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Different numeric bases have advantages over each other. For example, there is a known equation that can be used to calculate the nth digit of pi, but only in hexadecimal.

The main reason for using different bases in the modern world is the use of computers. Consider the way computers work - everything is an on-off switch. It can have two states, on or off, which can be used to represent numbers, 1 or 0. This extends beautifully to binary math. With decimal math, we would need a switch that could hold ten different states, and that would be only for a single-digit decimal number.

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