QB_PH_SEC8_008: Digital Electronics

What is the resolution (in mV) of an 8-bit digital-to-analog converter (DAC) having a full-scale reference output voltage of $V_{\text{ref}} = 5.10\text{ V}$? (Round off to the nearest integer)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **DAC Step Size Formulation**: For an $n$-bit DAC with full-scale voltage $V_{\text{FS}}$: $\Delta V = \frac{V_{\text{FS}}}{2^n - 1}$ 2. **Numerical Substitution**: - Number of bits: $n = 8 \implies 2^n - 1 = 256 - 1 = 255$ levels. - $V_{\text{FS}} = 5.10\text{ V}$ $\Delta V = \frac{5.10\text{ V}}{255} = 0.020\text{ V} = 20\text{ mV}$ 3. **Nearest Integer**: 20 mV.