How would you implement the Boolean expression A + B̅ using basic logic gates? 

Explanation:

The Boolean expression A + B̅ represents the logical OR operation between variable A and the negation (NOT operation) of variable B. This expression can be implemented using basic logic gates like OR and NOT gates. The "+" symbol in Boolean algebra denotes the OR operation, while the overline (B̅) represents the NOT operation applied to B.

Correct Option Analysis:

The correct option is:

Option 3: An OR gate with input A and the output of a NOT gate with input B.

This option correctly implements the Boolean expression A + B̅. The process involves two steps:

1. Negation of B: A NOT gate is used to invert the value of B. If B is 0, the NOT gate outputs 1; if B is 1, the NOT gate outputs 0. The output of this gate is B̅.
2. OR Operation: The OR gate takes two inputs: A and the output of the NOT gate (B̅). The OR gate outputs 1 if either A or B̅ is 1. This satisfies the Boolean expression A + B̅.

Implementation:

To implement the Boolean expression A + B̅, follow these steps:

1. Use a NOT gate to invert the input B. Connect the input B to the NOT gate, and the output will be B̅.
2. Connect the input A and the output of the NOT gate (B̅) to the inputs of an OR gate.
3. The output of the OR gate will represent the Boolean expression A + B̅.

Truth Table:

The truth table verifies that the output of the circuit matches the expected output of the Boolean expression A + B̅ for all possible combinations of inputs A and B.

as verified by the truth table. Understanding the functionality of basic logic gates is essential for designing and implementing digital circuits effectively.