List_of_numeral_systems

List of numeral systems

List of numeral systems

Add article description

There are many different numeral systems, that is, writing systems for expressing numbers.

For different types of numbers, such as rational numbers, real numbers, complex numbers, etc, see List of types of numbers.

By culture / time period

More information Name, Base ...

By type of notation

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

A binary clock might use LEDs to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional sexagesimal time.

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.[6] There have been some proposals for standardisation.[7]

More information Base, Name ...

Non-standard positional numeral systems

Bijective numeration

More information Base, Name ...

Signed-digit representation

More information Base, Name ...

Complex bases

More information , Base ...

Non-integer bases

More information , Base ...

n-adic number

More information Base, Name ...

Mixed radix

  • Factorial number system {1, 2, 3, 4, 5, 6, ...}
  • Even double factorial number system {2, 4, 6, 8, 10, 12, ...}
  • Odd double factorial number system {1, 3, 5, 7, 9, 11, ...}
  • Primorial number system {2, 3, 5, 7, 11, 13, ...}
  • Fibonorial number system {1, 2, 3, 5, 8, 13, ...}
  • {60, 60, 24, 7} in timekeeping
  • {60, 60, 24, 30 (or 31 or 28 or 29), 12, 10, 10, 10} in timekeeping
  • (12, 20) traditional English monetary system (£sd)
  • (20, 18, 13) Maya timekeeping

Other

Non-positional notation

All known numeral systems developed before the Babylonian numerals are non-positional,[47] as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.

