GATE CS 1999 Q2.8 — Combinational Circuits

The given sequential circuit consists of two cross-coupled gates:

• A 2-input NOR gate with inputs $A$ and $Z$ (the output of the NAND gate), producing the output $Y$.
• A 3-input NAND gate with inputs $B$, $C$, and the feedback signal $Y$, producing the output $Z$.

We are given that in the steady state, the line $Y = 1$. Let us analyze the gates under this condition:

1. Analyze the NOR gate:

   The output of the NOR gate is given by:

   $$Y = \overline{A + Z}$$

   For $Y = 1$, the input to the NOR gate must be $0$:

   $$A + Z = 0 \implies A = 0 \quad \text{and} \quad Z = 0$$
2. Analyze the NAND gate:

   The output of the NAND gate is given by:

   $$Z = \overline{B \cdot C \cdot Y}$$

   Since we established $Z = 0$, the inputs to the NAND gate must all be $1$:

   $$B \cdot C \cdot Y = 1$$

   Since $Y = 1$, this simplifies to:

   $$B \cdot C = 1 \implies B = 1 \quad \text{and} \quad C = 1$$

Combining these results, the only possible values in this steady state are:

$A = 0$, $B = 1$, and $C = 1$