1
GATE EE 2015 Set 2
+1
-0.3
Consider the following Sum of products expression, $$F.$$
$$F = ABC + \overline A \overline B C + A\overline B C + \overline A BC + \overline A \overline B \overline C$$

The equivalent Product of Sums expression is

A
$$F = \left( {A + \overline B + C} \right)\left( {\overline A + B + C} \right)\left( {\overline A + \overline B + C} \right)$$
B
$$F = \left( {A + \overline B + \overline C } \right)\left( {A + B + C} \right)\left( {\overline A + \overline B + \overline C } \right)$$
C
$$F = \left( {\overline A + B + \overline C } \right)\left( {A + \overline B + \overline C } \right)\left( {A + B + C} \right)$$
D
$$F = \left( {\overline A + \overline B + C} \right)\left( {A + B + \overline C } \right)\left( {A + B + C} \right)$$
2
GATE EE 2015 Set 1
+1
-0.3
$$f\left( {A,\,B,\,C,\,D} \right) = \Pi M\left( {0,1,3,4,5,7,9,11,12,13,14,15} \right)$$ is a Maxterm representation of a Boolean function $$f(A,B,C,D)$$ where $$A$$ is the $$MSB$$ and $$D$$ is the $$LSB$$. The equivalent minimized representation of this function is
A
$$\left( {A + \overline C + D} \right)\left( {\overline A + B + D} \right)$$
B
$$A\overline C D + \overline A BD$$
C
$$\overline A C\overline D + A\overline B C\overline D + A\overline B \overline C \overline D$$
D
$$\left( {B + \overline C + D} \right)\left( {A + \overline B + \overline C + D} \right)\left( {\overline A + B + C + D} \right)$$
3
GATE EE 2012
+1
-0.3
In the sum of products function $$f\,\left( {X,\,Y,\,Z} \right) = \sum \left( {2,\,\,3,\,\,4,\,\,5} \right),$$ the prime implicants are
A
$$\overline X Y,\,X\overline Y$$
B
$$\overline X Y,\,X\overline Y \overline Z ,X\overline Y Z$$
C
$$X\overline Y Z,\overline X YZ,X\overline Y$$
D
$$\,\overline X Y\overline Z ,\overline X YZ,X\overline Y \overline Z ,X\overline Y Z$$
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