But if I understand it correctly, they already need to use 2 bits, one for the sign and another one for the value, so there is already one wasted state, which could be used for -0.
How exactly would you do that? 3 states need 1.58 bits which is a tad more than 1.5. Two 3-states have 3²=9 states while three bits only give you 2³=8 states.
I wonder if there's some encoding tricks you can use to reduce it to 8 (or less?) effective states, given that you're only using them with a reduced set of mathematical operations. E.g., can you automatically convert all (-1, 1) to (1, -1) and save one encoded state, since they add up to the same result anyway?
You can use a bit for zero or non-zero and then use bits only for providing the sign to non-zero values, for example. The sign part will be variable length but can probably be made very fast with hardware support.
