# Base 2 - Binary See: [[Binary]] # Base 3 - Ternary # Base 4 - Quaternary # Base 5 - Quinary # Base 6 - Seximal / Senary See; [[Seximal]] # Base 8 - Octal See: [[Octal]] Octal was popular with programmers in the 20th century because it can concisely represent 3 bits. Many early computing [[ISA|architectures]] were based on bit groupings divisible by 3, rather than 8 as modern computers do. Many old standards use octal notation as a result. Unix file permissions are displayed using octal encoding. Pamean and Yuki human languages of North America use base 8 for counting. # Base 10 - Decimal See: [[Decimal]] The standard number base used by most cultures and natural human languages today. ## Quasi-Decimal Before the widespread adoption of "zero" as a number many human numeral systems still used 10 as the base. However, because these are not proper positional systems they are called "*quasi*-decimal". # Base 12 - Dozenal See: [[Dozenal]] # Base 16 - Hexadecimal See: [[Hexadecimal]] # Base 20 - Vigesimal 20 is a common base number in indo-european languages including French, Danish, Albanian, and most Celtic languages. But most famously [[Basque]]. I can't find anything about this online, but the IE languages which use this counting scheme are all adjacent to or even within the borders of what was the likely extent of the [[Basque]] language judging by Roman-era toponyms throughout europe. See also: [[origins of the weird counting words in some european languages]] ## Base 5&20 - Quinary-Vigesimal A very widespread composite base used in natural languages, particularly the Eskimo–Aleut and [[Mayan languages]]. Most interesting to me as the base used for perhaps the best numeral system in use today: [[Kaktovik Numerals]]. # Base 30 - Trigesimal # Base 32 - Duotrigesimal See: [[Base32]] # Base 34 The "Pseudo-Hexadecimal" used by [[Traveller (RPG)#Cepheus Engine]] is base 34. - https://www.orffenspace.com/cepheus-srd/introduction.html#pseudo-hexadecimal-notation # Base 36 - Hexatrigesimal See: [[Base 36]] # Base 60 - Sexagesimal See: [[Sexagesimal]] # Base 64 See: [[Base 64]] # Base 83 See: [[Base 83]] # Base 100 - Centesimal Used by the [[Conlanging|conlang]] [[Ithkuil]]. # Base 128 # Base 256 Used by [[PGPfone Wordlist]] to verify key fingerprints. - https://github.com/kyrias/pwl/ - https://github.com/ctsrc/Base256 # References - https://en.wikipedia.org/wiki/List_of_numeral_systems ## Vigesimal - https://gaelicgrammar.org/~gaelic/mediawiki/index.php/Numerals ## Conlang - https://musa.bet