GATE CS Combinational Circuits Previous Year Questions

GATE CS 2024 Set 1 | Question 28

MSQ · 1 mark

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Logic circuit in which input X feeds one input of an AND gate directly and the other input through a NOT gate; the output of the AND gate is Y.

With no propagation delays, the output \(\boldsymbol{Y}\) is always logic Zero With no propagation delays, the output \(\boldsymbol{Y}\) is always logic One With propagation delays, the output \(\boldsymbol{Y}\) can have a transient logic One after \(\boldsymbol{X}\) transitions from logic Zero to logic One With propagation delays, the output \(\boldsymbol{Y}\) can have a transient logic Zero after \(\boldsymbol{X}\) transitions from logic One to logic Zero

Explanation

Answer: (A), (C)

The AND gate receives \(X\) directly and \(\overline{X}\) through the inverter, so ideally \(Y = X \cdot \overline{X} = 0\) for every input: A is true and B is false.

Now let the NOT gate take time \(t\) to respond.

\(X\) rises from 0 to 1: the direct input becomes 1 at once, but for time \(t\) the inverter still outputs its old value 1. Both AND inputs are briefly 1, so \(Y\) shows a short glitch to logic One (a static hazard). C is true.
\(X\) falls from 1 to 0: the direct input drops to 0 at once, while the inverter output is still 0 and rises only after \(t\). The two inputs are never 1 together, so \(Y\) simply stays at 0. With no 1 to dip from, no transient Zero can appear, so D is false.

Answer: A, C

GATE CS 2024 Set 1 | Question 64

NAT · 2 marks

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.

Three 2-to-1 multiplexers. M1 takes X1 on input 0 and X2 on input 1, with select S1 driven by A and output Q1; M2 takes X3 on input 0 and X4 on input 1, with select S2 driven by B and output Q2; Q1 feeds input 0 and Q2 feeds input 1 of M3, whose select S3 is driven by C and whose output is Y.

For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is _________

Your answer

Explanation

Answer: 4

A 2-to-1 multiplexer passes its input 0 when the select line is 0 and its input 1 when the select line is 1.

M1 chooses between X1 = 1 and X2 = 1, so Q1 = 1 whatever A is.
M2 chooses between X3 = 0 and X4 = 0, so Q2 = 0 whatever B is.
M3 passes Q1 when C = 0 and Q2 when C = 1, so \(Y = \overline{C}\).

Y = 1 exactly when C = 0, while A and B can take any values: \(2 \times 2 = 4\) of the 8 combinations.

Answer: 4