GATE CS 2001 Q2.11 — Combinational Circuits

For a $2:1$ multiplexer with select line $c$, input $a$ (selected when $c=0$), and input $b$ (selected when $c=1$), the output expression is:

From the given circuit diagram:

• The select line is connected to $X_1$, so $c = X_1$.
• The upper input (corresponding to $c=0$) is $a = X_2'$.
• The lower input (corresponding to $c=1$) is $b = X_2$.

Substituting these values into the MUX output expression:

This is the boolean expression for the XNOR gate, which corresponds to Option C.