A truth table is given, which of the following has this type of truth table?

Options

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

Answer

To determine which logic gate corresponds to the given truth table, we can follow these steps:

### Step 1: Understand the Truth Table
The truth table provided has two inputs, A and B, and one output, Y. The values for A are 0, 1, 0, 1, and for B are 0, 0, 1, 1. The output Y is given as 1, 0, 0, 0.

| A | B | Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |

### Step 2: Analyze the Output
From the truth table, we can see that:
- When both A and B are 0, Y is 1.
- When A is 0 and B is 1, Y is 0.
- When A is 1 and B is 0, Y is 0.
- When both A and B are 1, Y is 0.

### Step 3: Identify the Logic Gate
The output pattern matches the behavior of a NOR gate. The NOR gate outputs 1 only when both inputs are 0.

The logical expression for a NOR gate is:
\[ Y = \overline{A + B} \]
This means Y is true (1) only when both A and B are false (0).

### Step 4: Confirm with the Truth Table of NOR Gate
Let's confirm this with the truth table for a NOR gate:

| A | B | A + B | Y = ¬(A + B) |
|---|---|-------|--------------|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |

As we can see, the output Y matches perfectly with the provided truth table.

### Conclusion
The logic gate that corresponds to the given truth table is the NOR gate.