Question

In the following combination of logic gates, the output \( Y \) can be written in terms of inputs \( A \) and \( B \) as

• A. \( (A \cdot B) + (A' \cdot B) \)
• B. \( (A \cdot B) + (A' \cdot B') \)
• C. \( (A \cdot B') + (A \cdot B) \)
• D. \( (A \cdot B) + (A' \cdot B') \)

Hint:

The combination of AND and OR gates can be simplified by writing down the individual logic operations and applying the rules of Boolean algebra.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to determine the Boolean expression for the final output \( Y \) by tracing the logic signals through each gate.
Step 2: Detailed Explanation:
Looking at the circuit:
1. The top input is \( A \), and the bottom input is \( B \).
2. Input \( A \) goes into a NOT gate, giving \( \overline{A} \).
3. Input \( B \) goes into a NOT gate, giving \( \overline{B} \).
4. The first AND gate (top) receives \( \overline{A} \) and \( B \). Its output is \( \overline{A} \cdot B \).
5. The second AND gate (bottom) receives \( A \) and \( \overline{B} \). Its output is \( A \cdot \overline{B} \).
6. These two outputs enter an OR gate. The final output is \( Y = (\overline{A} \cdot B) + (A \cdot \overline{B}) \).
Step 4: Final Answer:
The output is \( (A \cdot \overline{B}) + (\overline{A} \cdot B) \), which is the XOR operation.