An analog input card can convert a -10V to +10V signal into a digital value of 0-27648
For an input of 0 V the obvious digital output would be 27648 / 2. How will you generate that from your formula?
I don't know the device you have in mind but I suspect that the ADC will need both positive and negative references.



simulate this circuit &ndash; Schematic created using CircuitLab
Figure 1. Output vs input.
I'd go with
$$ out = 2^{n}\frac {V_{in}}{2V_{ref}}+ 2^{n-1} $$
$$ out = 2^{n}\left(\frac {V_{in}}{2V_{ref}}+ \frac 1 2\right) $$