We are probably all familiar with comparators. A typical “inverting” comparator circuit is shown in Figure 1. Resistors R1 and R2 provide a reference voltage at the non-inverting input and the input voltage Vin is applied at the inverting input. Most comparators have open drain outputs so a...
You don't, even with a dedicated comparator - it's either ('equal or higher' and lower), or ('equal or lower' and higher), there's only two possible states.
If you use it as a linear amplifier in an appropriate configuration instead of a comparator (and it is properly calibrated), you can then see when the inputs are equal by reading it with and ADC, or using two comparators in a "window comparator" configuration.
Or it the "equality" is not too critical, just use two comparators directly, to get equal / greater / less output combinations.
If you want to eliminate noise (but would still have Vos uncertainty) then
supercool your comparator and its circuitry to absolute zero. Of course that
does not necessarily eliminate popcorn noise or interaction with galactic
noise induced problems (like neutrinos, gamma rays.....other yet to be
discovered particles).