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For example you can encode MM using first digit except bottom segment (6^2=64>=60),


you just need to agree on some order or the above 6 display elements, so that they represent MM in binary.
(Each element of display is a binary digit "on"=1, "off"=0.)
Same way you can use second digit to encode seconds.
The remaining 4 elements of display (two bottom segments plus two dots) can be used to encode HH (4^2=16>=12).
I don't see any particular ordering that feels natural.

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You are missing some parameters in your problem. What do you mean by "how can this watch be designed to work?" Is it not already designed to work? Are you asking how an LCD device works?

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To display HH:MM:SS in 12-hour format you need ⌈log

2(12*60*60)⌉ = 16 bits of information, but your display has only 15 elements. Therefore the task is impossible if each element can only be "on" or "off". You need to cheat a little bit, for example add blinking or something like that.

 

Edit:

I miscounted the elements:) The display has 16 not 15 of them, so you

can use it without cheating.
Edited by witzar
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You are missing some parameters in your problem. What do you mean by "how can this watch be designed to work?" Is it not already designed to work? Are you asking how an LCD device works?

Reword: "is expected to" for "shall" tell the right time..

 

The device is a simple "level indicator"  that is to be converted to a watch.
You can replace the chip but retain the LCD screen.
How  would you design or program such chip? 

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