Page 215 - FUNDAMENTALS OF COMPUTER

NPP

NPP Number System, Boolean Algebra and Logic Circuits 215

A B 0 1

0 1 1

1 0 0

(b) The given equation- (b) {X`m J`m g_rH$aU h¡-
Y = A.B.C + A.B.C A.B.C+ .
It is a three variable problem. The three `h VrZ Mam| d VrZ {_ZQ>_m] dmbm g_rH$aU h¡Ÿ&
minterms corresponds to three 1’s. The combi- AV… {ZåZ VrZ g§»`mAm| Ho$ gmnoj 1 {bI|Jo…
nations are as follows:
C . B . A  100 ,
→
→
C . B . A  001,
C . B . A  101
→
Therefore three 1’s and five 0’s are there in AV… Hw$b VrZ 1 VWm nm±M 0 go {_bH$a K-_on
K-map. The K-map is as follows: ~ZoJm…

A B C 00 01 11 10

0 0 1 0 0

1 1 1 0 0

(c) The given equation: (c) {X`m J`m g_rH$aU h¡:

Y = D . C . B . A + D . C . B . A + D . C . B . A .
It is a four variable problem. The three `h Mma am{e`m| VWm VrZ {_ZQ>_m] dmbm g_rH$aU
minterms corresponds to three combinations a h¡Ÿ& {ZåZ Mma g§»`mAm| Ho$ gmnoj h_| 1 {bIZm hmoJm:
follows:
D . C . B . A  1 1 1 0
→
→
D . C . B . A  1 001
D . C . B . A  1 1 1 1
→