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: Circuit Analysis
The circuit comprises: - A NOR gate yielding \( (A + \overline{B}) \), - An AND gate receiving \( (A + \overline{B}) \) and \( \overline{A} \cdot B \) as inputs, - A final truth table assessment. 
Step 2: Boolean Expression Derivation 
The circuit's expression is formulated as: \[ Y = (A + \overline{B}) \cdot (\overline{A} \cdot B) \] 
Step 3: Truth Table Construction 

Observation from the table indicates a constant output of \( 0 \) for all input combinations. 
Step 4: Determination 
Given that the circuit's output is invariably \( 0 \), the established result is \( Y = 0 \).

 Final Output: The output \( Y \) is consistently \( 0 \).