GATE CSE 2023 | Combinational Circuits Question 4 | Digital Logic

GATE CSE 2023

MCQ (Single Correct Answer)

-0.67

A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.

GATE CSE 2023 Digital Logic - Combinational Circuits Question 4 English

Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function $$\overline A + \overline A \,.\,\overline C + A\,.\,\overline B \,.\,C$$ ?

(1, 1, 0, 0, 1, 1, 1, 0)

(1, 1, 0, 0, 1, 1, 0, 1)

(1, 1, 0, 1, 1, 1, 0, 0)

(0, 0, 1, 1, 0, 1, 1, 1)

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the two cascaded $$2$$-to-$$1$$ multiplexers as shown in the figure. GATE CSE 2016 Set 1 Digital Logic - Combinational Circuits Question 8 English

The minimal sum of products form of the output $$X$$ is

$$\overline P \overline Q + PQR$$

$$\overline P Q + QR$$

$$PQ + \overline P \overline Q R$$

$$\overline Q \overline R + PQR$$

GATE CSE 2014 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the $$4$$-to-$$1$$ multiplexer with two select lines $${S_1}$$ and $${S_0}$$ given below GATE CSE 2014 Set 1 Digital Logic - Combinational Circuits Question 9 English

GATE CSE 2014 Set 1 Digital Logic - Combinational Circuits Question 9 English

The minimal sum-of-products form of the Boolean expression for the output $$F$$ of the multiplexer is

$$\overline P Q + Q\overline R + P\overline Q R$$

$$\overline P Q + \overline P Q\overline R + PQ\overline R + P\overline Q R$$

$$\overline P QR + \overline P Q\overline R + Q\overline R + P\overline Q R$$

$$PQ\overline R $$

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $$n$$ variables. What is the minimum size of the multiplexer needed?

$${2^n}$$ line to $$1$$ line

$${2^{n + 1}}$$ line to $$1$$ line

$${2^{n - 1}}$$ line to $$1$$ line

$${2^{n - 2}}$$ line to $$1$$ line

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