GATE CS 2026 Set 2 Q.59: Combinational Circuits

Consider the digital circuit shown below with two input lines A and B, two select lines S0 and S1, and an output line Y. The blocks Q and M represent active high 2:4 decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce Y=1 is ____________. (answer in integer)

Note: One input combination is an instance of [A B S1 S0].

Digital circuit with an active-high 2:4 decoder Q (inputs A, B; outputs D0 to D3) connected to a 4-to-1 multiplexer M (select lines S1, S0; output Y), where M input 0 is D0, input 1 is constant 0, input 2 is constant 1, and input 3 is D3.

Your answer

Official answer and solution

Official answer: 6
From: Official GATE 2026 answer key

Solution

Evaluate the MUX output $Y$ for each of the four select-line combinations $(S_1, S_0) \in \{00, 01, 10, 11\}$ .

For the active-high 2:4 decoder $Q$ with inputs $(A, B)$ , $D_0 = A'B'$ and $D_3 = AB$ . For the 4-to-1 multiplexer $M$ with select lines $(S_1, S_0)$ :

When $S_1 S_0 = 00$ : $Y = I_0 = D_0 = A'B'$ , which equals $1$ when $(A, B) = (0, 0)$ (1 combination: 0000).
When $S_1 S_0 = 01$ : $Y = I_1 = 0$ , which is never $1$ (0 combinations).
When $S_1 S_0 = 10$ : $Y = I_2 = 1$ , which equals $1$ for all $4$ values of $(A, B)$ (4 combinations: 0010, 0110, 1010, 1110).
When $S_1 S_0 = 11$ : $Y = I_3 = D_3 = AB$ , which equals $1$ when $(A, B) = (1, 1)$ (1 combination: 1111).

Total input combinations producing $Y = 1$ is $1 + 0 + 4 + 1 = 6$ .

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 59 of 65
Section: Computer Science and Information Technology

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