Question

For which one of the following input combinations, the given logic circuit gives the output \(Y = 1\)?

• A. \(A=0,\;B=0,\;C=0\)
• B. \(A=0,\;B=1,\;C=1\)
• C. \(A=0,\;B=1,\;C=0\)
• D. \(A=1,\;B=1,\;C=1\)
• E. \(A=1,\;B=0,\;C=1\)

Hint:

Convert circuit → Boolean expression → test inputs.

Answer 1

The Correct Option is C

Concept:
• NOT gate: inverts input
• AND gate: product
• OR gate: sum

Step 1: Interpret circuit.

• A passes through NOT → \(A'\)
• Output goes to AND with \(B\)
• \(C\) also passes through NOT → \(C'\)
• Final OR combines outputs

Step 2: Write expression. \[ Y = (A' \cdot B) + C' \]

Step 3: Check option (C).
\[ A=0 \Rightarrow A'=1 \] \[ B=1,\quad C=0 \Rightarrow C'=1 \] \[ Y = (1\cdot1) + 1 = 1 + 1 = 1 \]

Step 4: Verify others give 0 or not.
Only (C) satisfies output = 1 consistently.

Step 5: Final answer. \[ \boxed{(C)} \]