Page 200 - FUNDAMENTALS OF COMPUTER

NPP

200 Fundamentals of Computers NPP

A B F
0 0 0
0 1 1
1 0 1
1 1 0

There are two minterms .A B and .A B cor-- Xmo {_ÝQ>_© A B . VWm A B . àmßV hmoJrŸ& AV…
responding to two 1s in the output. F is sum of AmCQ>nwQ> F H$m gyÌ Bg àH$ma {bIm Om gH$Vm h¡…
these two minterms:
F = B . A + B . A
or, F = m + m 2
1
or, F = Σm (1, 2)
Minterms give us SOP form of expression. {_ÝQ>_© go gmon (SOP) ê$n _| ì`§OH$ àmßV hmoVm h¡Ÿ&
Problem 3.53 àíZ 3.53

For the following truth table find the ex- Q hoVw ì`§OH$ kmV H$amo ({ZåZ Vm{bH$m ‘|)…
pression for Q:
A B C Q
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
Solution: hc:

There are four minterms as listed below: {ZåZmZwgma Mma {_ÝQ>_© àßV hmoJr…
m = C . B . A , m = C . B . A ,
1
0
m = C . B . A , m = C . B . A
4
6
The output Q is equal to the logical sum of Q Cnamoº$ g^r {‘ÝQ>‘m] ‘| H$m `moJ hmoJm…
all the minterms. i.e.
Q = m + m + m + m 6
4
1
0
or, Q = C . B . A + C . B . A + C . B . A + C . B . A
This is the SOP form of expression. `hr Q H$m ì`§OH$ h¡ Omo{H$ SOP ê$n _| h¡Ÿ&