*Question E7A09:
What logical operation is performed by a two-input exclusive NOR gate?*  

*Correct Answer is  C: It produces a 0 at its output if one and only one of its inputs is 1*  

### AI Response: (may contain errors)  

The question asks about the logical operation performed by a two-input exclusive NOR (XNOR) gate. Let's break down the operation of an XNOR gate:

### Explanation:

1. **XNOR Gate Operation:**
   - An XNOR gate outputs a `1` (true) if both inputs are the same, either both `0` or both `1`.
   - It outputs a `0` (false) if the inputs are different, meaning one is `0` and the other is `1`.

2. **Correct Answer:**
   - **C: It produces a 0 at its output if one and only one of its inputs is 1.**
     - This is correct because the XNOR gate outputs `0` when the inputs are different, which occurs when one input is `1` and the other is `0`.

3. **Why Other Choices Are Incorrect:**
   - **A: It produces a 0 at its output only if all inputs are 0.**
     - Incorrect. An XNOR gate outputs `1` when both inputs are `0`.
   - **B: It produces a 1 at its output only if all inputs are 1.**
     - Incorrect. While it does output `1` when both inputs are `1`, it also outputs `1` when both inputs are `0`.
   - **D: It produces a 1 at its output if one and only one input is 1.**
     - Incorrect. This describes the behavior of an XOR gate, not an XNOR gate.

### Truth Table for XNOR Gate:

| Input A | Input B | XNOR Output |
|---------|---------|-------------|
|    0    |    0    |      1      |
|    0    |    1    |      0      |
|    1    |    0    |      0      |
|    1    |    1    |      1      |

This truth table shows that the XNOR gate outputs `0` only when one input is `1` and the other is `0`, confirming the correct answer.