GATE EE 2008 Digital Electronics Q 1 - Grad Plus

# GATE EE 2008 Digital Electronics Q 1

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) \left(X+Z\right)\cdot\left(\overline X+\overline Y+\overline Z\right)\cdot\left(Y+Z\right)

b) \left(\overline X+\overline Z\right)\cdot\left(X+Y+Z\right)\cdot\left(\overline Y+\overline Z\right)

c) \left(\overline X+\overline Y+Z\right)\cdot\left(\overline X+Y+Z\right)\cdot\left(X+\overline Y+Z\right)\cdot\left(X+Y+\overline Z\right)

d) \left(\overline X+\overline Y+Z\right)\cdot\left(\overline X+Y+\overline Z\right)\cdot\left(X+\overline Y+Z\right)\cdot\left(X+\overline Y+\overline Z\right)

Ans: (a)

Explanation

For active high inputs,

F=\sum\left(1,\;3,\;5,\;6\right)=IIM\left(0,\;2,\;4,\;7\right) =\left(Y+Z\right)\cdot\left(X+Z\right)\cdot\left(\overline X+\overline Y+\overline Z\right)
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