I agree with everyone else I think. Instead of racking your brains to figure out how to do that with gates, figure out what naturally uses this system and map numbers to that system. We use binary two's compliment because that's what gates really like.

But "grey code" is kind of wierd, similar to your negbinary system, and it's not good for gates. But, it's very good for positional encoding of a shaft, since only one bit changes at a time.

So, think about what really works that way. It sounds like something swinging back and forth and getting higher each swing, like an amplifier sinewave, with + being left and - being right.

So think about a spring-driven system. The restoring force is proportional to the displacement, and this produces nice sine waves. If force is constantly being added (or the restoring force constantly weakening) what power curve would be needed to give each turn-around point twice as far away as the previous?

IAC, keep us posted.

—John