ F = C . B + Ah¡Ÿ&
The result is: F = C . B + A
(c) The given expression is: (c) {X`m h¡:

F = ( A + B C+ + D ) ( . A + B + C + D ) . ( A + B + C + D ) ( . A + B + C + D )
The K-map can be drawn by filling four Cnamoº$ ì`§OH$ _| Mma _oŠgQ>_© h¡Ÿ& AV… Mma 0
zeros for the maxterms:
VWm AÝ` ñWmZm| na 1 AmEJm…

A B C D 00 01 11 10

00 0 1 0 1

01 1 0 1 1

11 0 1 1 1

10 1 1 1 1