*Question E8A09:
How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?*  

*Correct Answer is  D: 256*  

### AI Response: (may contain errors)  

To determine how many different input levels can be encoded by an analog-to-digital converter (ADC) with 8-bit resolution, we can use the following reasoning:

1. **Understanding Bit Resolution**: 
   - An 8-bit ADC can represent values using 8 bits. Each bit can be either 0 or 1, which means there are $2^n$ possible combinations for $n$ bits.
   - For 8 bits, the number of different levels is calculated as:
   $$ 
   2^8 = 256 
   $$

2. **Correct Answer**: 
   - The correct answer is **D: 256**. This is because an 8-bit ADC can encode 256 distinct levels, ranging from 0 to 255.

3. **Why Other Choices Are Incorrect**:
   - **A: 8**: This choice incorrectly suggests that there are only 8 levels, which would be true for a 3-bit ADC ($2^3 = 8$).
   - **B: 8 multiplied by the gain of the input amplifier**: This choice misinterprets the relationship between bit resolution and input levels. The gain of the amplifier does not affect the number of levels an ADC can encode; it affects the amplitude of the input signal.
   - **C: 256 divided by the gain of the input amplifier**: Similar to choice B, this option incorrectly suggests that the gain of the amplifier alters the number of levels. The gain affects the signal's amplitude but not the quantization levels of the ADC.

4. **Summary**:
   - An 8-bit ADC can encode **256** different input levels, which is derived from the formula $2^n$ where $n$ is the number of bits. The gain of the input amplifier does not change the number of levels that the ADC can represent.