The number of bits in an A/D converter is only related to the number of comparators for a "flash" type converter. For all other types the number of comparators is just one or a few. In a Successive-Approximation type, for example, there is only one comparator, with the number of bits determined by how many approximation measurements are made using the successive-approximation algorithm. 12 approximations will give a 12-bit result.
In the case of a Sigma-Delta converter, the number of effective bit resolution is determined by the number of quantizer bits, the oversample rate, and the degree of digital filtering. The number of bits is then determined by the theoretical signal to noise that this combination produces. For example a 72dB signal to noise ratio would correspond approximately to a 12-bit converter.