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List of numeral systems

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

By culture / time period

"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system."1: 38  The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers.2 Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base).

NameBaseSampleApprox. First Appearance
Proto-cuneiform numerals10&60c. 3500–2000 BCE
Indus numeralsunknown3c. 3500–1900 BCE4
Proto-Elamite numerals10&603100 BCE
Sumerian numerals10&603100 BCE
Egyptian numerals10
3000 BCE
Babylonian numerals10&60 2000 BCE
Aegean numerals10𐄇 𐄈 𐄉 𐄊 𐄋 𐄌 𐄍 𐄎 𐄏  ( ) 𐄐 𐄑 𐄒 𐄓 𐄔 𐄕 𐄖 𐄗 𐄘  ( ) 𐄙 𐄚 𐄛 𐄜 𐄝 𐄞 𐄟 𐄠 𐄡  ( ) 𐄢 𐄣 𐄤 𐄥 𐄦 𐄧 𐄨 𐄩 𐄪  ( ) 𐄫 𐄬 𐄭 𐄮 𐄯 𐄰 𐄱 𐄲 𐄳  ( )1500 BCE
Chinese numeralsJapanese numeralsKorean numerals (Sino-Korean)Vietnamese numerals (Sino-Vietnamese)10

零一二三四五六七八九十百千萬億 (Default, Traditional Chinese)〇一二三四五六七八九十百千万亿 (Default, Simplified Chinese)

1300 BCE
Roman numerals5&10I V X L C D M1000 BCE5
Hebrew numerals10א ב ג ד ה ו ז ח טי כ ל מ נ ס ע פ צק ר ש ת ך ם ן ף ץ800 BCE
Indian numerals10

