Is resolution strictly defined in volts?

Studiot

Bear in mind that for any A/D converter the step size is compared against an internal reference so is fixed.
In particular it does not depend upon the input voltage.
Each step will be in exactly the same place (at the same voltage) regardless of the input voltage.

So saying that the max input voltage or full scale input voltage equals 2000 mV and there are 1024 (8 bit) steps or that the resolution is 2000/1024 mV is one and the same thing.

I like Serena

Can't help responding, nitpicker that I am.
Sorry.

1024 is 10 bits (not 8 bits).

If there are 1024 levels, then there are 1023 steps.

It still depends on the specification of the chip what the stepsize is.
It could both be 2000/1024 mV or 2000/1023 mV (or even something else).
I, for one, certainly wouldn't make an assumption which one it is.
Only when I see it on an oscilloscope (or something like that) will I believe which one it is (for a specific chip).

Studiot

10 bits yes what was I thinking? Thanks.

However there is only one possible interpretation of the process that takes an input voltage and replaces it with a unique digital code with one of 1024 possible values.