Question

The output \( Y \) of the following logic circuit for given inputs is: 

• A. A · B(A + B)
• B. \( A \cdot B \)
• C. \( 0 \)
• D. \( A \cdot B \)

Hint:

To analyze a logic circuit, break it down gate by gate and construct a truth table. If all outputs are zero for every input combination, the circuit always outputs zero.

Answer 1

The Correct Option is C

Step 1: Understanding the Circuit 
The given circuit consists of: - A NOR gate producing \( (A + \overline{B}) \), - An AND gate taking \( (A + \overline{B}) \) and \( \overline{A} \cdot B \) as inputs, - A final truth table evaluation. 
Step 2: Determining the Boolean Expression 
The circuit expression is given as: \[ Y = (A + \overline{B}) \cdot (\overline{A} \cdot B) \] 
Step 3: Constructing the Truth Table 

From the table, we observe that for all inputs, the output remains \( 0 \). 
Step 4: Conclusion 
Since the output of the circuit is always \( 0 \), the correct answer is \( Y = 0 \).

 Final Answer: The output \( Y \) is always \( 0 \).