Question

Logic circuit shows the inputs $A$, $B$ and $C$. The output $Y$ is ‘0’ (zero) when

• A. $A = 1,\ B = 0,\ C = 1$
• B. $A = 1,\ B = 1,\ C = 0$
• C. $A = 1,\ B = 1,\ C = 1$
• D. $A = 0,\ B = 1,\ C = 1$

Hint:

Always convert logic circuits into Boolean expressions before evaluating input conditions.

Answer 1

The Correct Option is C

Step 1: Identify the logic gates.
From the circuit diagram: - Input $A$ passes through a NOT gate.
- Inputs $B$ and $C$ pass through a NAND gate.
- Outputs of NOT and NAND gates are connected to an OR gate.
Step 2: Write expressions for each gate output.
Output of NOT gate: \[ \overline{A} \] Output of NAND gate: \[ \overline{BC} \] Step 3: Write the final output expression.
\[ Y = \overline{A} + \overline{BC} \] Step 4: Check option (C).
For $A = 1,\ B = 1,\ C = 1$: \[ \overline{A} = 0,\quad \overline{BC} = \overline{1} = 0 \] \[ Y = 0 + 0 = 0 \]