Summary

Clock shows hours and minutes in "binary" form. From left to right there are 13 digits in four groups, 10 hours, 1 hour, 10 minutes, 1 minute. The digits which are lit, must be added in each group to get the exact time. The 1,2,4,8 weights have different colors. With a little practice, it is very easy to read the time. Your friends will be happy when you explain ...

Construction : the black front plate with transparant digits forms the display. Attached with 2mm screws there follows a panel with many LEDs (2 for each digit), and 2 dots. The Arduino parts are mounted on this too.

The digits are optically isolated from one another for good contrast. The transparent parts are 0.5mm smaller than the cutout, it sort of clicks in. Glue it in, though. For the Arduino parts I did not design any case or holder, this depends on what you have...

Arduino PCB, power : any AVR or STM32, ESP8266 etc. can do the job if it has i2c and enough (14) pins to drive the LEDs plus two digital inputs. Use ready made DS1307 module for timekeeping. ULN2003 drivers drive the LEDs. Do not supply the LEDs from the Arduino's internal supply LDO, it may not have the necessary power. Any 5V micro USB adapter can be used for supply (2-300mA). To get more or less uniform intensity for all colors, experiment with the LED serial resistors, use a potentiometer (do not turn it down to zero) in series, adjust the intensity then replace the pot with a resistor.

Program : reads clock chip data, masks out the digits and drives the LEDs via ULN2003, checks the adjust switches. Uncomment the testing lines when building to help you with the LED connections.

My prototype : used SMD LEDs because I had these, but it was nerve-cracking. Just 3D print out the LED panel, take the normal 3 to 5 mm LEDS and wire it up.

3D print with support.