Question

A 10-bit ADC has a reference voltage of 10.24 V. The resolution (step size) of the converter is:

• A. \(1\text{ mV}\)
• B. \(10\text{ mV}\)
• C. \(10.24\text{ mV}\)
• D. \(100\text{ mV}\)

Hint:

To get quick resolution estimates for converters, use \( \text{Resolution} \approx \frac{V_{\text{ref}}}{2^n} \). Powers of 2 are highly structured: \( 2^{10} = 1024 \). Dividing \( 10.24 \) by \( 1024 \) yields exactly \( 0.01\text{ V} \), which translates to \( 10\text{ mV} \) immediately.

Answer 1

The Correct Option is B

Concept: The resolution of an Analog-to-Digital Converter (ADC) determines the smallest change in the analog input voltage signal that can produce a change in the digital output code. It represents the step size of the converter and is quantified mathematically as the total input reference voltage range divided by the total number of discrete step levels. Key formula used here:
• Resolution (Step Size) = \( \frac{V_{\text{ref}}}{2^n - 1} \) or sometimes approximated as \( \frac{V_{\text{ref}}}{2^n} \) for large \( n \) values in practical applications. Let's calculate using the precise discrete-step representation.

Step 1: Identify the specified operational parameters.
From the problem description, we extract:
• Number of bits (\( n \)) = \( 10 \)
• Full-scale reference voltage (\( V_{\text{ref}} \)) = \( 10.24\text{ V} \)

Step 2: Compute the total number of intervals or quantization levels.
For a converter featuring \( n = 10 \) bits, the total number of binary output states possible is: \[ 2^n = 2^{10} = 1024 \] The total number of discrete measurement steps or intervals between these levels is: \[ 2^n - 1 = 1024 - 1 = 1023 \] Note: In standard electrical engineering ADC problems, standard definitions often define resolution as either step size \( \frac{V_{\text{ref}}}{2^n} \) or full-range division over \( 2^n - 1 \). Let's evaluate both to see which matches standard multi-choice thresholds. \[ \text{Using } 2^n \text{ framework:} \quad \text{Resolution} = \frac{10.24\text{ V}}{1024} = 0.01\text{ V} \] \[ \text{Using } 2^n - 1 \text{ framework:} \quad \text{Resolution} = \frac{10.24\text{ V}}{1023} \approx 0.01000977\text{ V} \]

Step 3: Convert the voltage units to millivolts.
Converting the calculated step size from volts to millivolts (\( 1\text{ V} = 1000\text{ mV} \)): \[ \text{Resolution} = 0.01\text{ V} \times 1000\text{ mV/V} = 10\text{ mV} \] This precisely and cleanly matches Option (B).