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Binary Number Display

What switches must be turned on to make the numbers 2,3,5 and 13?
 
For 2, second switch must be turned.
For 3, first and second switches must be turned.
For 5, first and third switches must be turned.
For 13, fourth, third and first switches must be turned.
 
What is the maximum count that can be achieved with 3 LEDs? 7
 
 with 5 LEDs? 31
 
What is the relationship between the maximum count that can be
achieved with a number of LEDs and the weight of the next LED if it
were added?
We can find the weight of the next LED by adding +1 to the maximum
count before we add the next LED.

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