Question

A 10-bit ADC has a full-scale of 10.230 V, when the digital output is \( (11 \, 1111 \, 1111)_2 \). The quantization error of the ADC in millivolt is \(\underline{\hspace{2cm}}\).

Hint:

For an ADC, the quantization error is half of the step size, and the step size can be calculated as the full scale divided by \( 2^{\text{Number of Bits}} \).

Answer 1

Correct Answer: 4.9

For a 10-bit ADC, the quantization error is the difference between two successive quantization levels. The quantization step size \( \Delta \) is given by:
\[ \Delta = \frac{\text{Full Scale}}{2^{\text{Number of Bits}}} \] Here, the full scale is \( 10.230 \, \text{V} \), and the number of bits is 10. Thus: \[ \Delta = \frac{10.230}{1024} \approx 0.010 \, \text{V}. \] The quantization error is half the step size: \[ \text{Quantization Error} = \frac{\Delta}{2} \approx \frac{0.010}{2} = 0.005 \, \text{V} = 5 \, \text{mV}. \] Thus, the quantization error is \( 5 \, \text{mV} \).