A logic circuit has two inputs A and B . These inputs are fed simultaneously into a NAND gate and an OR gate. The outputs of these two gates are then connected to the inputs of an unknown logic gate ' X '. If the final output of the entire circuit is found to be equivalent to that of an XOR gate, identify the logic gate ' X '.

Step-by-step solution

Let the inputs be A and B . The output of the NAND gate is Y₁ = AB = A + B . The output of the OR gate is Y₂ = A + B . The final output Y is given to be equivalent to an XOR gate, so Y = A B = A B + A B . We need to find the operation of gate X such that Y₁ [X] Y₂ = Y . Let us test the AND operation for gate X : Y = Y₁ Y₂ Y = ( A + B ) (A + B) Y = A A + A B + B A + B B Y = 0 + A B + A B + 0 Y = A B + A B This matches the XOR gate expression. Therefore, the unknown gate ' X ' must be an AND gate. Answer: AND gate