Question

The resultant gate and its Boolean expression for the given circuit is

• A. OR, \( A + B \)
• B. NOR, \( \overline{A + B} \)
• C. NAND, \( \overline{A \cdot B} \)
• D. AND, \( A \cdot B \)

Hint:

In logic circuits, OR gates give an output of \( 1 \) when at least one input is \( 1 \). Use the gate operation rules to determine the correct Boolean expression.

Answer 1

The Correct Option is A

Step 1: Analyzing the circuit.
The circuit consists of an OR gate followed by a NOT gate (inverter). The OR gate gives the output \( A + B \), and the NOT gate inverts the output to produce \( \overline{A + B} \).
Step 2: Boolean expression.
The output of the circuit is given by the expression \( A + B \), and the NOT gate inverts it. The final Boolean expression is \( A + B \).
Step 3: Conclusion.
The correct Boolean expression is \( A + B \), corresponding to option (A) OR gate.