قائمة أنظمة العد

تتضمن هذه المقالة قائمة أنظة العد، وهي عبارة عن أنظمة الكتابة المسستخدم لتمثيل الأرقام.

حسب الثقافة

الاسم

القاعدة

مثال

أول ظهور تقريبي

الأعداد البابلية

60

3100 ق.م.

الأعداد المصرية

10

or

3000 ق.م.

أعداد المايا

20

الأرقام الصينية، الأرقام اليابانية، الأرقام الكورية (الصينية-الكورية)

10

零一二三四五六七八九

الأعداد الرومانية

10

Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ

1000 ق.م.

الأرقام اليونانية

10

α β γ δ ε ϝ ζ η θ ι

بعد 100 ق.م.

Chinese rod numerals

10

القرن الأول

الأعداد الهندية العربية

10

0 1 2 3 4 5 6 7 8 9

القرن التاسع

Location arithmetic لجون ناپيير

2

a b ab c ac bc abc d ad bd

1617 في Rabdology, a non-positional binary system

حسب نوع الترميز

أنظمة العد القياسية

القاعدة	الاسم	الاستخدام
2	ثنائي	الحاسوب الرقمي
3	ثلاثي	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 economical integer base
4	رباعي	Data transmission and Hilbert curves; Chumashan languages, and Kharosthi numerals
5	خماسي	Gumatj, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
6	سداسي	Diceware, Ndom, Kanum, and Proto-Uralic language (suspected)
8	ثماني	Charles XII of Sweden, Unix-like permissions, DEC PDP-11, compact notation for binary numbers
10	عشري	Most widely used by modern civilizations^[1]^[2]^[3]
11	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
12	نظام عد ثنائي عشر	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.
13	نظام عد ثلاثي عشر	Conway base 13 function
14	نظام عد رباعي عشر	Programming for the HP 9100A/B calculator^[4] and image processing applications^[5]
15	Pentadecimal	Telephony routing over IP, and the Huli language
16	Hexadecimal	Base16 encoding; compact notation for binary data; tonal system
20	Vigesimal	Celtic, Maya, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages
24	Tetravigesimal	Kaugel language
27	Heptavigesimal	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,^[6] to provide a concise encoding of alphabetic strings,^[7] or as the basis for a form of gematria.^[8]
30	Trigesimal	The Natural Area Code
32	Duotrigesimal	Base32 encoding and the Ngiti language
36	Hexatrigesimal	Base36 encoding; use of letters with digits
60	Sexagesimal	Babylonian numerals; degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari and Sumerian languages
64	Tetrasexagesimal	Base64 encoding
85	Pentoctogesimal	Ascii85 encoding

أنظم العد الغير قياسية

Bijective numeration

القاعدة	الاسم	الاستخدام
1	Unary (Bijective base-1)	Tally marks
10	Bijective base-10
26	Bijective base-26	Spreadsheet column numeration. Also used by John Nash as part of his obsession with numerology and the uncovering of "hidden" messages.^[9]

Signed-digit representation

القاعدة	الاسم	الاستخدام
2	Balanced binary (Non-adjacent form)
3	Balanced ternary	Ternary computers
10	Balanced decimal	John Colson Augustin Cauchy

القواعد السلبية

القاعدة	الاسم	الاستخدام
−2	Negabinary
−3	Negaternary
−10	Negadecimal

القواعد المركبة

القاعد	الاسم	الاستخدام
2i	Quater-imaginary base
−1 ± i	Twindragon base	Twindragon fractal shape

القواعد الغير صحيحة

القاعدة	الاسم	الاستخدام
φ	Golden ratio base	Early Beta encoder^[10]
e	Base $e$	Lowest radix economy
π	Base $π$ "Pi-nary"
√2	Base $\sqrt{2}$
¹²√2	Base $\sqrt[12]{2}$	Scientific pitch notation

أخرى

الترميز الغير متوضع

انظر أيضاً

المصادر

^ 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, 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, http://digitalcommons.butler.edu/wordways/vol26/iss2/2/ .
^ 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

[1] The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.

[2] Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994.

[3] 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

[4] HP Museum

[5] Free Patents Online

[6] 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, PMID 12463836 .

[7] Stephens, Kenneth Rod (1996), Visual Basic Algorithms: A Developer's Sourcebook of Ready-to-run Code, Wiley, p. 215, ISBN 9780471134183 .

[8] Sallows, Lee (1993), "Base 27: the key to a new gematria", Word Ways 26 (2): 67–77, http://digitalcommons.butler.edu/wordways/vol26/iss2/2/ .

[9] Nasar, Sylvia (2001). A Beautiful Mind. Simon and Schuster. pp. 333–6. ISBN 0-7432-2457-4.

[10] 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

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]