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NPP Number System, Boolean Algebra and Logic Circuits 225

The Karnaugh map can be drawn as: Cnamoº$ ì`§OH$ hoVw K-_on {ZåZmZwgma ~Zm`m Om
gH$Vm h¡…
A B C D 00 01 11 10

00 0 0 0 0

01 0 0 0 0

11 0 1 1 1

10 0 0 0 0

As we see two overlapping pairs are Xmo AmodaboqnJ noAa {ZåZ SOP ì`§OH$ àXmZ H$a|Jo…
formed and the simplified expression in SOP
form will be as follows:
Y = A.B.D + A.B.C
Problem 3.66 àíZ 3.66
Simplify the following Boolean expres- K-_on {d{Y go gac H$amo:
sion using k-map method- K:

(a) Y = (A + B ) (A. + B )
(b) F = (A + B + C ) (A. + B + C ) (A. + B + C )

(c) F = ( A B C D. A B C D+ + + ) ( + + + )

) (A +
( A + B + C + D. B + C + D )
Solution: hc:
(a) The expression is: (a) {X`m J`m ì`§OH$ h¡:

Y = (A + B ) (A. + B )
It contains two maxterms. Drawing K-map Cnamoº$ ì`§OH$ _| Xmo _oŠñQ>_© h¢ AV… Xmo 0 VWm Xmo
for the Boolean expression and making the 1 AmE§JoŸ& Bg _on _| EH$ noAa {ZåZmZwgma ~ZoJm:
groups:
A B 0 1

0 0 0

1 1 1