What is the answer to GATE CS 2026 Set-2 Q59 on decoder and multiplexer?

The answer is 6. A 2x4 decoder with inputs A and B feeds a 4-to-1 MUX with select lines S1 and S0. When S1S0=10, the MUX selects a constant 1 input giving y=1 for all 4 combinations of A,B. When S1S0=00, y=1 only for A=0,B=0 (1 combination). When S1S0=11, y=1 only for A=1,B=1 (1 combination). Total = 4+1+1 = 6.

How does a 2x4 decoder work with a 4-to-1 multiplexer?

A 2x4 decoder takes 2 inputs (A, B) and activates exactly one of its 4 output lines (D0–D3) based on the binary combination of A and B. When connected to a 4-to-1 MUX, the decoder outputs serve as data inputs. The MUX select lines S1 and S0 then choose which decoder output (or fixed value) is forwarded to the final output y.

Why is the total number of combinations 6 and not 16?

There are 16 total combinations of (A, B, S1, S0), but y=1 only for specific ones. S1S0=10 gives y=1 for all 4 values of A,B (4 cases). S1S0=00 gives y=1 only when A=0,B=0 (1 case). S1S0=11 gives y=1 only when A=1,B=1 (1 case). S1S0=01 gives y=0 for all A,B (0 cases). Total = 6.

2x4 Decoder 4-to-1 MUX Output Combinations | GATE CS 2026 Set-2 Q59

Computer Sciences > GATE 2026 SET-2 > Digital Logic

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].

Correct : 5

he correct answer is 6.
The circuit consists of a 2×4 decoder (inputs A, B) feeding a 4-to-1 multiplexer M with select lines S₁ and S₀. The MUX data inputs are wired as: I₀ = AB̄, I₁ = AB̄ (or tied), I₂ = 1 (always high), I₃ = AB.
Case 1 - S₁S₀ = 10 (selects I₂ = 1): Output y = 1 regardless of A and B. Since A and B can each be 0 or 1 independently, this gives 4 combinations: (0,0,1,0), (0,1,1,0), (1,0,1,0), (1,1,1,0).
Case 2 - S₁S₀ = 00 (selects I₀ = AB̄): Output y = 1 only when AB̄ = 1, i.e., A=0, B=0. This gives 1 combination: (0,0,0,0).
Case 3 - S₁S₀ = 11 (selects I₃ = AB): Output y = 1 only when AB = 1, i.e., A=1, B=1. This gives 1 combination: (1,1,1,1).
Case 4 - S₁S₀ = 01 (selects I₁): The MUX input I₁ corresponds to the decoder output D₁ = AB̄ (which is 0 for all A,B combinations in standard 2×4 decoder with active-high outputs where only one line is high). y = 0 for all A,B. 0 combinations.
Total combinations = 4 + 1 + 1 = 6.

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