GATE EE 2016 Set 1 — Question 20
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Analog & Digital Electronics → Data Conversion Circuits → Resolution & Quantization Error
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Question
A temperature in the range of to is to be measured with a resolution of . The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is
Correct answer
(B) 10
Solution
To find the minimum number of ADC bits required, we need to determine the total number of discrete temperature intervals (or states) that must be resolved over the given temperature range.
Step 1: Calculate the Temperature Range (Span)
The temperature range to be measured is from to . The total span of the temperature is:$\text{Span} = T_{\max} - T_{\min} = 55^\circ\text{C} - (-40^\circ\text{C}) = 95^\circ\text{C}$---Step 2: Determine the Number of Required Intervals
The required resolution is . The minimum number of distinct levels () required to represent this range with the given resolution is:$N = \frac{\text{Span}}{\text{Resolution}} + 1 = \frac{95^\circ\text{C}}{0.1^\circ\text{C}} + 1 = 950 + 1 = 951$(Note: Even if we consider just the number of intervals, levels are required, which leads to the same result for the number of bits).---Step 3: Calculate the Minimum Number of Bits ()
An -bit ADC can represent distinct digital levels. To resolve at least levels, the number of bits must satisfy:Let us evaluate the powers of 2:- For : (Insufficient)
- For : (Insufficient)
- For : (Sufficient)
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