GATE CSE 2024 Set 1 | Boolean Algebra Question 2 | Digital Logic

GATE CSE 2024 Set 1

MCQ (More than One Correct Answer)

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Consider a Boolean expression given by $F(X, Y, Z) = \\Sigma(3,5,6,7)$.

Which of the following statements is/are CORRECT?

$F(X, Y, Z) = \\Pi(0,1,2,4)$

$F(X, Y, Z) = XY + YZ + XZ$

$F(X, Y, Z)$ is independent of input $Y$

$F(X, Y, Z)$ is independent of input $X$

GATE CSE 2021 Set 1

MCQ (More than One Correct Answer)

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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)?

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

$$X\overline Y + \overline Z$$

$$X\overline Y + Y\overline Z + \overline X \overline Y \overline Z $$

$$(X + \overline Z ) . (\overline Y + \overline Z )$$

GATE CSE 2020

MCQ (Single Correct Answer)

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Consider the Boolean function z(a,b,c).

GATE CSE 2020 Digital Logic - Boolean Algebra Question 4 English

Which one of the following minterm lists represents the circuit given above?

z = $$\sum {\left( {0,1,3,7} \right)} $$

z = $$\sum {\left( {1,4,5,6,7} \right)} $$

z = $$\sum {\left( {2,4,5,6,7} \right)} $$

z = $$\sum {\left( {2,3,5} \right)} $$

GATE CSE 2019

MCQ (Single Correct Answer)

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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: GATE CSE 2019 Digital Logic - Boolean Algebra Question 5 English