## On the Subject of Base On

As elegant as toki pona makes language, I got the grammar wrong last time I tried, so I’ll stick to what I actually know: Mathematics!

See Appendix MISALIAN B➔N for the Misalian base naming system reference. Note that numbers themselves in this appendix are in base ten.

This module consists of two screens, and a keypad containing all digits, minus and slash keys, and a vertical space key.

The bottom screen will always contain the name of a number base. Submitting the number the base name belongs to will solve the module. An incorrect number will result in a strike but will not reset the module.

Instead of the typical mostly Latin-derived base naming system, this module uses the Misalian base naming system instead, as instead of basing it off of the number in base ten, it uses the factorization of the number instead. Look at the appendix on the following pages to convert the base name to its corresponding number.

Pressing any labeled key will append that symbol to your answer. Holding the space key will slowly remove one symbol from your answer at a time. Pressing the space key will submit your answer.

## Appendix MISALIAN B➔N:Misalian Base Naming System ReferenceFrom Base to Number

 Main roots No. Prefix Suffix 2 bi- -binary 3 tri- -trinary 4 tetra- -quaternary 5 penta- -quinary 6 hexa- -seximal 7 hepta- -septimal 8 octo- -octal 9 enna- -nonary 10 deca- -gesimal 11 leva- -elevenary 12 doza- -dozenal 13 baker- -ker’s dozenal 16 tesser- -hex 17 mal- -suboptimal 20 icosi- -vigesimal 36 feta- -niftimal 100 hecto- -centesimal Other roots un-, hen- & -sna, nega-, vöt-
• Prefixes multiply a base by their corresponding number. The simplest non-trivial case is the prefix being one divisor and the suffix being another. The smaller divisor will always come first.
• Divisors will not always be single roots, divisors not in the table are divided recursively until all numbers being multiplied are roots in the table. Simply multiply these numbers together taking into account the rules below to get your divisors.
• The base name will always have the
minimum number of roots.
• If you find the prefix un-, that means to add 1 to the product of subsequent prefixes and suffixes.
• If you find the prefix hen- that means to add 1 to the product of prefixes between that hen- and the close-bracket particle -sna. Do inner hen- & -sna pairs first.
• Roots ending with ‘a’ or ‘o’ followed by a root beginning with a vowel have their ending vowel removed. Roots beginning with ‘i’ or ‘u’ preceded by a root ending
with an ‘i’ have their starting vowel removed.
• Bases 0, 1, 10, and 13 are called nullary, unary, decimal, and baker’s dozenal respectively.
• The prefix nega- is used for negative bases, multiplying by -1.
• The prefix vöt- is used for reciprocal bases, turning base N into 1/N. Note that multiplicative prefixes can still be added before vöt- to represent the numerator of the rational number.