Question

Output of the following logic circuit is:

• A. \( (\overline{A} + B) + (\overline{A} + \overline{C}) + (B + \overline{C}) \)
• B. \( (\overline{A} + B)(A + \overline{C})(B + \overline{C}) \)
• C. \( (\overline{A} + B)(\overline{A} + \overline{C})(B + \overline{C}) \)
• D. \( (\overline{A} + B) - (\overline{A} + \overline{C}) - (B + \overline{C}) \)

Hint:

Break complex logic circuits into smaller blocks. Use De Morgan’s laws and Boolean algebra for simplification.

Answer 1

The Correct Option is C

Analyzing the logic circuit from the diagram: - The circuit uses three OR gates and one AND gate. - First OR gate gives: \( (\overline{A} + B) \)
- Second OR gate gives: \( (\overline{A} + \overline{C}) \)
- Third OR gate gives: \( (B + \overline{C}) \)
- The final AND gate combines these outputs: \[ \Rightarrow (\overline{A} + B)(\overline{A} + \overline{C})(B + \overline{C}) \]