Using a HX711 amplifier with a current shunt

My main problem from the beginning is that (from what I have read) the Arduino won't be able to read with enough accuracy the voltage drop (since it is only 100 mV). That is why I wanted an amplifier, to see if it was possible to raise the voltage range to 0-5V and then read it, instead of the 0-100 mV that the shunt will give.

Amplifing the signal is no problem.
Achieving 12 bit accuracy with something you can build by hand is the problem.

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so your suggestion would be to use a simple amplifier?

I have no solution that will give you 12 bit accuracy (0.0244%).
With off-the-shelf modules you might achieve a 1% to 2% accuracy

What is the motor's voltage?
What is the motor's full load current?
What is the motor's stall current?

From my understanding op wants 15 bit accuracy to get reasonable precision directly from the shunt resistor.
Advice: amplify 100mV signal by a factor of 10 and take 1.1V reference.
Or amplify by 50 and take 5V reference.
10 bit accuracy will be more than fine.

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Untill you do, there is not much more I can suggest.

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