Which logic gate corresponds to the logical equation `Y =bar(A+B)` ?

Options

A. NAND
B. NOR
C. AND
D. Or

Explanation

To determine which logic gate corresponds to the logical equation \( Y = \overline{(A + B)} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Equation**: The equation \( Y = \overline{(A + B)} \) indicates that we are dealing with an OR operation followed by a NOT operation. The expression \( A + B \) represents the logical OR of inputs A and B.

2. **Identify the OR Operation**: The OR operation outputs true (1) if at least one of the inputs is true (1). The truth table for the OR operation is as follows:
- If \( A = 0 \) and \( B = 0 \), then \( A + B = 0 \)
- If \( A = 0 \) and \( B = 1 \), then \( A + B = 1 \)
- If \( A = 1 \) and \( B = 0 \), then \( A + B = 1 \)
- If \( A = 1 \) and \( B = 1 \), then \( A + B = 1 \)

3. **Apply the NOT Operation**: The NOT operation (denoted by the overline) inverts the output of the OR operation. Thus, we take the complement of the results from the OR operation:
- If \( A + B = 0 \), then \( \overline{(A + B)} = 1 \)
- If \( A + B = 1 \), then \( \overline{(A + B)} = 0 \)

4. **Construct the Truth Table**: Now we can create the truth table for the entire expression \( Y = \overline{(A + B)} \):
- If \( A = 0 \) and \( B = 0 \), then \( Y = 1 \)
- If \( A = 0 \) and \( B = 1 \), then \( Y = 0 \)
- If \( A = 1 \) and \( B = 0 \), then \( Y = 0 \)
- If \( A = 1 \) and \( B = 1 \), then \( Y = 0 \)

The truth table looks like this:

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

5. **Identify the Logic Gate**: The truth table we constructed corresponds to the behavior of a NOR gate. A NOR gate outputs true (1) only when both inputs are false (0).

### Conclusion:
The logic gate that corresponds to the logical equation \( Y = \overline{(A + B)} \) is the **NOR gate**.