Question

A $3$ line to $8$ line decoder, with active low outputs, is used to implement a $3-$ variable Boolean function as shown in the figure.



The simplified form of Boolean function $F(A,B,C)$ implemented in 'Product of Sum' form will be

• A. $(\overline{X}+\overline{Y}+Z).(\overline{X}+Y+\overline{Z}).(X+\overline{Y}+Z).(X+\overline{Y}+\overline{Z})$
• B. $(\overline{X}+\overline{Y}+\overline{Z}).(\overline{X}+Y+Z).(X+\overline{Y}+Z).(X+Y+\overline{Z})$
• C. $(\overline{X}+\overline{Z}).(X+Y+Z).(\overline{Y}+\overline{Z})$
• D. $(X+Z).(\overline{X}+\overline{Y}+\overline{Z}).(Y+Z)$

Answer 1

The correct option is D $(X+Z).(\overline{X}+\overline{Y}+\overline{Z}).(Y+Z)$

Let us consider active high input


$F=\sum (1,3,5,6)=\prod M(0,2,4,7)$
$=(Y+Z).(X+Z).(\overline{X}+\overline{Y}+\overline{Z})$