This is a
list of . numeral systems
By culture [ edit ]
By type of notation [ edit ]
Numeral systems are classified here as to whether they use
positional notation (also known as place-value notation), and further categorized by radix or base.
Standard positional numeral systems [ edit ]
The common names are derived
somewhat arbitrarily from a mix of Latin and Greek.
Cantor set (all points in [0,1] that can be represented in ternary with no 1s); counting Tasbih in Islam; hand-foot-yard and teaspoon-tablespoon-shot measurement systems; most integer base economical
Quaternary Data transmission and
Hilbert curves; Chumashan languages, and Kharosthi numerals
Gumatj, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
Diceware, Ndom language, and Proto-Uralic language (suspected)
Septenary Week cycle
Charles XII of Sweden, Unix-like permissions, DEC PDP-11, compact notation for binary numbers
Nonary compact notation of ternary numbers
Decimal Most widely used by modern civilizations
[1 ] [2 ] [3 ]
Undecimal Jokingly proposed during the
French revolution to settle a dispute between those proposing a shift to duodecimal and those who were content with decimal
Duodecimal Languages in the
Nigerian Middle Belt Janji, Gbiri-Niragu, Piti, and the Nimbia dialect of Gwandara; Chepang language of Nepal, and the Mahl dialect of Maldivian; dozen-gross-great gross counting; hours and months timekeeping; years of Chinese zodiac; foot and inch.
Tridecimal A cycle of the
Tetradecimal Programming for the
HP 9100A/B calculator and image processing applications [4 ] [5 ]
Pentadecimal Telephony routing over IP, and the
Base16 encoding; compact notation for binary data or quaternary numbers; tonal system
Octodecimal A cycle of the
Mesoamerican Long Count calendar
Celtic, Maya, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages
Kaugel language; hours timekeeping
Pentavigesimal Compact notation of quinary numbers
Hexavigesimal Uses of letters without digits, e.g. spreadsheet column numeration
Telefol and Oksapmin languages; compact notation of ternary numbers
Four week month of thirteen month calendar
Month cycle for various calendars; The Natural Area Code
Base32 encoding; compact notation of binary; and the Ngiti language
Base36 encoding; use of letters with digits; compact notation of senary numbers
Babylonian numerals; degrees-minutes-seconds and hours-minutes-seconds measurement systems
Base62 encoding; using all English letters (capital and lowercase) and digits but no others, used for e.g. URL shortening.
Base64 encoding; compact notation of binary, quaternary or octal numbers
Internally in computers
Degree division of circle
The common names of the negative base numeral systems are formed using the prefix
nega-, giving names such as:
Non-positional notation [ edit ]
All known numeral systems developed before the
Babylonian numerals are non-positional.
1-adic bijective numeration [ edit ]
See also [ edit ]
References [ edit ]
^ The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
^ Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994.
^ The Universal History of Numbers: From prehistory to the invention of the computer, Georges Ifrah, ISBN 0-471-39340-1, John Wiley and Sons Inc., New York, 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk
^ HP Museum
^ Free Patents Online
^ Ward, Rachel (2008), "On Robustness Properties of Beta Encoders and Golden Ratio Encoders", IEEE Transactions on Information Theory 54 (9): 4324–4334, doi: 10.1109/TIT.2008.928235