How to get these figures?

[MianQi]

I read an article here - How to use the ADXL345 accelerometer sensor it was said:

With the output resolution of ADXL345 being default to 10-bit, we can conclude that the change in acceleration of the object to which the ADXL345 is mounted must be at least 3.822 cm/s2 for +/- 2g or 7.64 cm/s2 for +/- 4g or 15.28 cm/s2 for +/- 8g or 30.57 cm/s2 for +/- 16g measurement range for 1-bit (LSB) change in the sensor response.

I want to know how to get this figures.

 

[tepalia02]

Calculate the resolution per bit:

• For a 10-bit resolution, each bit represents a fraction of the full-scale range.
• Resolution per bit = FSR / (2^10)

Convert this resolution into acceleration units (cm/s² in this case) based on the selected range:

• For ±2g range:
  • Resolution per bit = (±2g) / (1024 bits)
  • Calculate the value in cm/s² since 1g ≈ 9.81 m/s².
  • ≈ 0.00390625g/bit (in terms of gravity units)
    
    Convert gravity units to cm/s²:1g ≈ 9.81 m/s² ≈ 981 cm/s²
    
    0.00390625g/bit * 981 cm/s²/g ≈ 3.822 cm/s²/bit
    
    So, for the ±2g range of the ADXL345 accelerometer, each bit change in the sensor response corresponds to approximately 3.822 cm/s² of acceleration change.