Final answer:
To achieve a resolution of 10 mV for an ADC with a 5 V range, a word length of 9 bits is required, as this allows for 512 discrete steps, covering the entire voltage range.
Step-by-step explanation:
To determine the word length required for an analog-to-digital converter (ADC) with a specified resolution, we can start by understanding the relationship between resolution, word length, and voltage range. The resolution of an ADC is the smallest change in voltage it can detect. In this case, a resolution of 10 mV means that each step or 'word' the ADC can discern should represent a 10 mV change in analog voltage.
The voltage range for the sensor is from 0 V to 5 V, which is a total of 5000 mV. To find out how many steps are needed, we divide the total voltage range by the resolution: 5000 mV / 10 mV = 500 steps. Since the number of steps an ADC can take is 2 to the power of the word length (bits), we need to find the smallest number of bits such that 2n ≥ 500. Through trial and error or by using a logarithmic calculation, we can find that 29 = 512, which is slightly more than 500. Therefore, the word length needed is 9 bits.
It's important to note that while the resolution determines the ADC's sensitivity to voltage changes, the word length affects both the resolution and the total voltage range it can handle.