Bengali ০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ৯

Devanagari ० १ २ ३ ४ ५ ६ ७ ८ ९

Gujarati ૦ ૧ ૨ ૩ ૪ ૫ ૬ ૭ ૮ ૯

Kannada ೦ ೧ ೨ ೩ ೪ ೫ ೬ ೭ ೮ ೯

Malayalam ൦ ൧ ൨ ൩ ൪ ൫ ൬ ൭ ൮ ൯

Odia ୦ ୧ ୨ ୩ ୪ ୫ ୬ ୭ ୮ ୯

Punjabi ੦ ੧ ੨ ੩ ੪ ੫ ੬ ੭ ੮ ੯

Tamil ௦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯

Telugu ౦ ౧ ౨ ౩ ౪ ౫ ౬ ౭ ౮ ౯

Tibetan ༠ ༡ ༢ ༣ ༤ ༥ ༦ ༧ ༨ ༩

Urdu ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹

750–500 BCE
Greek numerals10ō α β γ δ ε ϝ ζ η θ ι ο Αʹ Βʹ Γʹ Δʹ Εʹ Ϛʹ Ζʹ Ηʹ Θʹ<400 BCE
Kharosthi numerals4&10𐩇 𐩆 𐩅 𐩄 𐩃 𐩂 𐩁 𐩀<400–250 BCE6
Phoenician numerals10𐤙 𐤘 𐤗 𐤛𐤛𐤛 𐤛𐤛𐤚 𐤛𐤛𐤖 𐤛𐤛 𐤛𐤚 𐤛𐤖 𐤛 𐤚 𐤖 7<250 BCE8
Chinese rod numerals10𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨 𝍩1st Century
Coptic numerals10Ⲁ Ⲃ Ⲅ Ⲇ Ⲉ Ⲋ Ⲍ Ⲏ Ⲑ2nd Century
Ge'ez numerals10፩ ፪ ፫ ፬ ፭ ፮ ፯ ፰ ፱ ፲ ፳ ፴ ፵ ፶ ፷ ፸ ፹ ፺ ፻ ፼ 93rd–4th Century15th Century (Modern Style)10: 135–136 
Armenian numerals10Ա Բ Գ Դ Ե Զ Է Ը Թ ԺEarly 5th Century
Khmer numerals10០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩Early 7th Century
Thai numerals10๐ ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙7th Century11
Abjad numerals10غ ظ ض ذ خ ث ت ش ر ق ص ف ع س ن م ل ك ي ط ح ز و هـ د ج ب ا<8th Century
Chinese numerals (financial)10零壹貳參肆伍陸柒捌玖拾佰仟萬億 (T. Chinese)零壹贰叁肆伍陆柒捌玖拾佰仟萬億 (S. Chinese)late 7th/early 8th Century12
Eastern Arabic numerals10٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠8th Century
Vietnamese numerals (Chữ Nôm)10𠬠 𠄩 𠀧 𦊚 𠄼 𦒹 𦉱 𠔭 𠃩<9th Century
Western Arabic numerals100 1 2 3 4 5 6 7 8 99th Century
Glagolitic numerals10Ⰰ Ⰱ Ⰲ Ⰳ Ⰴ Ⰵ Ⰶ Ⰷ Ⰸ ...9th Century
Cyrillic numerals10а в г д е ѕ з и ѳ і ...10th Century
Rumi numerals1010th Century
Burmese numerals10၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉11th Century13
Tangut numerals10𘈩 𗍫 𘕕 𗥃 𗏁 𗤁 𗒹 𘉋 𗢭 𗰗11th Century (1036)
Cistercian numerals1013th Century
Maya numerals5&20 <15th Century
Muisca numerals20<15th Century
Korean numerals (Hangul)10영 일 이 삼 사 오 육 칠 팔 구15th Century (1443)
Aztec numerals2016th Century
Sinhala numerals10෦ ෧ ෨ ෩ ෪ ෫ ෬ ෭ ෮ ෯ 𑇡 𑇢 𑇣𑇤 𑇥 𑇦 𑇧 𑇨 𑇩 𑇪 𑇫 𑇬 𑇭 𑇮 𑇯 𑇰 𑇱 𑇲 𑇳 𑇴<18th Century
Pentadic runes1019th Century
Cherokee numerals1019th Century (1820s)
Vai numerals10꘠ ꘡ ꘢ ꘣ ꘤ ꘥ ꘦ ꘧ ꘨ ꘩ 1419th Century (1832)15
Bamum numerals10ꛯ ꛦ ꛧ ꛨ ꛩ ꛪ ꛫ ꛬ ꛭ ꛮ 1619th Century (1896)17
Mende Kikakui numerals10𞣏 𞣎 𞣍 𞣌 𞣋 𞣊 𞣉 𞣈 𞣇 1820th Century (1917)19
Osmanya numerals10𐒠 𐒡 𐒢 𐒣 𐒤 𐒥 𐒦 𐒧 𐒨 𐒩20th Century (1920s)
Medefaidrin numerals20𖺀 𖺁/𖺔 𖺂/𖺕 𖺃/𖺖 𖺄 𖺅 𖺆 𖺇 𖺈 𖺉 𖺊 𖺋 𖺌 𖺍 𖺎 𖺏 𖺐 𖺑 𖺒 𖺓 2020th Century (1930s)21
N'Ko numerals10߉ ߈ ߇ ߆ ߅ ߄ ߃ ߂ ߁ ߀ 2220th Century (1949)23
Hmong numerals10𖭐 𖭑 𖭒 𖭓 𖭔 𖭕 𖭖 𖭗 𖭘 𖭑𖭐20th Century (1959)
Garay numerals102420th Century (1961)25
Adlam numerals10𞥙 𞥘 𞥗 𞥖 𞥕 𞥔 𞥓 𞥒 𞥑 𞥐 2620th Century (1989)27
Kaktovik numerals5&20 𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓 2820th Century (1994)29
Sundanese numerals10᮰ ᮱ ᮲ ᮳ ᮴ ᮵ ᮶ ᮷ ᮸ ᮹20th Century (1996)30

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

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.31 There have been some proposals for standardisation.32

