Spur gear differentials are naturally adders (with carry!); so, traditionally they've only ever been used for analogue logic. They're overly complicated for digital logic: you need two spur gears to build a single gate (NAND) to perform a single binary operation. If you want any sort of reasonable lash characteristics you're going to need ~60 teeth. At that point, two 60 teeth spur gears give you a 3600-valued adder. That'd take something like 300+ spur gears in binary: it just doesn't make any damn sense.

I think the last time I looked at this, if I used the cast spur gears available I needed a staged approach to "start" the computer and a 1100 hp motor to run it.