Base naming systems

Base-naming systems are systematic sets of nomenclature for naming number bases.

Many small bases that have practical usages already have well-established names, such as binary, octal, decimal, hexadecimal, while larger bases and less common bases tend to be simply referred as "Base N" (such as "base sixty-four", though many naming systems have been proposed to avoid the confusion of the number system the base is written in ("base 10" might not refer to decimal if the "10" is supposed to be interpreted in another base.) and to improve systematicity in the names.

* Lamadrid Convention
* SDN/SNN
* Misalian
* Ismarragam-based

The Lamadrid convention is an extension to the current convention for naming number bases (such as in binary, decimal, hexadecimal etc.). Base names derive from its decimal expansion, represented using Latin and Greek root words. The hundreds particle preceeds the units particle, then the decades particle.

### Examples

* Base 14 = tetradecimal (tetra-dec-imal)
* Base 39 = enneatrigesimal (ennea-triges-imal)
* Base 82 = duoöctogesimal (duo-octoges-imal)
* Base 105 = centoquinary (cento-quinary) (alternatively, "centopental" may be accepted if "pental" is preferred for base 5)
* Base 112 = centoduodecimal (cento-duo-dec-imal) (alternatively, "centodozenal" may be accepted if "dozenal" is preferred for base 12)
* Base 456 = quadringentohexaquinquagesimal (quadringento-hexa-quinquages-imal)

The root words used in this system are assumed to be in decimal; The SDN or SNN proposals are used for naming systems centered in other bases.

The Misalian base naming system, proposed by YouTuber jan misali names number bases multiplicatively (additively for prime bases) in a base-neutral manner. It was introduced in his video named "a base-neutral system for naming numbering systems".

This system preserves most of the established names and makes slight changes to others (ternary to trinary, senary to seximal, septenary to septimal, hexadecimal shortened to hex). Additionally, there are special names for bases 11, 13, 17, 20, 36 and 100.

Additionally, base 0 and 1 can be called "nullary" and "unary" in this system.

### 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".

In rare cases where the number can be expressed as the product of two numbers with root words (regardless of whether they are the closest pair of prime factors), the combination with the two root words are prioritized, for example base 600 is named "hexacentesimal" (6 × 100) rather than "tetrasexapentaquinary" (tetra-sexa-penta-quinary, 24 × 25 = 4 × 6 × 5 × 5)

### Abbreviations

In addition to giving each base a full name, the system also gives the abbreviated name, which is no shorter than three letters. It does so by first converting the full name to uppercase and removing any apostrophes, vowels not in the first three letters and the last letter (with the exception of hex), and then, cycles through a space of subsets of this modified name, picking the first one that isn't in use by a smaller base. The space of subsets is composed as follows:

* Shorter abbreviated names are preferred to longer ones. Out of bases up to 10,000, the system only gives a 5-letter name to 196, or 1.96% of them.
* Within abbreviated names of the same length, ones that use the letters occurring earlier in the name are preferred.
* An abbreviated name must use the first letter of the full name.

### List of base names

Below are the Misalian base names for bases up to 144. See a list with up to base 1,296 (=64, one unexian) and a file with base names up to base 1,679,616 (=68, one biexian). Names in bold derive from singular root words (i.e. not compounds). Additionally, underlined names agree with the current convention.

## Variants

Similarly, in order to shorten or simplify base names, one could invent root words for other numbers.
This base naming system is based on the ismarragam (argam names).

## References

1. ↑ http://www.numberbases.com/essay/MultiplicationSynopsis.pdf