Page 221 - FUNDAMENTALS OF COMPUTER

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NPP Number System, Boolean Algebra and Logic Circuits 221

A B C 00 01 11 10

0 1 1 0 1

1 x 0 1 x

( ) (0,1,7
( ) (0,1,7 _| Xmo
(b) The given equation Y = π M 3,5 .d ) (b) Cnamoº$ g_rH$aU Y = π M 3,5 .d )
has two maxterms represented by M and _oŠñQ>_© h¢ {OÝh| M go Xem©`m J`m h¡ VWm VrZ S>m|Q>
three don’t care conditions represented by Ho$`a H§$S>reÝg h¢ {OÝh| d go Xem©`m J`m h¡ Ÿ& M Ho$
d. Put zeros for maxterms and put X(cross)
for don’t care conditions. The three vari- ñWmZm| na 0, d Ho$ ñWmZm| na X VWm AÝ` ñWmZm|
able K-map is as follows: na 1 aIZo go K-_on {ZåZmZwgma àmßV hmoJm:
A B C 00 01 11 10

0 x x 0 1

1 1 0 x 1

(c) Q = C . B . A + C . B . A + C . B . A + B . A
The above equation is not in a canonical CnamoŠV g_rH$aU Ho$Zmo{ZH$b ê$n _| Zht h¡ Š`m|{H$

form, because the last term .A B contains B . A _| Ho$db Xmo Ma am{e`m± h¢ & AV… Bgo 1 go
only two literals. To make it canonical JwUm H$aZo na… .A
multiply the product by ‘1’: 1 . B
Replace 1: by (C + C ) because C is the miss- 1 Ho$ ñWmZ na (C + C ) {bIZo na …
ing variable.
= . B . A (C+ C ) = C . B . A + C . B . A

Replace .A B with the above expression B . A Ho$ ñWmZ na Cnamoº$ _mZ aIZo na
Q = C . B . A + C . B . A + C . B . A + C . B . A + C . B . A

The K-map would be as follows: Cnamoº$ ì`§OH$ H$m K-_on {ZåZmZwgma ~ZoJm:
A B C 00 01 11 10

0 1 1 0 0

1 1 1 1 0