ADC quantization - LSB random?
Quantisation is a natural by-product of the sampling and conversion process; we normally have some external front end circuitry.

Virtually all ADCs will have a sample and hold at the front end; just how this is converted depends on the specific ADC architecture.

As ultimately a decision threshold circuit determines whether a particular bit converts as a 1 or 0, the precision of that threshold is what determines just where the quantiser gives a 1 or 0.

There is no 'rounding' circuit as such.