List of number systems

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

## 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

 File:Binary clock.svg

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. There have been some proposals for standardisation. See a list of other proposals for names for number bases.

### Non-standard positional numeral systems

#### Negative bases

The common names of the negative base numeral systems are formed using the prefix *nega-*, giving names such as:

#### 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

* Quote notation
* Redundant binary representation
* Hereditary base-n notation
* Asymmetric numeral systems optimized for non-uniform probability distribution of symbols
* Combinatorial number system

### Non-positional notation

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

## See also

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## References

1. ↑ Proposal to add two numbers for the Phoenician script. Unicode Consortium (2007-07-25).
2. ↑ Template:Cite book
3. ↑ Template:Cite book
4. ↑ Template:Cite book
5. ↑ Burmese/Myanmar script and pronunciation.
6. ↑ For the mixed roots of the word "hexadecimal", see Template:Citation.
7. ↑ Multiplication Tables of Various Bases, p. 45, Michael Thomas de Vlieger, Dozenal Society of America
8. ↑ *The History of Arithmetic*, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
9. ↑ *Histoire universelle des chiffres*, Georges Ifrah, Robert Laffont, 1994.
10. ↑ *The Universal History of Numbers: From prehistory to the invention of the computer*, Georges Ifrah, Template:Isbn, John Wiley and Sons Inc., New York, 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk
11. ↑ Template:Cite journal
12. ↑ Template:Cite journal
13. ↑ HP 9100A/B programming, HP Museum
14. ↑ Free Patents Online
15. ↑ Template:Cite book
16. ↑ Base 26 Cipher (Number ⬌ Words) - Online Decoder, Encoder.
17. ↑ Template:Cite book
18. ↑ Template:Cite journal.
19. ↑ Template:Citation.
20. ↑ Template:Citation.
21. ↑ Template:Citation.
22. ↑ Base52.
23. ↑ Base56.
24. ↑ Base57.
25. ↑ Base57.
26. ↑ The Base58 Encoding Scheme (November 27, 2019). “"Thanks to Satoshi Nakamoto for inventing the Base58 encoding format"”
27. ↑ NewBase60.
28. ↑ Base92.
29. ↑ Base93 (26 September 2013).
30. ↑ Base94.
31. ↑ base95 Numeric System.
32. ↑ Template:Cite book
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34. ↑ Chrisomalis calls the Babylonian system "the first positional system ever" in Template:Citation.