Question

Resolution of an 8-bit ADC with 5V reference is

• A. \(5\text{ V} \)
• B. \(2.5\text{ V} \)
• C. \(19.5\text{ mV} \)
• D. \(39\text{ mV} \)

Hint:

Quick fractional shortcuts for common bit sizes: - 8-bit resolution scale factor is roughly \( \frac{1}{256} \approx 0.39% \) of total span. - \( 5\text{ V} / 256 \approx 19.53\text{ mV} \) Memorizing power-of-two divisions saves valuable calculation time during competitive multiple-choice exams!

Answer 1

The Correct Option is C

Concept: The resolution of an Analog-to-Digital Converter (ADC) represents the smallest step change in input voltage that can be detected and produce a change in the digital output code. It corresponds directly to the weight of the Least Significant Bit (LSB). Mathematically, the resolution for an $n$-bit ADC over a given reference voltage span $V_{\text{ref}}$ is defined by the expression: \[ \text{Resolution} = \frac{V_{\text{ref}}}{2^n - 1} \quad \left(\text{or occasionally approximated as } \frac{V_{\text{ref}}}{2^n}\right) \] Let us evaluate using the standard exact structural equation.

Step 1: Extracting values from the problem input.
From the problem description, we have:
• Number of bits, \( n = 8 \)
• Full-scale reference voltage, \( V_{\text{ref}} = 5\text{ V} \)

Step 2: Calculating total digital step intervals.
Calculate the total number of discrete step intervals ($2^n - 1$): \[ 2^n - 1 = 2^8 - 1 = 256 - 1 = 255 \]

Step 3: Computing numerical resolution value.
Substitute these integers into our resolution formula: \[ \text{Resolution} = \frac{5\text{ V}}{255} \] Performing the division long-hand: \[ \text{Resolution} \approx 0.0196078\text{ V} \] Let us convert this value into millivolts ($\text{mV}$) by multiplying by 1000: \[ \text{Resolution} \approx 0.0196078 \times 1000\text{ mV} \approx 19.6\text{ mV} \] If we use the closely related approximation formula $\frac{V_{\text{ref}}}{2^n}$: \[ \text{Resolution}_{\text{approx}} = \frac{5}{256} \approx 0.019531\text{ V} = 19.53\text{ mV} \] Both exact and approximate values lie extremely close to \(19.5\text{ mV}\), which matches option (3). Hence, the correct choice is option (3).