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GATE 2023 BM – Question 28

Analog and Digital Electronics · Number Systems and Boolean Algebra · 1 mark · Multiple select

Q, R and S are Boolean variables and ⊕ denotes XOR. Select the correct statements.

  1. (Q⊕R)⊕S = Q⊕(R⊕S)
  2. (Q⊕R)⊕S = 0 when two variables are 0 and the third is 1
  3. (Q⊕R)⊕S = 1 when Q=R=S=1
  4. ((Q⊕R)⊕(R⊕S))⊕(Q⊕S) = 1

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Show answer and explanation

Correct answer: (A) (Q⊕R)⊕S = Q⊕(R⊕S); (C) (Q⊕R)⊕S = 1 when Q=R=S=1

Explanation

XOR is associative, giving A. It equals one for an odd number of ones, so one input equal to one makes B false, while three ones make C true. In D each variable occurs twice; paired XOR terms cancel, leaving zero. Correct selections are A and C.

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