1
GATE CSE 2021 Set 1
MCQ (More than One Correct Answer)
+2
-0.67

Consider the following Boolean expression.

$$F = (X + Y + Z)(\overline X + Y)(\overline Y + Z)$$

Which of the following Boolean expressions is/are equivalent to $$\overline F$$ (complement of F)?

A
$$(\overline X + \overline Y + \overline Z )(X + \overline Y )(Y + \overline Z )$$
B
$$X\overline Y + \overline Z$$
C
$$X\overline Y + Y\overline Z + \overline X \overline Y \overline Z$$
D
$$(X + \overline Z ) . (\overline Y + \overline Z )$$
2
GATE CSE 2020
MCQ (Single Correct Answer)
+2
-0.67
Consider the Boolean function z(a,b,c).
Which one of the following minterm lists represents the circuit given above?
A
z = $$\sum {\left( {0,1,3,7} \right)}$$
B
z = $$\sum {\left( {1,4,5,6,7} \right)}$$
C
z = $$\sum {\left( {2,4,5,6,7} \right)}$$
D
z = $$\sum {\left( {2,3,5} \right)}$$
3
GATE CSE 2019
MCQ (Single Correct Answer)
+2
-0.67
Consider three 4-variable functions f1, f2 and f3, which are expressed in sum-of-minterms as

f1 = Σ(0, 2, 5, 8, 14),

f2 = Σ(2, 3, 6, 8, 14, 15),

f3 = Σ(2, 7, 11, 14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:
A
Σ (2, 14)
B
Σ (7, 8, 11)
C
Σ (2, 7, 8, 11, 14)
D
Σ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)
4
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Let $$\oplus$$ and $$\odot$$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

A
$$\overline {P \oplus Q} = P \odot Q$$
B
$$\overline P \oplus Q = P \odot Q$$
C
$$\overline P \oplus \overline Q = P \oplus Q$$
D
$$\left( {P \oplus \overline P } \right) \oplus Q = \left( {P \odot \overline P } \right) \odot \overline Q$$
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