In a digital logic circuit, two input signals A and B are fed simultaneously into a NAND gate and an OR gate. Let the output of the NAND gate be Y₁ and the output of the OR gate be Y₂ . These two outputs Y₁ and Y₂ are then fed as inputs to an unknown logic gate 'X'. If the final output Y of the gate 'X' behaves exactly like an XOR gate for the inputs A and B , identify the logic gate 'X'.

Step-by-step solution

The intermediate outputs are given by: Y₁ = A B (Output of NAND gate) Y₂ = A + B (Output of OR gate) The final output Y is given to be equivalent to an XOR gate: Y = A B = A B + A B We need to find the operation of gate 'X' such that Y is produced from Y₁ and Y₂ . Let us check the AND operation for gate 'X': Y = Y₁ Y₂ = ( A B ) (A + B) Using De Morgan's Law, A B = A + B So, Y₁ Y₂ = ( A + B ) (A + B) = A A + A B + B A + B B Since A A = 0 and B B = 0 , we get: Y₁ Y₂ = A B + A B = A B Thus, the unknown gate 'X' must b