1
GATE EE 2024
+1
-0.33

Simplified form of the Boolean function

$$F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S}$$

is

A
$\bar{P} S+\bar{Q} \bar{S}$
B

$\bar{P} \bar{Q}+\bar{Q} \bar{S}$

C

$\bar{P} Q+R \bar{S}$

D

$P \bar{S}+Q \bar{R}$

2
GATE EE 2017 Set 1
+1
-0.3
The Boolean expression $$AB + A\overline C + BC$$ simplifies to
A
$$BC + A\overline C$$
B
$$AB + A\overline C + B$$
C
$$AB + A\overline C$$
D
$$AB + BC$$
3
GATE EE 2017 Set 2
+1
-0.3
For a $$3$$ -input logic circuit shown below, the output $$Z$$ can be expressed as
A
$$Q + \overline R$$
B
$$P\overline Q + R$$
C
$$\overline Q + R$$
D
$$P + \overline Q + R$$
4
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
$$\left( {B + \overline C + D} \right)\left( {A + \overline B + \overline C + D} \right)\left( {\overline A + B + C + D} \right)$$
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