GATE CS 2024 Set 1 — Question 64
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Digital Logic → Combinational Circuits → Multiplexers & Demultiplexers
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Question
Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. and are inputs of M1. and are inputs of M2. and are select lines of M1, M2, and M3, respectively.
For an instance of inputs and , the number of combinations of that give the output is _________
Correct answer
4 to 4
Solution
To find the number of combinations of that result in , we analyze the logic of the multiplexers given the specific inputs:
Given and :
.
Thus, is always , regardless of the value of the select line .
Given and :
.
Thus, is always , regardless of the value of the select line .
Substituting the values of and obtained above:
.
Total combinations = . The specific combinations are and .
1.Multiplexer M1:
The output is given by the expression for a 2-to-1 MUX: .Given and :
.
Thus, is always , regardless of the value of the select line .
2.Multiplexer M2:
The output is given by: .Given and :
.
Thus, is always , regardless of the value of the select line .
3.Multiplexer M3:
The final output is given by: .Substituting the values of and obtained above:
.
4.Condition for :
We require the output . From the expression , this implies , which means .5.Counting the combinations of :
- The select line can be either or ( possible values).
- The select line can be either or ( possible values).
- The select line must be ( possible value).
Total combinations = . The specific combinations are and .
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