). with the input voltage range set at +/- 500mv, what is the smallest difference in voltage that can be resolved? show your calculation.

The smallest difference in voltage that can be resolved is referred to as the resolution. The resolution can be calculated with the following formula:
resolution=voltage range / digital range
The voltage range in our case is from -500mV to 500mV, which gives 1000mV.
The digital range on the other hand is 2^(number of bits).
It depends on what type of bit board we are using. If the ADC we are using is a 16 bit board, then 2^16=65536.
So, the resolution is:
resolution=1000mV/65536=0.015 mV

What is the things about?

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