Question

The logic block shown has an output \( F \) given by _________

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

Hint:

When analyzing logic circuits, trace the signal flow step by step and apply the logic gate rules (AND, OR, NOT).

Answer 1

The Correct Option is D

Step 1: Analyzing the circuit.
The circuit consists of NOT gates and AND gates. First, observe the inputs \( A \) and \( B \). The NOT gate applied to \( B \) gives \( \overline{B} \). Then, the output of this NOT gate is connected to an AND gate, which is the final output \( F \). Since there is no involvement of other terms or combinations, the output of the circuit will simply be \( \overline{B} \). Step 2: Analyzing the options.
- (A) Incorrect, the output is not just \( A + B \), which would require an OR gate, but there is no indication of an OR gate in the circuit.
- (B) Incorrect, \( A \cdot B \) would be the output of an AND gate involving both inputs, but there is no AND gate using both inputs.
- (C) Incorrect, \( A + \overline{B} \) would be the result of an OR gate combining \( A \) and the inverted \( B \), but the circuit shows a simpler configuration.
- (D) Correct, the final output is simply \( \overline{B} \), as determined by the NOT gate applied to \( B \). Step 3: Conclusion.
The correct answer is (D) \( \overline{B} \).