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The Boolean expression for a logic circuit is given by Y = ( A + B) A . Out of the four possible input combinations of A and B , for how many combinations will the output Y be 1 ?

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

Given Boolean expression: Y = ( A + B) A Using De Morgan's theorem, (X + Y) = X Y . Therefore, ( A + B) = A B = A B Substituting this back into the expression for Y : Y = (A B ) A Using the Boolean algebra rule A A = A : Y = A B The output Y = 1 only when A = 1 and B = 1 (which means B = 0 ). Thus, out of the four possible input combinations (0,0), (0,1), (1,0), (1,1) , only the combination A = 1, B = 0 gives Y = 1 . The output is 1 for exactly 1 combination. Answer: 1

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