Page 202 - FUNDAMENTALS OF COMPUTER

202 Fundamentals of Computers NPP

0 = 00, 1 = 01, 3 = 11
A B F
0 0 1
0 1 1
1 0 0
1 1 1
(c) The given expression is: (c) {X`m J`m ì`§OH$:
Q = C . B . A + B . A + C . B . A
This expression is not in a canonical SOP Ho$Zmo{ZH$b ê$n _| Zht h¡ Ÿ³¶m|{H$ .A B ‘| Ho$db Xmo
form because .A B has only two variables. C is
missing. Therefore to convert it into canonical d¡[aE~b h¡& C Zht h¡& AV… .A B H$mo (C + C ) go JwUm
SOP form multiply by (C + C ) to get: H$aZo na…
A.B = .A B (C + C )

or, NPP C . B . A + C . B . A
Put it in the original equation: Cnamoº$ _mZ ì`§OH$ _| aIZo na…
Q = C . B . A + C . B . A + C . B . A + C . B . A = + A.B.C + A.B.C A.B.C
Since .A C . B is repeated, we can write once. My±{H$ .A C . B Xmo ~ma Am J`m h¡, AV… h_ Cgo EH$
The three minterms give three 1s in the output.
The truth table can be drawn as: hr ~ma {bI gH$Vo h¢ Ÿ& VrZ {_ÝQ>_© Ho$ gmnoj AmCQ>nwQ>
_| VrZ "1" hm|Jo…
A B C Q
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 0
Maxterms _oŠgQ>_©
“Maxterms are fundamental sums corre- _oŠgQ>_© "0" Ho$ gmnoj \§$S>m_|Q>b `moJ hmoVo h¢Ÿ& AWm©V²
sponding to ‘0’ in the output.” Consider the fol- Ohm± AmCQ>nwQ> _| "0" àmßV hmo, Cg g§`moOZ Ho$ gmnoj
lowing truth table: \§$S>m_|Q>b `moJ àmßV {H$`m OmVm h¡, Cgo _oŠgQ>_© H$hVo
h¢Ÿ& {ZåZ gË`-Vm{bH$m H$mo g_Pmo…