Answer:
0.0002441 volts
Explanation:
You want to know the resolution of a data acquisition system with a 12-bit A/D converter that has a 10V range, if it follows an amplifier with a gain of 10.
Input range
The ×10 amplifier in front of the A/D converter means an input of 1V will be amplified to the 10V full-scale level at the A/D converter.
Interval between output codes
The converter divides that 1V range into 2^12 (equal) intervals, each with its own unique output code. The resolution at the input of the system will be ...
(1V)/(2^12) = 1/4096 V ≈ 0.0002441 V
The resolution in volts of the data acquisition system is about 0.0002441 volts.
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Additional comment
This number assumes the A/D converter is perfectly linear, and there are no missing codes. An actual A/D converter specification usually includes a specification on non-linearity that tells how the "bit width" varies over the input range. Some output codes may be different by a relatively small fraction of 244.1 µV, while others may be different by almost twice that (or even more).
Usually, the linearity of the ×10 amplifier can be taken for granted. In some cases, however, that may also be a factor in the apparent resolution of the data acquisition system.
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