11,051 Pages

The Misalian base-naming system is a system for naming various positional numbering bases in English created by jan Misali. The system, itself, is not positional, instead relying on the prime factorization of numbers.[1]

The first unexian base names are available as a webpage,[2] while the first biexian base names are available as a text file.[3]

## Roots, prefixes and suffixes

• Base 0 is "nullary".
• Base 1 is "unary".
• Prime bases without a root name are expressed as "one plus number"; for proper names of bases, the prefix is "un-", while for prefix forms, the circumfix is "hen-...-sna-".
• Base 2 is "binary".
• "bi-" is a prefix meaning "times two".
• Base 3 is "trinary".
• "tri-" is a prefix meaning "times three".
• Base 4 is "quaternary".
• "tetra-" is a prefix meaning "times four".
• Base 5 is "quinary".
• "penta-" is a prefix meaning "times five".
• Base 6 is "seximal".
• "hexa-" is a prefix meaning "times six".
• Base 7 is "septimal".
• "hepta-" is a prefix meaning "times seven".
• Base 8 is "octal".
• "octo-" is a prefix meaning "times eight".
• Base 9 is "nonary".
• "enna-" is a prefix meaning "times nine".
• Base 10 is "decimal".
• However, if this name is preceded by a prefix, it becomes "-gesimal".
• "deca-" is a prefix meaning "times ten".
• Base 11 is "elevenary".
• "leva-" is a prefix meaning "times eleven".
• Base 12 is "dozenal".
• "doza-" is a prefix meaning "times twelve".
• Base 13 is "baker's dozenal", a name credited to Kate of Tangerine's Neocities Page.[4]
• However, if this name is preceded by a prefix, it becomes "-ker's dozenal".
• "baker-" is a prefix meaning "times thirteen".
• Base 16 is "hex".
• "tesser-" is a prefix meaning "times sixteen".
• Base 17 is "suboptimal". It is named for the fact that it has the worst representations of rational numbers of any base from 2 to 20.[5]
• "mal-" is a prefix meaning "times seventeen".
• Base 20 is "vigesimal".
• "icosi-" is a prefix meaning "times twenty".
• Base 36 is "niftimal". Derived from the seximal word "nif", niftimal has been proposed by jan Misali as a compression method for seximal.[6]
• "feta-" is a prefix meaning "times thirty-six".
• Base 100 is "centesimal".
• "hecto-" is a prefix meaning "times one hundred".
• "nega-" is a prefix negating the number following it; for example, "negadecimal" is base -10. This extends the system from all natural numbers to all integers.
• "vot-" or "vöt-" is a prefix for the reciprocal of the number following it; for example, "votdecimal" is base 1/10. It is named after the conlang Vötgil, which, to name numbers, lists their decimal digits in reverse order, thus employing votdecimal. This extends the system to all rational numbers.
• The final two suffixes, albeit not used together with the standard roots, prefixes and suffixes above, extend the system to all numbers that can be named.
• "-nary" is a suffix which can be added to the English name of any number less than six to form a name for a system that uses that number as a base.
• "-imal" is a suffix which can be added to the English name of any number greater than six to form a name for a system that uses that number as a base.

## Forming compounds

For any base that is neither prime nor has a basic root form, the algorithm is to take the two closest factors of the number and write the smaller one in prefix form and the larger one in root/suffix form.

For example, 120 can be decomposed into two factors that are either prime or have root forms in two ways: 10 × 12 and 6 × 20. However, as 10 and 12 are closer to each other than 6 and 20, base 120 is known as decadozenal rather than "hexavigesimal".

## Sources

Community content is available under CC-BY-SA unless otherwise noted.