Question

Identify the correct truth table of the given logic circuit. 

• A. A
• B. B
• C. C
• D. D

Hint:

Always reduce complex logic circuits into Boolean expressions before drawing the truth table.

Answer 1

The Correct Option is B

Step 1: Identify the logic gates used in the circuit.
From the diagram, the upper gate connected to input \( A \) is an AND gate with both inputs same, hence its output is \[ A \cdot A = A \] The lower left gate is a NAND gate with inputs \( A \) and \( B \), producing output \[ (A \cdot B)' \]
Step 2: Analyze the middle gate.
The output of the NAND gate is fed into an AND gate whose both inputs are the same, so its output remains \[ (A \cdot B)' \]
Step 3: Write expression for final output.
The final gate is an AND gate combining the two signals, hence \[ Y = A \cdot (A \cdot B)' \]
Step 4: Simplify the Boolean expression.
Using Boolean algebra, \[ (A \cdot B)' = A' + B' \] \[ Y = A(A' + B') = AA' + AB' = AB' \]
Step 5: Construct the truth table from the expression \( Y = AB' \).
\[ \begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \hline \end{array} \]
This matches exactly with Option (B).