Dear Jacki_2016,

If I understand your question correctly, I think what you are asking is what are the consequences if an N bit ideal A/D has an accuracy limitation such that it is accurate to N - 1 bit.

Do you know if the error mechanism results in an error with a specific PDF or bias or are the errors truly random? If the probability of an error is  random, then the linearity of your N bit A/D will be no better than that for a (N-1) bit A/D. The histogram in that case, if I understand what your notion of a histogram is, will show it to be a N-1 bit quantizer in lieu of an N bit quantizer.

Does this help Jacki_2016, or did I misunderstand your question?
Shawn