BaseNameUsage
2BinaryDigital computing, imperial and customary volume (bushel-kenning-peck-gallon-pottle-quart-pint-cup-gill-jack-fluid ounce-tablespoon)
3Ternary, trinary33Cantor 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
4QuaternaryChumashan languages and Kharosthi numerals
5QuinaryGumatj, Ateso, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
6Senary, seximalDiceware, Ndom, Kanum, and Proto-Uralic language (suspected)
7Septimal, Septenary34Weeks timekeeping, Western music letter notation
8OctalCharles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, Yuki, Pame, compact notation for binary numbers, Xiantian (I Ching, China)
9Nonary, nonalCompact notation for ternary
10Decimal, denaryMost widely used by contemporary societies353637
11Undecimal, unodecimal, undenaryA base-11 number system was mistakenly attributed to the Māori (New Zealand) in the 19th century38 and one was reported to be used by the Pangwa (Tanzania) in the 20th century,39 but was not confirmed by later research and is believed to also be an error.40 Briefly proposed during the French Revolution to settle a dispute between those proposing a shift to duodecimal and those who were content with decimal. Used as a check digit in ISBN for 10-digit ISBNs. Applications in computer science and technology.414243 Featured in popular fiction.
12Duodecimal, dozenalLanguages 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; 12-hour clock and months timekeeping; years of Chinese zodiac; foot and inch; Roman fractions; penny and shilling
13Tredecimal, tridecimal4445Conway base 13 function.
14Quattuordecimal, quadrodecimal4647Programming for the HP 9100A/B calculator48 and image processing applications;49 pound and stone.
15Quindecimal, pentadecimal5051Telephony routing over IP, and the Huli language.52
16Hexadecimal, sexadecimal, sedecimalCompact notation for binary data; tonal system; ounce and pound.
17Septendecimal, heptadecimal5354
18Octodecimal5556A base in which 7n is palindromic for n = 3, 4, 6, 9.
19Undevicesimal, nonadecimal5758
20VigesimalBasque, Celtic, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages; shilling and pound
5&20Quinary-vigesimal596061Greenlandic, Iñupiaq, Kaktovik, Maya, Nunivak Cupʼig, and Yupʼik numerals – "wide-spread... in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon"62
21The smallest base in which all fractions ⁠1/2⁠ to ⁠1/18⁠ have periods of 4 or shorter.
23Kalam language,63 Kobon language
24Quadravigesimal6424-hour clock timekeeping; Greek alphabet; Kaugel language.
25Sometimes used as compact notation for quinary.
26Hexavigesimal6566Sometimes used for encryption or ciphering,67 using all letters in the English alphabet
27SeptemvigesimalTelefol,68 Oksapmin,69 Wambon,70 and Hewa71 languages. 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,72 to provide a concise encoding of alphabetic strings,73 or as the basis for a form of gematria.74 Compact notation for ternary.
28Months timekeeping.
30TrigesimalThe Natural Area Code, this is the smallest base such that all of ⁠1/2⁠ to ⁠1/6⁠ terminate, a number n is a regular number if and only if ⁠1/n⁠ terminates in base 30.
32DuotrigesimalFound in the Ngiti language.
33Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong.
34Using all numbers and all letters except I and O; the smallest base where ⁠1/2⁠ terminates and all of ⁠1/2⁠ to ⁠1/18⁠ have periods of 4 or shorter.
35Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O.
36Hexatrigesimal7576Covers the ten decimal digits and all letters of the English alphabet.
37Covers the ten decimal digits and all letters of the Spanish alphabet.
38Covers the duodecimal digits and all letters of the English alphabet.
40QuadragesimalDEC RADIX 50/MOD40 encoding used to compactly represent file names and other symbols on Digital Equipment Corporation computers. The character set is a subset of ASCII consisting of space, upper case letters, the punctuation marks "$", ".", and "%", and the numerals.
42Largest base for which all minimal primes are known.
47Smallest base for which no generalized Wieferich primes are known.
49Compact notation for septenary.
50QuinquagesimalSQUOZE encoding used to compactly represent file names and other symbols on some IBM computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits.
58Covers base 62 apart from 0 (zero), I (capital i), O (capital o) and l (lower case L).77
60SexagesimalBabylonian numerals and Sumerian; degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari; covers base 62 apart from I, O, and l, but including _(underscore).78
62Can be notated with the digits 0–9 and the cased letters A–Z and a–z of the English alphabet.
64TetrasexagesimalI Ching in China.This system is conveniently coded into ASCII by using the 26 letters of the Latin alphabet in both upper and lower case (52 total) plus 10 numerals (62 total) and then adding two special characters (+ and /).
72The smallest base greater than binary such that no three-digit narcissistic number exists.
80OctogesimalUsed as a sub-base in Supyire.
85Ascii85 encoding. This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 855 is only slightly bigger than 232. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters.
89Largest base for which all left-truncatable primes are known.
90NonagesimalRelated to Goormaghtigh conjecture for the generalized repunit numbers (111 in base 90 = 1111111111111 in base 2).
95Number of printable ASCII characters.79
96Total number of character codes in the (six) ASCII sticks containing printable characters.
97Smallest base which is not perfect odd power (where generalized Wagstaff numbers can be factored algebraically) for which no generalized Wagstaff primes are known.
100CentesimalAs 100=102, these are two decimal digits.
121Number expressible with two undecimal digits.
125Number expressible with three quinary digits.
128Using as 128=27.
144Number expressible with two duodecimal digits.
169Number expressible with two tridecimal digits.
185Smallest base which is not a perfect power (where generalized repunits can be factored algebraically) for which no generalized repunit primes are known.
196Number expressible with two tetradecimal digits.
210Smallest base such that all fractions ⁠1/2⁠ to ⁠1/10⁠ terminate.
225Number expressible with two pentadecimal digits.
256Number expressible with eight binary digits.
360Degrees of angle.

