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Radix Sort: Conceptual

Base Numbering Systems

The value of different positions in a number increases by a multiplier of 10 in increasing positions. This means that a digit ‘8’ in the rightmost place of a number is equal to the value 8, but that same digit when shifted left one position (i.e., in 80) is equal to `10 * 8`

. If you shift it again one position you get 800, which is `10 * 10 * 8`

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This is where it’s useful to incorporate the shorthand of exponential notation. It’s important to note that 10^{0} is equal to 1. Each position corresponds to a different exponent of 10.

So why 10? It’s a consequence of how many digits are in our alphabet for numbering. Since we have 10 digits (0-9) we can count all the way up to 9 before we need to use a different position. This system that we used is called base-10 because of that.

What if we had a different number of digits in our alphabet? How would we count with an alphabet with just two digits (0 and 1)?