how to convert the difference in voltages into a digital signal
The classic method of comparing two analog signals is to use an analog comparator. 







simulate this circuit &ndash; Schematic created using CircuitLab

This is an op-amp like device that produces a high on the output if the Plus pin is at a higher voltage than the voltage on the Minus pin. (Some, like an LM339, require a pull-up on the output to attain the required logic high level.)

However, there is an issue with comparators in that >= requirement. Comparators have a minimum offset error between the two pins so = is a bit of a relative term that can be problematic if the signals you are comparing are frequently at or near the same voltage. Even if the offset can be tuned out, if the signals are equal, the output is undefined, or can actually oscillate.

For such conditions is it more prudent to digitize the signals into a digital byte or word using an analog to digital convertor and compare those values mathematically. However, in that instance you have to remember there is a minimum step size in the digitization, so again "equals" is really a relative number ( = +- Half a step).

More often, the requirement is "I want a HIGH if Signal A goes higher than signal B, but I don't want it to go LOW again till signal A goes lower than say .1V Below signal B." This is called hysteresis and can easily be created by adding positive hysteresis feedback to the op-amp circuit.

For very small signals it gets more difficult. In order to provide reasonable accuracy some amplification of the original signals is sometimes warranted to give you a signal scale that is sufficiently high to reduce the effects of the inherent errors and offsets in the system. In some situations it is better to subtract the signals in an analog circuit before amplification to ensure both signals are treated equally.