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The digital waveforms for two inputs A and B and the corresponding output Y of a logic circuit over four time intervals t₁, t₂, t₃ and t₄ are observed as follows: During t₁ : A is low, B is low, Y is high. During t₂ : A is high, B is low, Y is low. During t₃ : A is low, B is high, Y is low. During t₄ : A is high, B is high, Y is low. The Boolean expression for the output Y is :

Options

  1. AY = A B
  2. BY = A + B
  3. CY = A B
  4. DY = A+B

Correct answer

D. Y = A+B

Step-by-step solution

From the given waveform data, we can construct the truth table by taking 'low' as 0 and 'high' as 1 : array |c|c|c| A & B & Y 0 & 0 & 1 1 & 0 & 0 0 & 1 & 0 1 & 1 & 0 array The output Y is 1 only when both inputs A and B are 0 . For all other combinations, the output is 0 . This is the characteristic of a NOR gate. Therefore, the Boolean expression is Y = A+B . Answer: Y = A+B

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