In Boolean expression, a gate may be expressed as `Y=bar(A+B)`. Which one of the following is it?

Options

A. OR gate
B. AND gate
C. NOR gate
D. NAND gate

Explanation

To determine which gate is represented by the Boolean expression \( Y = \overline{(A + B)} \), we can follow these steps:

### Step 1: Understand the Expression
The expression \( Y = \overline{(A + B)} \) means that we first perform the OR operation on \( A \) and \( B \), and then we take the NOT of the result.

### Step 2: Create a Truth Table
To analyze this expression, we can create a truth table for \( Y \):

| A | B | A + B | Y = \overline{(A + B)} |
|---|---|-------|------------------------|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |

### Step 3: Analyze the Truth Table
From the truth table:
- When both \( A \) and \( B \) are 0, \( Y \) is 1.
- When either \( A \) or \( B \) is 1 (or both), \( Y \) is 0.

### Step 4: Identify the Gate
The truth table we created matches the behavior of a NOR gate. A NOR gate outputs 1 only when both inputs are 0.

### Conclusion
Thus, the Boolean expression \( Y = \overline{(A + B)} \) corresponds to a NOR gate.

### Final Answer
The gate represented by the expression \( Y = \overline{(A + B)} \) is a **NOR gate**.

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