Question

An analog-to-digital converter with resolution 0.01 V converts analog signals between 0 V to +10 V to an unsigned binary output. The minimum number of bits (in integer) in the output is _________

Hint:

The number of bits required for an ADC can be calculated using the formula \( n = \lceil \log_2{\text{number of levels}} \rceil \).

Answer 1

Correct Answer: 10

The range of analog signals is from 0 V to +10 V, which is a difference of 10 V. The resolution of the ADC is 0.01 V. To determine the number of levels, we divide the range by the resolution: \[ \frac{10}{0.01} = 1000 \text{ levels}. \] To find the number of bits needed, we calculate the minimum number of bits \( n \) such that: \[ 2^n \geq 1000. \] Taking the logarithm base 2: \[ n \geq \log_2{1000} \approx 9.97. \] Rounding up, we find that the minimum number of bits is \( 10 \). Thus, the minimum number of bits in the output is \( 10 \).