Sensitivity and Resolution of Strain Gauges with the ADC

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Joined Oct 12, 2022
In an assigned exercise I have 6 strain gauges with:
- a range of [-5000uε .. 5000uε]
- S = 2uε/Volt
They are connected to the CAN bus, and an ADC with 18 bits and Vref = 5V is used.

1) Calculate the maximum voltage output range of the strain gauges based on the sensitivity and strain range, and determine the resolution of strain measurement (in uε) that can be achieved with 18 bit ADC.
2) If the strain reading from one of the measurement nodes is -1200uε .. calculate the digital value trasmitted over the CAN bus with the 18 bit ADC.

The range of [-5000uε .. 5000uε] correspond to 10000 uε total
deltaVout = 10000 / S = 10000 / 2 [uε/(uε/V)] = 5000V (max output voltage range)
resolution = 10000*1/(2^18) = 3.81*10^-6 uε
I just don't understand how to do this point. I have the solution, but I don't know how it got there.
The formula used is: Vin = n*Vref / 2^18 --> n = Vin*2^18 / Vref = 99614

Why this formula? How do you get there? How much is Vin?