GATE CS 1994 Q1.8 — Combinational Circuits

To find the logic expression for the output of the given circuit, we can trace the output of each gate step-by-step from the inputs:

1. NAND Gate: The inputs are $A$ and $B$. The output of this gate is: $$G_1 = \overline{AB}$$
2. First AND Gate: The inputs are the output of the NAND gate ($G_1$) and $C$. The output of this gate is: $$G_2 = G_1 \cdot C = (\overline{AB})C$$
3. Second AND Gate: The inputs are $C$ and $D$. The output of this gate is: $$G_3 = CD$$
4. OR Gate (Final Output): The final output combines the outputs of the two AND gates ($G_2$ and $G_3$): $$Y = G_2 + G_3 = (\overline{AB})C + CD$$

Now, we simplify the expression using De Morgan's Law ($\overline{AB} = \overline{A} + \overline{B}$):

This matches the expression given in Option B.