# six is a bit small, innit?

yes, this is a slight disadvantage for seximal. numbers get long a bit sooner than they otherwise would. my birthyear, 1 3130, has five entire digits! the distance from the Earth to the Sun is about 155 0000 0000 grandsticks, and the amount of information contained in a ten digit decimal phone number requires twelve seximal digits. surely, that's impossible to fix. that's just the nature of using a smaller base; it's a tradeoff between complexity and size.

well, this same problem exists for another popular small base: binary. in fact, it's much worse in binary. a ten digit phone number's worth of information requires FIFSY binary digits! the solution is a system called hex (short for hexadecimal), which on top of being the reason I don't call base six "heximal" is a way to make binary numbers one fourth the length, by having one digit for all dozen four combinations of four binary digits.

seximal | binary | hex |
---|---|---|

0 | 0000 | 0 |

1 | 0001 | 1 |

2 | 0010 | 2 |

3 | 0011 | 3 |

4 | 0100 | 4 |

5 | 0101 | 5 |

10 | 0110 | 6 |

11 | 0111 | 7 |

12 | 1000 | 8 |

13 | 1001 | 9 |

14 | 1010 | A |

15 | 1011 | B |

20 | 1100 | C |

21 | 1101 | D |

22 | 1110 | E |

23 | 1111 | F |

introducing HEXASEXIMAL COMPRESSION, a way to make any seximal number half the length!

now, you might be thinking, where are we gonna find nif digits? check it out, there's ten Arabic numerals and foursy two letters in the Latin alphabet. that means that just by extending the way hex works, we've got our nif digits right there!

+0 | +1 | +2 | +3 | +4 | +5 | |
---|---|---|---|---|---|---|

00+ | 0 | 1 | 2 | 3 | 4 | 5 |

10+ | 6 | 7 | 8 | 9 | A | B |

20+ | C | D | E | F | G | H |

30+ | I | J | K | L | M | N |

40+ | O | P | Q | R | S | T |

50+ | U | V | W | X | Y | Z |

so, using this system, I can say I was born in 1JI, that the Sun is about 1Z0000 grandsticks away, and a ten digit decimal phone number's worth of information can be written with just six digits.

if you already know Arabic numerals and the Latin alphabet separately, then converting back and forth between seximal and hexaseximal isn't as hard as you might think. it's easiest to just remember the multiples of six (0, 6, C, I, O, and U) and then to count up from there. so, for example, 43 is 40+3; 40 is O, so you count O, P, Q, R to find how to write 43 in hexaseximal. if you have trouble remembering what order the Latin alphabet goes in, plenty of people use a mnemonic device where they sing the names of the letters to the tune of the nursery rhyme "Twinkle Twinkle Little Star".

naturally, with this many digits to distinguish, you'll need to be careful to make sure that none of them look too similar to each other. 0 and O look pretty much the same if you're not careful, and in some fonts 1 and I are even harder to distinguish. so, make sure when you're handwriting in hexaseximal that you put slashes through your 0's and that you put serifs on 1's and I's.