*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)  

An analog-to-digital converter (ADC) with 8-bit resolution can encode a certain number of different input levels. The number of levels is determined by the resolution of the ADC.

### Explanation:

1. **Correct Answer: D: 256**

   - An 8-bit ADC can represent $2^8$ different levels. This is because each bit can be either 0 or 1, and with 8 bits, the total number of combinations is:
     $$2^8 = 256$$
   - Therefore, an 8-bit ADC can encode 256 different input levels.

2. **Why the other choices are incorrect:**

   - **A: 8**  
     This choice is incorrect because it suggests that the number of levels is equal to the number of bits, which is not true. The number of levels is $2^n$, where $n$ is the number of bits.

   - **B: 8 multiplied by the gain of the input amplifier**  
     This choice is incorrect because the number of levels is determined solely by the number of bits in the ADC, not by any external gain. The gain of the input amplifier affects the range of input voltages, not the number of levels.

   - **C: 256 divided by the gain of the input amplifier**  
     This choice is incorrect for similar reasons as choice B. The gain of the input amplifier does not affect the number of levels the ADC can encode. The number of levels remains $2^8 = 256$ regardless of the gain.

### Key Formula:

- For an ADC with $n$-bit resolution, the number of different input levels is:
  $$2^n$$

This formula is crucial for understanding how the resolution of an ADC determines its capability to encode different input levels.