# Digital Alarm Clock Most of the alarm clock's bulbs are busted as shown above in black shades. Although still working it is not possible to tell what time is it. If we can fix it to display a pattern every seconds, maybe it will be possible to tell time.
How can it show the Hours,Minutes and Seconds of the day in 12H format?

• Not sure if I quite understand the question. Are you saying that the only LCD segments which work are the ones forming the two "8"s either side of the right-hand colon, and the colon itself? What about the "SAT" and "PM"? Oct 23, 2016 at 18:38
• note.We cant fix the busted bulbs
– TSLF
Oct 23, 2016 at 18:39
• @randal'thor- we can leave them they are working properly
– TSLF
Oct 23, 2016 at 18:41

If I'm understanding the question correctly, the only working segments are those forming the "8"s either side of the right-hand colon, together with this colon itself: Each one of these segments can be switched on and off if required, but the broken segments can't be fixed. Since there are 16 different working lights and 2 different settings for each, the total number of possibilities we can display using the clock as shown is $2^{16}=65536$.

But the number of possibilities for the time of day in hours, minutes, and seconds, shown using the 12-hour system, is $12*60*60=43200$. This is less than $65536$, so we can display all possible times of day using only the working segments of the clock.

• What time is it in your design?
– TSLF
Oct 23, 2016 at 19:00
• So if I understand correctly, you assume that the AM/PM display still works? -- Ah, indeed, OP says 12h format. Also, you missed some braces in 2^{16}. Oct 23, 2016 at 19:45
• This only works if you can control the two parts of the colon individually, right? Oct 23, 2016 at 22:56
• @TSLF The segments shown would indicate a value outside of the 43200-second range. Oct 24, 2016 at 0:52
• If we want to make it readble , we can use the perimeter of 8 that is like 0- bothe side for the minute and seconds while the colon dots and the center element of both 8's for the hour - [ 0] [ -:-] [ 0] for MM:HH:SS , w/ combininations:( 2^6) (2^4) (2^6) =(64)(16)(64)
– TSLF
Oct 24, 2016 at 3:37

The clockwise sequence patterns for 12-Hours and 60-Min/Sec  