I imagine an algebra on the set of three values with an addition operation like this:
0 + 0 = 0 0 + 1 = random value 0 or 1 with 50/50 probability 1 + 0 = random value 0 or 1 with 50/50 probability 1 + 1 = 1
The idea is that if this were implemented as an electronic gate where the two inputs were binary 0 or 1, the output is off, half-on, or full-on, representing a kind of summation. The half-on value would vary randomly very fast to represent a PWM-like half-amplitude.
Without having thought far, I suspect that (since the actual output values are just 0 and 1) this output could be fed into other similar gates, resulting in a variety of intermediate random-PWM-amplitude levels.
Is there a name for this mathematical concept? I would like to read about it.