*Question E7F06:
What is the minimum number of bits required to sample a signal with a range of 1 volt at a resolution of 1 millivolt?*  

*Correct Answer is  D: 10 bits*  

### AI Response: (may contain errors)  

To determine the minimum number of bits required to sample a signal with a range of 1 volt at a resolution of 1 millivolt, we can use the following approach:

1. **Understanding the Range and Resolution**:
   - The total range of the signal is 1 volt (from 0 to 1 V).
   - The resolution is 1 millivolt, which is $0.001$ volts.

2. **Calculating the Number of Levels**:
   - The number of discrete levels that can be represented within the range can be calculated by dividing the total range by the resolution:
   $$ 
   \text{Number of Levels} = \frac{\text{Range}}{\text{Resolution}} = \frac{1 \text{ V}}{0.001 \text{ V}} = 1000 
   $$

3. **Calculating the Number of Bits**:
   - The number of bits ($n$) required to represent a certain number of levels can be found using the formula:
   $$ 
   2^n \geq \text{Number of Levels} 
   $$
   - In this case, we need to find the smallest $n$ such that:
   $$ 
   2^n \geq 1000 
   $$

4. **Finding the Minimum Bits**:
   - Testing powers of 2:
     - $2^{10} = 1024$ (which is greater than 1000)
     - $2^9 = 512$ (which is less than 1000)
   - Therefore, the minimum number of bits required is $n = 10$.

### Summary of Choices:
- **Correct Answer: D: 10 bits**
  - This is correct because it allows for 1024 discrete levels, which is sufficient to cover the 1000 levels needed for a 1 V range at 1 mV resolution.

- **Incorrect Choices**:
  - **A: 4 bits**
    - $2^4 = 16$ levels, which is far too few for 1000 levels.
  - **B: 6 bits**
    - $2^6 = 64$ levels, still insufficient for 1000 levels.
  - **C: 8 bits**
    - $2^8 = 256$ levels, which does not meet the requirement of 1000 levels.

### Conclusion:
To sample a 1 V signal with a resolution of 1 mV, you need at least 10 bits to ensure you can represent all possible values accurately.