NIMCET 2008 — Computer PYQ

Step 1: First Gate (Leftmost)

The inputs are $x$ and $y$. The output of this NOR gate is:

Step 2: Second and Third Gates (Middle)

The second gate (top middle) has inputs $x$ and $G_1$:

Using De Morgan's Law ($\overline{A+B}=\bar{A}\cdot \bar{B}$):

The third gate (bottom middle) has inputs $y$ and $G_1$:

Applying De Morgan's Law:

Step 3: Fourth Gate (Final Output)

The final NOR gate takes $G_2$ and $G_3$ as inputs:

Step 4: Identify the Function

We know that the expression for an XOR (Exclusive OR) gate is:

Therefore, the final output is the inverse of XOR:

The function $\overline{\bar{x}y+x\bar{y}}$ is the definition of an Exclusive NOR (XNOR) gate.

Final Answer:

The correct option is (b) Exclusive NOR.