Page 257 - FUNDAMENTALS OF COMPUTER

NPP

NPP Number System, Boolean Algebra and Logic Circuits 257

Therefore we have two overlapping pairs AV… h_| D H$m ŠdmS> ^r àmßV hmoJm Ÿ& Xmo no`a d
of ‘1’ and one quad of ‘D’. The simplified ex- EH$ D-ŠdmS> H$s ghm`Vm go {ZåZ gab ì`§OH$ àmßV
pression can be written as: Y = A.B + A.C. + A.D.
hmoJm: Y = A.B + A.C + A.D
Problem 3.73 àíZ 3.73
Simplify the following expression using {ZåZ ~y{b`Z ì`§OH$ H$mo do[aE~b _oqnJ {d{Y H$s
variable mapping method:
ghm`Vm go gab H$amo:
F = A.B.C A.B.C A.B.C.D A.B.C.D+ + +
Solution: hc:

The given expression can be written as: {XE JE ì`§OH$ H$mo {ZåZmZwgma {bIm Om gH$Vm h¡…

F = m + 1 m + 4 m .D + 3 m .D
7

A B C 00 01 11 10

0 0 1 D 0

1 1 0 D 0

There are two singles of ‘1’. But D can make 1 Ho$ Xmo qgJb ~Z|JoŸ& D H$m EH$ no`a 1= D + D
a pair with adjacent ‘1’. There is a single of D . {bIH$a ~Zm`m Om gH$Vm h¡Ÿ& D H$m EH$ qgJb {_boJmŸ&

A B C 00 01 11 10

0 0 D + D D 0

1 1 0 D 0

The simplified expression can be written gab ì`§OH$ {ZåZmZwgma {bIm Om gH$Vm h¡…
as:

F = C . B . A + D . C . B . A + C . B . A + D . C . A