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228 Fundamentals of Computers NPP
CD 00 01 11 10
AB
00 0 0 1 1
01 0 1 0 0
11 0 0 1 1
10 0 1 1 1
There are two quads, one pair and one Xmo ŠdmS>, EH$ noAa VWm EH$ qgJb go gab ì`§OH$
single. The simplified expression is:
{ZåZmZwgma àmßV hmoJm:
f = C . A + C . B + D . B . A + D . C . B . A
Problem 3.68 NPP àíZ 3.68
Simplify the following Boolean expres- K-_on H$s ghm`Vm go gab H$amo:
sion using Karnaugh map method:
(a) F = πM (4, 6, 7)
(b) Y = πM (0, 3, 5, 6, 7, 12, 15)
(c) F = C . B . A + A . C . B + C . B . A + B . A + A
Solution: hc:
(a) The given expression is F = πM (4, 6, 7) (a) Cnamoº$ ì`§OH$ F = πM (4, 6, 7) go K-_on
The Karnaugh map can be drawn as below: {ZåZmZwgma ~Zm`m Om gH$Vm h¡:
A B .C 00 01 11 10
0 1 1 1 1
1 0 1 0 0
The Karnaugh map contains one quad EH$ ŠdmS> d EH$ noAa Amodabon H$a aho h¢Ÿ& AV…
Overlapping with the pair. The simplified ex- gabrH¥$V ì`§OH$ {ZåZmZwgma àmßV hmoJm:
pression can be written as:
F = A + C . B
(b) The given expression is Y = πM (0, 3, 5, (b) Cnamoº$ ì`O§H$ Y = πM (0, 3, 5, 6, 7, 12, 15)
6, 7, 12, 15). The Karnaugh map and groups can go gmV 0 àmßV hm|JoŸ& AÝ` ñWmZm| na 1 aIH$a VWm J«wn
be drawn as follows:
~ZmZo na K-_on {ZåZmZwgma àmßV hmoJm:
