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mediumMCQGATE IN 2025 Question Paper (01-Feb-2025) (Shift 2)Instrumentation Engineering
1 mark (−0.33)

The minimized expression of the Boolean function Y(P, Q, R) implemented by the multiplexer (MUX) circuit shown in the figure is

image

  1. A
  2. B
  3. C
  4. D

Solution & Step-by-step Explanation

The given problem involves a multiplexer (MUX) circuit implementing a Boolean function Y(P, Q, R). We need to determine the minimized expression for this function.

MUX Circuit

Let's analyze the MUX circuit step-by-step:

1. The first MUX selects inputs based on the select lines P and Q (represented as S_1 and S_0 respectively).
2. The inputs to this MUX are 0, 1, 1, and 0, corresponding to 00, 01, 10, and 11 select line combinations.
3. This implements the function P \oplus Q (XOR gate), since: - When P = 0 and Q = 0 or P = 1 and Q = 1, the output is 0. - When P = 0 and Q = 1 or P = 1 and Q = 0, the output is 1.
4. The second MUX uses the output of the first MUX and select line R.
5. The second MUX outputs a logical function based on: - When R = 0, the output is the result from the first MUX, which is P \oplus Q. - When R = 1, the output is 1. - Effectively, the second MUX implements a logical OR operation: R + (P \oplus Q).

Thus, the minimized expression of the Boolean function is:

Y = R + (P \oplus Q)

Therefore, the correct answer is:

Y = R + (P \oplus Q)

Practice this question

Try it yourself before checking the explanation above.

The minimized expression of the Boolean function Y(P, Q, R) implemented by the multiplexer (MUX) circuit shown in the figure is

image
A
B
C
D

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