GATE CS 2026 Set 2 — Question 59
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Digital Logic → Combinational Circuits → Encoders & Decoders
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Question
Consider the digital circuit shown below with two input lines and , two select lines and , and an output line . The blocks and represent active high 2:4 decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce is ____________. (answer in integer)Note: One input combination is an instance of .
Correct answer
6 to 6
Solution
1.Analyze the 2:4 Decoder :
The decoder has inputs and . Since it is active high, the outputs are:- (High when )
- (High when )
- (High when )
- (High when )
The select lines are (MSB) and (LSB). The data inputs are:
- (constant low)
- (constant high)
Substituting the specific inputs from the circuit:
3.Count combinations where :
- Case 1:
Combination: (1 combination)
- Case 2:
- Case 3:
Combinations: (4 combinations)
- Case 4:
Combination: (1 combination)
4.Total number of combinations:
Total = .Continue learning with Success Tracker
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