Drumnbach, you should write science fiction! That's incredible, literally!
The idea of a three-way bit, or 'trit', as they may be called, has crossed my mind. I have no idea how a hard drive works, but I'm sure it would be possible to make one with three possible states to every bit, and then design a new breed of processor to go with it. Maybe it's just because such a system would be unnecessary, and would probably be completely incompatible with any hardware or software built on the binary system.
In fact, if a bit works similarly to a lightbulb, or a magnetic field, it can be switched on or off, and also charged to different degrees, so we could have a virtually unlimited base unit for a bit; 3, 5, 10, 20, the options are countless. 10 would probably be the simplest, because it's used primarily in mathematics.
It's an interesting thought though!