See also

References

  1. [1]
    Everson, Michael (July 25, 2007). "Proposal to add two numbers for the Phoenician script" (PDF). UTC Document Register. Unicode Consortium. L2/07-206 (WG2 N3284).
  2. [2]
    Cajori, Florian (September 1928). A History Of Mathematical Notations Vol I. The Open Court Company. p. 18. Retrieved June 5, 2017.
  3. [3]
    Chrisomalis, Stephen (January 18, 2010). Numerical Notation: A Comparative History. Cambridge University Press. pp. 135–136. ISBN 978-0-521-87818-0.
  4. [4]
    Chrisomalis 2010, p. 200.
  5. [5]
    "Burmese/Myanmar script and pronunciation". Omniglot. Retrieved June 5, 2017.
  6. [6]
    For the mixed roots of the word "hexadecimal", see Epp, Susanna (2010), Discrete Mathematics with Applications (4th ed.), Cengage Learning, p. 91, ISBN 9781133168669.
  7. [7]
    Multiplication Tables of Various Bases, p. 45, Michael Thomas de Vlieger, Dozenal Society of America
  8. [8]
    "Definition of SEPTENARY". www.merriam-webster.com. Retrieved November 21, 2023.
  9. [9]
    The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
  10. [10]
    Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994.
  11. [11]
    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
  12. [12]
    Overmann, Karenleigh A (2020). "The curious idea that Māori once counted by elevens, and the insights it still holds for cross-cultural numerical research". Journal of the Polynesian Society. 129 (1): 59–84. doi:10.15286/jps.129.1.59-84. Retrieved July 24, 2020.
  13. [13]
    Thomas, N.W (1920). "Duodecimal base of numeration". Man. 20 (1): 56–60. doi:10.2307/2840036. JSTOR 2840036. Retrieved July 25, 2020.
  14. [14]
    Ulrich, Werner (November 1957). "Non-binary error correction codes". Bell System Technical Journal. 36 (6): 1364–1365. doi:10.1002/j.1538-7305.1957.tb01514.x.
  15. [15]
    Das, Debasis; Lanjewar, U.A. (January 2012). "Realistic Approach of Strange Number System from Unodecimal to Vigesimal" (PDF). International Journal of Computer Science and Telecommunications. 3 (1). London: Sysbase Solution Ltd.: 13.
  16. [16]
    Rawat, Saurabh; Sah, Anushree (May 2013). "Subtraction in Traditional and Strange Number System by r's and r-1's Compliments". International Journal of Computer Applications. 70 (23): 13–17. Bibcode:2013IJCA...70w..13R. doi:10.5120/12206-7640. ... unodecimal, duodecimal, tridecimal, quadrodecimal, pentadecimal, heptadecimal, octodecimal, nona decimal, vigesimal and further are discussed...
  17. [17]
    Das & Lanjewar 2012, p. 13.
  18. [18]
    Rawat & Sah 2013.
  19. [19]
    HP 9100A/B programming, HP Museum
  20. [20]
    Free Patents Online
  21. [21]
    Das & Lanjewar 2012, p. 14.
  22. [22]
    Nykl, Alois Richard (September 1926). "The Quinary-Vigesimal System of Counting in Europe, Asia, and America". Language. 2 (3): 165–173. doi:10.2307/408742. JSTOR 408742. OCLC 50709582 – via Google Books. p. 165: A student of the American Indian languages is naturally led to investigate the wide-spread use of the quinary-vigesimal system of counting which he meets in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon.
  23. [23]
    Eells, Walter Crosby (October 14, 2004). "Number Systems of the North American Indians". In Anderson, Marlow; Katz, Victor; Wilson, Robin (eds.). Sherlock Holmes in Babylon: And Other Tales of Mathematical History. Mathematical Association of America. p. 89. ISBN 978-0-88385-546-1 – via Google Books. Quinary-vigesimal. This is most frequent. The Greenland Eskimo says 'other hand two' for 7, 'first foot two' for 12, 'other foot two' for 17, and similar combinations to 20, 'man ended.' The Unalit is also quinary to twenty, which is 'man completed.' ...
  24. [24]
    Chrisomalis 2010, p. 200: "The early origin of bar-and-dot numeration alongside the Middle Formative Mesoamerican scripts, the quinary-vigesimal structure of the system, and the general increase in the frequency and complexity of numeral expressions over time all point to its indigenous development.".
  25. [25]
    Laycock, Donald (1975). "Observations on Number Systems and Semantics". In Wurm, Stephen (ed.). New Guinea Area Languages and Language Study, I: Papuan Languages and the New Guinea Linguistic Scene. Pacific Linguistics C-38. Canberra: Research School of Pacific Studies, Australian National University. pp. 219–233.
  26. [26]
    Dibbell, Julian (2010). "Introduction". The Best Technology Writing 2010. Yale University Press. p. 9. ISBN 978-0-300-16565-4. There's even a hexavigesimal digital code—our own twenty-six symbol variant of the ancient Latin alphabet, which the Romans derived in turn from the quadravigesimal version used by the ancient Greeks.
  27. [27]
    Young, Brian; Faris, Tom; Armogida, Luigi (2019). "A nomenclature for sequence-based forensic DNA analysis". Genetics. 42. Forensic Science International: 14–20. […] 2) the hexadecimal output of the hash function is converted to hexavigesimal (base-26); 3) letters in the hexavigesimal number are capitalized, while all numerals are left unchanged; 4) the order of the characters is reversed so that the hexavigesimal digits appear […]
  28. [28]
    "Base 26 Cipher (Number ⬌ Words) - Online Decoder, Encoder".
  29. [29]
    Laycock, Donald (1975). "Observations on Number Systems and Semantics". In Wurm, Stephen (ed.). New Guinea Area Languages and Language Study, I: Papuan Languages and the New Guinea Linguistic Scene. Pacific Linguistics C-38. Canberra: Research School of Pacific Studies, Australian National University. pp. 219–233.
  30. [30]
    Saxe, Geoffrey B.; Moylan, Thomas (1982). "The development of measurement operations among the Oksapmin of Papua New Guinea". Child Development. 53 (5): 1242–1248. doi:10.1111/j.1467-8624.1982.tb04161.x. JSTOR 1129012..
  31. [31]
  32. [32]
    Nauka i Zhizn, 1992, issue 3, p. 48.
  33. [33]
    Grannis, Shaun J.; Overhage, J. Marc; McDonald, Clement J. (2002), "Analysis of identifier performance using a deterministic linkage algorithm", Proceedings. AMIA Symposium: 305–309, PMC 2244404, PMID 12463836.
  34. [34]
    Stephens, Kenneth Rod (1996), Visual Basic Algorithms: A Developer's Sourcebook of Ready-to-run Code, Wiley, p. 215, ISBN 9780471134183.
  35. [35]
    Sallows, Lee (1993), "Base 27: the key to a new gematria", Word Ways, 26 (2): 67–77.
  36. [36]
    Gódor, Balázs (2006). "World-wide user identification in seven characters with unique number mapping". Networks 2006: 12th International Telecommunications Network Strategy and Planning Symposium. IEEE. pp. 1–5. doi:10.1109/NETWKS.2006.300409. ISBN 1-4244-0952-7. S2CID 46702639. This article proposes the Unique Number Mapping as an identification scheme, that could replace the E.164 numbers, could be used both with PSTN and VoIP terminals and makes use of the elements of the ENUM technology and the hexatrigesimal number system. […] To have the shortest IDs, we should use the greatest possible number system, which is the hexatrigesimal. Here the place values correspond to powers of 36...
  37. [37]
    Balagadde1, Robert Ssali; Premchand, Parvataneni (2016). "The Structured Compact Tag-Set for Luganda". International Journal on Natural Language Computing (IJNLC). 5 (4). Concord Numbers used in the categorisation of Luganda words encoded using either Hexatrigesimal or Duotrigesimal, standard positional numbering systems. […] We propose Hexatrigesimal system to capture numeric information exceeding 10 for adaptation purposes for other Bantu languages or other agglutinative languages.{{cite journal}}: CS1 maint: numeric names: authors list (link)
  38. [38]
    "Base52". GitHub. Retrieved January 3, 2016.
  39. [39]
    "Base56". Retrieved January 3, 2016.
  40. [40]
    "Base57". GitHub. Retrieved January 3, 2016.
  41. [41]
    "Base57". GitHub. Retrieved January 22, 2019.
  42. [42]
    "The Base58 Encoding Scheme". Internet Engineering Task Force. November 27, 2019. Archived from the original on August 12, 2020. Retrieved August 12, 2020. Thanks to Satoshi Nakamoto for inventing the Base58 encoding format
  43. [43]
    "NewBase60". Retrieved January 3, 2016.
  44. [44]
    "base95 Numeric System". Archived from the original on February 7, 2016. Retrieved January 3, 2016.
  45. [45]
    Nasar, Sylvia (2001). A Beautiful Mind. Simon and Schuster. pp. 333–6. ISBN 0-7432-2457-4.
  46. [46]
    Ward, Rachel (2008), "On Robustness Properties of Beta Encoders and Golden Ratio Encoders", IEEE Transactions on Information Theory, 54 (9): 4324–4334, arXiv:0806.1083, Bibcode:2008arXiv0806.1083W, doi:10.1109/TIT.2008.928235, S2CID 12926540
  47. [47]
    Chrisomalis 2010, p. 254: Chrisomalis calls the Babylonian system "the first positional system ever".
Share this article:

This article uses material from the Wikipedia article List_of_numeral_systems, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.