Why doesn’t it just flash the digits (eg. 5:58 would flash 5, then 5, then 8?) it would always be able to tell time with 3 flashes (assuming 12 hour mode not 24 hour mode). This remainder math seems unnecessary and just takes longer.
Why would 11:02 be hard to tell apart? I think you misunderstood what I was saying. The hours would always flash first. For 11:02 it would flash 11, then 12(12 being 0 since the next place could not have Any number > a 5) then flash 2. For 1:12 it would flash 1, then 1, then 2.
Nifty. How about PWM'ing the LEDs to shift the illumination slowly from one hour marker to the next? With practice I'll bet you could read it to within +/- 5 minutes. That would get rid of the need to blink the LEDs at all.
Bonus level: get rid of the button by adding an accelerometer that is polled a couple of times per second to watch for an activation gesture.
I had the same thought, also making the "virtual hour hand" dimmer would instantly distinguish it from the minutes, and you could also add another "virtual second hand" that visibly "rotates" around the dial to further enhance the analogue-ness.
This project reminds me of one comment by Walter Bright regarding the use of 40 ICs for a DIY digital clock but never got it working correctly [1].This really shows how far the IC technology has changed for the better from it's early days.