Page 204 - FUNDAMENTALS OF COMPUTER

204 Fundamentals of Computers NPP

3.22 Finding the expression in POS form 3.22 nmog (POS) ê$n _| ì`§OH$ ~ZmZm
If the truth table is given to us we can find Xr JB© gË` Vm{bH$m _| gmao _oŠgQ>_© {ZH$mbmo VWm
the expression in POS form. Find all the CZH$m Vm{H©$H$ JwUm (AND) H$amoŸ& AmCQ>nwQ> ’§$³eZ
maxterms and take logical product. Thus, “The g^r ‘¡³gQ>åg© H$m bm°{OH$b àmoS>³Q> h¡& O¡go {ZåZ gË`
output function is logical product of all the
maxterms” e.g. Consider the following truth Vm{bH$m H$mo XoImo…
table:
A B F
0 0 1
0 1 0
1 0 1
1 1 0
There are two maxterms : {ZåZ Xmo _oŠgQ>_© àmßV hm|Jr…

M = A + B , M = A + B
1
3
The expression for F is product of the two F Bg àH$ma {bIm Om gH$Vm h¡Ÿ&
maxterms: NPP
F = M 1 . M 3

or F = (A + B ) (A. + B )
Or the same expression can be written as: _oŠgQ>_© H$m JwUZ\$c:
F = πM(1, 3)
Problem 3.56 àíZ 3.56
For the given truth Table find the exp- F H$m ì`§OH$ kmV H$s{OE:
ression for F:
X Y Z F
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 0
Solution: hc:
There are four Maxterms as: Mma _oŠg Q>_© d F H$m gyÌ Bg àH$ma h¡…
M = X + Y + Z , M = X + Y + Z ,
4
0
M = X + Y + Z , M = X + Y + Z
7
5