As we saw in bases humans use base ten. Other
bases, binary, octal, and hexadecimal, are commonly in use primarily
thanks to digital computers.

### Base twelve

Base | Name |
---|---|

two | binary |

three | ternary |

eight | octal |

ten | decimal, or denary |

twelve | duodenary, or duodecimal |

sixteen | hexadecimal |

Base twelve requires of course twelve digits for the amounts zero
through eleven. We don't have any digits to represent ten and eleven so
we'll do what the computer scientists (somewhat unimaginatively) did
with hexadecimal and use letters instead, so A_{12} is ten and
B_{12} is eleven.

But what's twelve in base twelve? 10_{12} of course! It follows
exactly the same mechanism of returning the column to zero and
incrementing the next one along. So 100_{12} is twelve times
twelve (one hundred and forty four).

Recall the powers from bases:

- 10 = 10
^{1} - 100 = 10
^{2} - 1000 = 10
^{3}

The important thing to remember is that these series of digits are just
a way of writing down a particular quantity. The quantity "thirty
six" is still the same number of things whether it's
30_{12} or 36_{10}. The base of the numbering system is
an agreed on standard and the lens and language with which we see and
express numbers.

Let's look at some basic arithmetic in base twelve...