*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 function of a two-input exclusive NOR (XNOR) gate. Let's break down the correct answer and the reasoning behind it.

### Correct Answer Explanation:
- **Correct Answer**: It produces a 0 at its output if one and only one of its inputs is 1.
  
The XNOR gate outputs a high signal (1) when both inputs are the same (either both 0 or both 1). Therefore, it outputs a low signal (0) when one input is 1 and the other is 0. This behavior can be summarized as follows:
- If both inputs are 0: Output = 1
- If both inputs are 1: Output = 1
- If one input is 0 and the other is 1: Output = 0

### Why the Other Choices are Incorrect:
- **Choice A**: It produces a 0 at its output only if all inputs are 0.
  - This is incorrect because the XNOR gate outputs 1 when both inputs are 0, not 0.

- **Choice B**: It produces a 1 at its output only if all inputs are 1.
  - This is incorrect because the XNOR gate outputs 1 when both inputs are the same, which includes the case when both are 0.

- **Choice D**: It produces a 1 at its output if one and only one input is 1.
  - This is incorrect because the XNOR gate outputs 0 when one input is 1 and the other is 0, not 1.

### Summary of XNOR Logic:
The truth table for a two-input XNOR gate is as follows:

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

### Rule of Thumb:
- An XNOR gate can be thought of as the complement of an XOR gate. If you know that an XOR gate outputs 1 when the inputs are different, then the XNOR gate outputs 1 when the inputs are the same.

This understanding of the XNOR gate will help you answer similar questions on the exam.