Convert ADC Bins into Voltage [closed]

Question

Let's say I have a 12-bit Analog to Digital Converter (4096 bins). And let's say I have a signal from 0 to 5 Volts.

What is the proper conversion formula to convert ADC bins into Volts?

V = ADC / 4096 * 5

or

V = ADC / 4095 * 5

Do I divide by 4096 because there are 4096 bins in the ADC?

Or do I divide by 4095 because that is the highest value that the ADC returns?

Answer 1

Brian's suggestion about checking ADC datasheet is ideal. BUT! Assuming your maximum voltage (5V) equates to the maximum ADC input (12-bits = 4095), the following conversion should work for you:

const float maxAdcBits = 4095.0f; // Using Float for clarity
const float maxVolts = 5.0f;      // Using Float for clarity
const float voltsPerBit = (maxVolts / maxAdcBits);

float yourVoltage = ADCReading * voltsPerBit;

A quick inspection of the math with Excel leads me to believe this is correct.

Answer 2

V = ADC / 4096 * 5

is the correct formula for converting the digital value back to (an approximation of) the analog voltage.

This is according to The Data Conversion Handbook, edited by Walt Kester (Newnes, 2005), and available at (as of 2018/10/18) at:

https://www.analog.com/en/education/education-library/data-conversion-handbook.html

See in particular Figures 2.4 and 2.5 in Chapter 2:

In your case, FS would be 5 V. (And of course you're using a 12-bit ADC, not a 3-bit one.) Note that even if the ADC value is the maximum possible value (4095 in your case), the corresponding analog voltage will be slightly less than the "full-scale" voltage (5 V in your case).