It is not a coincidence that we use base 10; we have 10 fingers. One can imagine a different base, however. Using the rules found in base 10, you can describe base 8:

The digits used in base 8 are 0–7.

The columns are powers of 8: 1s, 8s, 64s, and so on.

With n columns you can represent 0 to (8

^{n}–1).

To distinguish numbers written in each base, write the base as a subscript next to the number. The number fifteen in base 10 would be written as 15_{10} and read as “one, five, base ten.”

Thus, to represent the number 15_{10} in base 8 you would write 17_{8}. This is read “one, seven, base eight.” Note that it can also be read “fifteen” as that is the number it continues to represent.

Why 17? The 1 means 1 eight, and the 7 means 7 ones. One eight ...

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