A logic circuit has two inputs A and B . These inputs are fed simultaneously into an OR gate and a NAND gate. The outputs of these two gates are then connected to the inputs of an unknown logic gate G . The final output of the circuit is X . The truth table for the circuit is given below: A B X 0 0 0 0 1 1 1 0 1 1 1 0 Identify the logic gate G .

Step-by-step solution

Let the output of the OR gate be Y₁ and the output of the NAND gate be Y₂ . Y₁ = A + B Y₂ = A B The given truth table corresponds to the XOR operation, where the output X is 1 only when the inputs A and B are different. Let us check the outputs Y₁ and Y₂ for all combinations of A and B : If A=0, B=0 Y₁=0, Y₂=1 . We need X=0 . If A=0, B=1 Y₁=1, Y₂=1 . We need X=1 . If A=1, B=0 Y₁=1, Y₂=1 . We need X=1 . If A=1, B=1 Y₁=1, Y₂=0 . We need X=0 . Notice that X is exactly the logical AND of Y₁ and Y₂ . X = Y₁ Y₂ = (A + B)