Page 216 - FUNDAMENTALS OF COMPUTER

NPP

216 Fundamentals of Computers NPP

The K-map is as follows: AV… K-_on {ZåZmZwgma hmoJm:
A B C D 00 01 11 10

00 0 0 0 0

01 0 0 0 0

11 0 0 1 1

10 0 1 0 0

Problem 3.62 àíZ 3.62
Draw the Karnaugh map for the follow- {ZåZ ì`§OH$m| hoVw K-_on ~ZmAmo:
ing Boolean expressions:
(a) F = (A + B ) (A. + ) B

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

(c) Q = (X+ Y ) (X. + Y )

(d) W = (P + Q + R + Z ) (P. + Q + R + Z )
Solution: hc:

(a) The expression F = (A + B ) (A. + ) B is in (a) ì`§OH$ F = (A + B ) (A. + ) B `moJm| H$m JwUZ\$b
POS form. There are two maxterms (A + B) h¡ (POS). Bg_| Xmo _oŠgQ>_© (A+B) VWm (A + ) B

and (A + ) B and corresponds to following h¡ Ÿ& `o XmoZm| {ZåZ g§»`mAm| Ho$ gmnoj h¢:
combination-

(A + B ) → 0 0 , (A + ) B  10
→
(put a ‘1’ where there is a bar else put ‘0’). (Ohm± ~ma Am`m dhm± 1 {bI| AÝ`Wm 0 {bI|)&
We put a ‘0’ for a maxterm. Therefore Karnaugh _oŠgQ>_m] Ho$ gmnoj 0 {bIZo na {ZåZmZwgma K-_on àmßV
map will be:
hmoJm…

A B 0 1

0 0 1

1 0 1