Non-standard positional numeral systems

Bijective numeration

BaseNameUsage
1Unary (Bijective base‑1)Tally marks, Counting. Unary numbering is used as part of some data compression algorithms such as Golomb coding. It also forms the basis for the Peano axioms for formalizing arithmetic within mathematical logic. A form of unary notation called Church encoding is used to represent numbers within lambda calculus.

Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the more likely the email is considered spam.

10Bijective base-10To avoid zero
26Bijective base-26Spreadsheet column numeration. Also used by John Nash as part of his obsession with numerology and the uncovering of "hidden" messages.80

Signed-digit representation

BaseNameUsage
2Balanced binary (Non-adjacent form)
3Balanced ternaryTernary computers
4Balanced quaternary
5Balanced quinary
6Balanced senary
7Balanced septenary
8Balanced octal
9Balanced nonary
10Balanced decimalJohn ColsonAugustin Cauchy
11Balanced undecimal
12Balanced duodecimal

Complex bases

BaseNameUsage
2iQuater-imaginary baserelated to base −4 and base 16
i 2 {\displaystyle i{\sqrt {2}}} Base i 2 {\displaystyle i{\sqrt {2}}} related to base −2 and base 4
i 2 4 {\displaystyle i{\sqrt[{4}]{2}}} Base i 2 4 {\displaystyle i{\sqrt[{4}]{2}}} related to base 2
2 ω {\displaystyle 2\omega } Base 2 ω {\displaystyle 2\omega } related to base 8
ω 2 3 {\displaystyle \omega {\sqrt[{3}]{2}}} Base ω 2 3 {\displaystyle \omega {\sqrt[{3}]{2}}} related to base 2
−1 ± iTwindragon baseTwindragon fractal shape, related to base −4 and base 16
1 ± iNegatwindragon baserelated to base −4 and base 16

Non-integer bases

BaseNameUsage
3 2 {\displaystyle {\frac {3}{2}}} Base 3 2 {\displaystyle {\frac {3}{2}}} a rational non-integer base
4 3 {\displaystyle {\frac {4}{3}}} Base 4 3 {\displaystyle {\frac {4}{3}}} related to duodecimal
5 2 {\displaystyle {\frac {5}{2}}} Base 5 2 {\displaystyle {\frac {5}{2}}} related to decimal
2 {\displaystyle {\sqrt {2}}} Base 2 {\displaystyle {\sqrt {2}}} related to base 2
3 {\displaystyle {\sqrt {3}}} Base 3 {\displaystyle {\sqrt {3}}} related to base 3
2 3 {\displaystyle {\sqrt[{3}]{2}}} Base 2 3 {\displaystyle {\sqrt[{3}]{2}}}
2 4 {\displaystyle {\sqrt[{4}]{2}}} Base 2 4 {\displaystyle {\sqrt[{4}]{2}}}
2 12 {\displaystyle {\sqrt[{12}]{2}}} Base 2 12 {\displaystyle {\sqrt[{12}]{2}}} usage in 12-tone equal temperament musical system
2 2 {\displaystyle 2{\sqrt {2}}} Base 2 2 {\displaystyle 2{\sqrt {2}}}
− 3 2 {\displaystyle -{\frac {3}{2}}} Base − 3 2 {\displaystyle -{\frac {3}{2}}} a negative rational non-integer base
− 2 {\displaystyle -{\sqrt {2}}} Base − 2 {\displaystyle -{\sqrt {2}}} a negative non-integer base, related to base 2
10 {\displaystyle {\sqrt {10}}} Base 10 {\displaystyle {\sqrt {10}}} related to decimal
2 3 {\displaystyle 2{\sqrt {3}}} Base 2 3 {\displaystyle 2{\sqrt {3}}} related to duodecimal
φGolden ratio baseearly Beta encoder81
ρPlastic number base
ψSupergolden ratio base
1 + 2 {\displaystyle 1+{\sqrt {2}}} Silver ratio base
eBase e {\displaystyle e} best radix economy
πBase π {\displaystyle \pi }
eπBase e π {\displaystyle e\pi }
e π {\displaystyle e^{\pi }} Base e π {\displaystyle e^{\pi }}

n-adic number

BaseNameUsage
2Dyadic number
3Triadic number
4Tetradic numberthe same as dyadic number
5Pentadic number
6Hexadic numbernot a field
7Heptadic number
8Octadic numberthe same as dyadic number
9Enneadic numberthe same as triadic number
10Decadic numbernot a field
11Hendecadic number
12Dodecadic numbernot a field

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,82 as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.

