This is a
list of , that is, writing systems for expressing numbers. 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, in some cases including roots from both languages within a single name. [1 ]
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, Kanum, and Proto-Uralic language (suspected)
Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, compact notation for binary numbers
Decimal Most widely used by modern civilizations
[2 ] [3 ] [4 ]
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.
Conway base 13 function
Programming for the
HP 9100A/B calculator and image processing applications [5 ] [6 ]
Telephony routing over IP, and the
Hexadecimal Base16 encoding; compact notation for
binary data; tonal system
Celtic, Maya, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages
Base 26 encoding; sometimes used for encryption or ciphering.
Mapping the nonzero digits to the alphabet and zero to the space is occasionally used to provide
checksums for alphabetic data such as personal names, to provide a concise encoding of alphabetic strings, [8 ] or as the basis for a form of [9 ] gematria. [10 ]
Natural Area Code
Base32 encoding and the Ngiti language
Base36 encoding; use of letters with digits
Babylonian numerals; degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari and Sumerian languages
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. [13 ]
See also [ edit ]
References [ edit ]
^ For the mixed roots of the word "hexadecimal", see Epp, Susanna (2010), (4th ed.), Cengage Learning, p. 91, Discrete Mathematics with Applications ISBN 9781133168669 .
^ 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
^ Grannis, Shaun J.; Overhage, J. Marc; McDonald, Clement J. (2002), "Analysis of identifier performance using a deterministic linkage algorithm", Proc AMIA Symp., pp. 305–309, PMC 2244404, PMID 12463836 .
^ Stephens, Kenneth Rod (1996), Visual Basic Algorithms: A Developer's Sourcebook of Ready-to-run Code, Wiley, p. 215, ISBN 9780471134183 .
^ Sallows, Lee (1993), "Base 27: the key to a new gematria", Word Ways 26 (2): 67–77 .
^ Nasar, Sylvia (2001). A Beautiful Mind. Simon and Schuster. pp. 333–6. ISBN 0-7432-2457-4.
^ 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
^ Chrisomalis calls the Babylonian system "the first positional system ever" in Chrisomalis, Stephen (2010), , Cambridge University Press, p. 254, Numerical Notation: A Comparative History ISBN 9781139485333 .