I think you are using the dac for delta modulation or sigma-delta modulation.
Note: It is very important for you to know that also this dac has only 1-bit, the resolution for the dac has to be as "linear" as your overall adc!! However, for a 1 bit you will always get perfect linearity. But therefore the signal source of the dac (the voltage reference) has to keep constant, especially not signal dependent!!
Therefore use switches (or switch arrays) and a buffered voltage refernence.
If I'm wrong with my assumption, a simple comperator will do it!
Hope I could help you.