See also

References

  1. Chrisomalis, Stephen (2004). "A cognitive typology for numerical notation". Cambridge Archaeological Journal. 14 (1): 37–52. doi:10.1017/S0959774304000034. /wiki/Doi_(identifier) ↩

  2. Chrisomalis, Stephen (2004). "A cognitive typology for numerical notation". Cambridge Archaeological Journal. 14 (1): 37–52. doi:10.1017/S0959774304000034. /wiki/Doi_(identifier) ↩

  3. Chrisomalis 2010, pp. 330-333. - Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. ISBN 978-0-521-87818-0. https://books.google.com/books?id=ux--OWgWvBQC&pg=PA135 ↩

  4. Chrisomalis 2010, pp. 330-333. - Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. ISBN 978-0-521-87818-0. https://books.google.com/books?id=ux--OWgWvBQC&pg=PA135 ↩

  5. Chrisomalis, Stephen (2004). "A cognitive typology for numerical notation". Cambridge Archaeological Journal. 14 (1): 37–52. doi:10.1017/S0959774304000034. /wiki/Doi_(identifier) ↩

  6. Glass, Andrew; Baums, Stefan; Salomon, Richard (September 18, 2003). "Proposal to Encode Kharoṣ ṭhī in Plane 1 of ISO/IEC 10646" (PDF). Unicode.org. https://www.unicode.org/L2/L2003/03314-kharoshthi.pdf ↩

  7. 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). https://www.unicode.org/L2/L2007/07206-n3284-phoenician.pdf ↩

  8. Cajori, Florian (September 1928). A History Of Mathematical Notations Vol I. The Open Court Company. p. 18. Retrieved June 5, 2017. /wiki/Florian_Cajori ↩

  9. "Ethiopic (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://unicode.org/charts/PDF/U1200.pdf ↩

  10. Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. ISBN 978-0-521-87818-0. 978-0-521-87818-0 ↩

  11. Chrisomalis 2010, p. 200. - Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. ISBN 978-0-521-87818-0. https://books.google.com/books?id=ux--OWgWvBQC&pg=PA135 ↩

  12. Guo, Xianghe (July 27, 2009). "武则天为反贪发明汉语大写数字——中新网" [Wu Zetian invented Chinese capital numbers to fight corruption]. 中新社 [China News Service]. Retrieved August 15, 2024. https://www.chinanews.com.cn/hb/news/2009/07-27/1792519.shtml ↩

  13. "Burmese/Myanmar script and pronunciation". Omniglot. Retrieved June 5, 2017. http://www.omniglot.com/writing/burmese.htm ↩

  14. "Vai (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://unicode.org/charts/PDF/UA500.pdf ↩

  15. Kelly, Piers. "The invention, transmission and evolution of writing: Insights from the new scripts of West Africa". Open Science Framework. https://osf.io/preprints/socarxiv/253vc/download ↩

  16. "Bamum (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://unicode.org/charts/PDF/UA6A0.pdf ↩

  17. Kelly, Piers. "The invention, transmission and evolution of writing: Insights from the new scripts of West Africa". Open Science Framework. https://osf.io/preprints/socarxiv/253vc/download ↩

  18. "Mende Kikakui (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://unicode.org/charts/PDF/U1E800.pdf ↩

  19. Everson, Michael (October 21, 2011). "Proposal for encoding the Mende script in the SMP of the UCS" (PDF). UTC Document Register. Unicode Consortium. L2/11-301R (WG2 N4133R). https://www.unicode.org/L2/L2011/11301r-n4133-mende.pdf ↩

  20. "Medefaidrin (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://unicode.org/charts/PDF/U16E40.pdf ↩

  21. Rovenchak, Andrij (July 17, 2015). "Preliminary proposal for encoding the Medefaidrin (Oberi Okaime) script in the SMP of the UCS (Revised)" (PDF). UTC Document Register. Unicode Consortium. L2/L2015. https://www.unicode.org/L2/L2015/15117r2-medefaidrin.pdf ↩

  22. "NKo (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://unicode.org/charts/PDF/U07C0.pdf ↩

  23. Donaldson, Coleman (January 1, 2017). "Clear Language: Script, Register And The N'ko Movement Of Manding-Speaking West Africa" (PDF). repository.upenn.edu. UPenn. https://www.unicode.org/L2/L2015/15117r2-medefaidrin.pdf ↩

  24. "Consideration of the encoding of Garay with updated user feedback (revised)" (PDF). Unicode Character Code Charts. Unicode Consortium. https://www.unicode.org/L2/L2022/22048-garay-script.pdf ↩

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