Just a free idea off the top of my head. I was thinking it would be neat to have a binary clock on a ring.
After a little experiment with a small sheet of paper, it looks like it would be idea if the "digits" were all on one side (one quarter) of the ring. It would be readable for both right and left with the correct orientation.
The lights would have to be very small, e.g. 1mm in diameter, and with decent vertical spacing, only the hours and minutes could be shown. For the paranoid that wonder whether it's actually ticking, you could add one more led that blinks for each tick.
If anyone out there sees this and makes it a reality, I would be very interested in pictures!