Name the gate , which represents the Boolean expression y = A. B for inputs A, B

Options

A. (a)AND
B. (b)NOR
C. (c)NAND
D. (d)NOT

Answer

To solve the question, we need to identify the logic gate that corresponds to the Boolean expression \( y = A \cdot B \).

### Step-by-Step Solution:

1. **Understanding the Boolean Expression**:
- The expression given is \( y = A \cdot B \). In Boolean algebra, the dot (·) represents the logical AND operation.

2. **Identifying the Logic Gate**:
- The logic gate that performs the AND operation is known as the AND gate. This gate outputs true (1) only when both inputs are true (1).

3. **Drawing the AND Gate**:
- An AND gate has two inputs (A and B) and one output (Y). The output Y will be true only when both A and B are true.

4. **Truth Table for the AND Gate**:
- The truth table for the AND gate is as follows:
- When \( A = 0 \) and \( B = 0 \), \( Y = 0 \)
- When \( A = 0 \) and \( B = 1 \), \( Y = 0 \)
- When \( A = 1 \) and \( B = 0 \), \( Y = 0 \)
- When \( A = 1 \) and \( B = 1 \), \( Y = 1 \)
- This confirms that the output is true only when both inputs are true.

5. **Conclusion**:
- Since the Boolean expression \( y = A \cdot B \) corresponds to the AND operation, we can conclude that the gate representing this expression is the **AND gate**.

### Final Answer:
The gate that represents the Boolean expression \( y = A \cdot B \) is the **AND gate**.

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