A logic circuit has two inputs A and B . These inputs are connected simultaneously to a NOR gate and a NAND gate. The outputs of these two gates are then fed into a final NOR gate to produce the output Y . The inputs A and B are provided as sequences of binary logic levels over four consecutive time intervals: A = 0, 1, 0, 1 and B = 0, 0, 1, 1 . Which of the following sequences represents the correct output Y over th

Step-by-step solution

Let the intermediate outputs be Y₁ and Y₂ . The output of the first NOR gate is Y₁ = A+B . The output of the NAND gate is Y₂ = AB . These are fed into a final NOR gate, so the final output Y is: Y = Y₁ + Y₂ = A+B + AB Applying De Morgan's Law ( P+Q = P Q ): Y = A+B AB Y = (A+B) (AB) Expanding this expression: Y = A AB + B AB = AB + AB = AB Thus, the entire circuit is equivalent to a two-input AND gate. Given the input sequences: A = 0, 1, 0, 1 B = 0, 0, 1, 1 The output sequence Y = A B will be: Y = 0 0, 1 0, 0 1, 1