GATE CSE 2019 | Boolean Algebra Question 8 | Digital Logic

GATE CSE 2019

MCQ (Single Correct Answer)

-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 : GATE CSE 2019 Digital Logic - Boolean Algebra Question 7 English

GATE CSE 2019 Digital Logic - Boolean Algebra Question 7 English

Σ (2, 14)

Σ (7, 8, 11)

Σ (2, 7, 8, 11, 14)

Σ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)

GATE CSE 2018

MCQ (Single Correct Answer)

-0.6

Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

$$\overline {P \oplus Q} = P \odot Q$$

$$\overline P \oplus Q = P \odot Q$$

$$\overline P \oplus \overline Q = P \oplus Q$$

$$\left( {P \oplus \overline P } \right) \oplus Q = \left( {P \odot \overline P } \right) \odot \overline Q $$

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

Consider a carry lookahead adder for adding two $$n$$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is

$$\Theta \left( 1 \right)$$

$$\Theta \left( {\log \left( n \right)} \right)$$

$$\Theta \left( {\sqrt n } \right)$$

$$\Theta \left( n \right)$$

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the operations

$$f\left( {x,y,z} \right) = X'YZ + XY' + Y'Z'$$ and
$$g\left( {x,y,z} \right) = X'YZ + X'YZ' + XY$$.

Which one of the following is correct?

Both $$\left\{ f \right\}$$ and $$\left\{ g \right\}$$ are functionally complete

Only $$\left\{ f \right\}$$ is functionally complete