Question
What is the minimum number of bits required to sample a signal with a range of 1 volt at a resolution of 1 millivolt?
Answer Options
- A) 4 bits
- B) 6 bits
- C) 8 bits
- D) 10 bits
Correct Answer: D
Explanation
The number of bits used by an Analog-to-Digital Converter (\text{ADC}) determines its digital resolution—the smallest change in voltage it can detect. The number of unique discrete steps, or levels, that an \text{N}-bit \text{ADC} can measure is 2^N. To find the required number of bits, the desired resolution must first be determined.
The desired resolution is 1 \text{ millivolt} over a total range of 1 \text{ volt}. This means the total range must be divided into 1 \text{ V} / 0.001 \text{ V} = 1000 discrete steps. We must find the smallest number of bits (N) such that 2^N \ge 1000. Since 2^9 = 512 (too few) and 2^{10} = 1024, the minimum number of bits required is \mathbf{10 \text{ bits}}.
This topic was automatically created to facilitate community discussion about this exam question. Feel free to share study tips, memory tricks, or additional explanations!