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@Robin
As LED's are more than ten time uP usage, we'll just use LED draw
7+7+5 = 19 seg's - we'll use 20 for easy math
Approx ~20ma ea draw is 20 x 20 = 400mA total draw
Usage:
5 x 1sec = 5sec/hr x 24 = 120sec/dy
Capacity 50mAh
Total draw is 8 times capacity, so 60min / 8 ~ 7min total
I get 3.5 days+
A CR2032 might be a better choice @235mAh nearly five times the capacity
Use a PWM signal at 50% duty cycle maybe?