Question:
The output F of the digital circuit shown can be written in the form _________
The output F of the digital circuit shown can be written in the form _________
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In digital circuits, it's important to trace the logic flow through gates and multiplexers to determine the correct Boolean expression for the output.
Updated On: Nov 25, 2025
- ( \overline{A} \cdot \overline{B} \)
- ( \overline{A} + \overline{B} \)
- ( A + \overline{B} \)
- ( \overline{A} \cdot B \)
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The Correct Option is A, B
Solution and Explanation
Step 1: Analyzing the logic circuit.
In the given circuit, the output is derived from the inputs \( A \) and \( B \) through two different logic gates. The MUX (multiplexer) switches the logic levels based on the value of \( S_0 \), and the output follows the pattern defined by the combination of \( A \) and \( B \). Step 2: Analyzing the options.
- (A) Correct, the output is the AND operation between \( \overline{A} \) and \( \overline{B} \), representing the combination of the inputs via the logic gates.
- (B) Correct, this option represents a logical OR between \( \overline{A} \) and \( \overline{B} \), which is another possible representation of the output.
- (C) Incorrect, this represents an OR operation but with \( A \) instead of \( \overline{A} \), which doesn't match the given logic gate function.
- (D) Incorrect, this represents an AND operation between \( \overline{A} \) and \( B \), which doesn't match the actual circuit behavior. Step 3: Conclusion.
Thus, the correct answers are (A) and (B).
In the given circuit, the output is derived from the inputs \( A \) and \( B \) through two different logic gates. The MUX (multiplexer) switches the logic levels based on the value of \( S_0 \), and the output follows the pattern defined by the combination of \( A \) and \( B \). Step 2: Analyzing the options.
- (A) Correct, the output is the AND operation between \( \overline{A} \) and \( \overline{B} \), representing the combination of the inputs via the logic gates.
- (B) Correct, this option represents a logical OR between \( \overline{A} \) and \( \overline{B} \), which is another possible representation of the output.
- (C) Incorrect, this represents an OR operation but with \( A \) instead of \( \overline{A} \), which doesn't match the given logic gate function.
- (D) Incorrect, this represents an AND operation between \( \overline{A} \) and \( B \), which doesn't match the actual circuit behavior. Step 3: Conclusion.
Thus, the correct answers are (A) and (B).
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