Somebody correct me if I'm wrong, but the stream isn't an integer, it's a probability, or a number between 0 and 1. The point of it is that you shouldn't need to cache it, that would defeat the point of it being a stream.
Still, it seems like if you wanted reduced power, and could accept reduced precision, wouldn't you just do the same thing in binary by using only a few bits? Not even 8 bits, but like 3 or 4 bits?