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Alutor language facts for kids

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By culture / time period

Name Base Sample Approx. First Appearance
Alutor Numerals 35,000 BCE
Babylonian numerals 60 Babylonian 1.svg Babylonian 2.svg Babylonian 3.svg Babylonian 4.svg Babylonian 5.svg Babylonian 6.svg Babylonian 7.svg Babylonian 8.svg Babylonian 9.svg Babylonian 10.svg 3,100 BCE
Egyptian numerals 10
Z1 V20 V1 M12 D50 I8 I7 C11
3,000 BCE
Chinese numerals, Japanese numerals, Korean 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)

零壹貳參肆伍陸柒捌玖拾佰仟萬億 (Financial, T. Chinese)

零壹贰叁肆伍陆柒捌玖拾佰仟萬億 (Financial, S. Chinese)

1,600 BCE
Aegean numerals 10 𐄇 𐄈 𐄉 𐄊 𐄋 𐄌 𐄍 𐄎 𐄏  ( 1 2 3 4 5 6 7 8 9 )
𐄐 𐄑 𐄒 𐄓 𐄔 𐄕 𐄖 𐄗 𐄘  ( 10 20 30 40 50 60 70 80 90 )
𐄙 𐄚 𐄛 𐄜 𐄝 𐄞 𐄟 𐄠 𐄡  ( 100 200 300 400 500 600 700 800 900 )
𐄢 𐄣 𐄤 𐄥 𐄦 𐄧 𐄨 𐄩 𐄪  ( 1000 2000 3000 4000 5000 6000 7000 8000 9000 )
𐄫 𐄬 𐄭 𐄮 𐄯 𐄰 𐄱 𐄲 𐄳  ( 10000 20000 30000 40000 50000 60000 70000 80000 90000 )
1,500 BCE
Roman numerals I V X L C D M 1,000 BCE
Hebrew numerals 10 א ב ג ד ה ו ז ח ט
י כ ל מ נ ס ע פ צ
ק ר ש ת ך ם ן ף ץ
800 BCE
Indian numerals 10 Tamil ௦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯

Devanagari ० १ २ ३ ४ ५ ६ ७ ८ ९ Tibetan ༠ ༡ ༢ ༣ ༤ ༥ ༦ ༧ ༨ ༩

750 – 690 BCE
Greek numerals 10 ō α β γ δ ε ϝ ζ η θ ι
ο Αʹ Βʹ Γʹ Δʹ Εʹ Ϛʹ Ζʹ Ηʹ Θʹ
<400 BCE
Phoenician numerals 10 𐤙 𐤘 𐤗 𐤛𐤛𐤛 𐤛𐤛𐤚 𐤛𐤛𐤖 𐤛𐤛 𐤛𐤚 𐤛𐤖 𐤛 𐤚 𐤖 <250 BCE
Chinese rod numerals 10 𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨 𝍩 1st Century
Ge'ez numerals 10 ፩, ፪, ፫, ፬, ፭, ፮, ፯, ፰, ፱
፲, ፳, ፴, ፵, ፶, ፷, ፸, ፹, ፺, ፻
3rd – 4th Century, 15th Century (Modern Style)
Armenian numerals 10 Ա Բ Գ Դ Ե Զ Է Ը Թ Ժ Early 5th Century
Khmer numerals 10 ០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩ Early 7th Century
Thai numerals 10 ๐ ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙ 7th Century
Abjad numerals 10 غ 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
Eastern Arabic numerals 10 ٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠ 8th Century
Western Arabic numerals 10 0 1 2 3 4 5 6 7 8 9 9th Century
Cyrillic numerals 10 А҃ В҃ Г҃ Д҃ Е҃ Ѕ҃ З҃ И҃ Ѳ҃ І҃ ... 10th Century
Tangut numerals 10 Template:Tangut 1036
Burmese numerals 10 ၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉ 11th Century
Maya numerals 20 0 maia.svg 1 maia.svg 2 maia.svg 3 maia.svg 4 maia.svg 5 maia.svg 6 maia.svg 7 maia.svg 8 maia.svg 9 maia.svg 10 maia.svg 11 maia.svg 12 maia.svg 13 maia.svg 14 maia.svg 15 maia.svg 16 maia.svg 17 maia.svg 18 maia.svg 19 maia.svg <15th Century
Muisca numerals 20 Muisca cyphers acc acosta humboldt zerda.svg <15th Century
Aztec numerals 20 16th Century
Sinhala numerals 10 ෦ ෧ ෨ ෩ ෪ ෫ ෬ ෭ ෮ ෯

𑇡 𑇢 𑇣 𑇤 𑇥 𑇦 𑇧 𑇨 𑇩 𑇪 𑇫 𑇬 𑇭 𑇮 𑇯 𑇰 𑇱 𑇲 𑇳 𑇴

<18th Century
Kaktovik Inupiaq numerals 20 Kaktovik Inupiaq Numerals.svg 1994

By type of notation

Quick facts for kids
Algerian Arabic
Darja, دارجة
Native to Algeria
Native speakers 42.5 million  (2020)e18
3 million L2 speakers in Algeria (no date)
Language family
Afro-Asiatic
Writing system Arabic script
Árabe argelino.png

Algerian Arabic (known as Darja in Algeria) is a dialect derived from the form of Arabic spoken in northern Algeria. It belongs to the Maghrebi Arabic language continuum and is partially mutually intelligible with Tunisian and Moroccan.

Like other varieties of Maghrebi Arabic, Algerian has a mostly Semitic vocabulary. It contains Berber and Latin (African Romance) influences and has numerous loanwords from French, Andalusian Arabic, Ottoman Turkish and Spanish.

Algerian Arabic is the native dialect of 75% to 80% of Algerians and is mastered by 85% to 100% of them. It is a spoken language used in daily communication and entertainment, while Modern Standard Arabic (MSA) is generally reserved for official use and education.

Standard positional numeral systems

Binary clock
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. There have been some proposals for standardisation.

Base Name Usage
2 Binary Digital computing, imperial and customary volume (bushel-kenning-peck-gallon-pottle-quart-pint-cup-gill-jack-fluid ounce-tablespoon)
3 Ternary 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 Quaternary Data transmission, DNA bases and Hilbert curves; Chumashan languages, and Kharosthi numerals
5 Quinary Gumatj, Ateso, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
6 Senary Diceware, Ndom, Kanum, and Proto-Uralic language (suspected)
7 Septenary Weeks timekeeping, Western music letter notation
8 Octal Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, compact notation for binary numbers, Xiantian (I Ching, China)
9 Nonary Base9 encoding; compact notation for ternary
10 Decimal / Denary Most widely used by modern civilizations
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; check digit in ISBN. A base-11 number system was attributed to the Māori (New Zealand) in the 19th century and the Pangwa (Tanzania) in the 20th century.
12 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; 12-hour clock and months timekeeping; years of Chinese zodiac; foot and inch; Roman fractions
13 Tridecimal Base13 encoding; Conway base 13 function
14 Tetradecimal Programming for the HP 9100A/B calculator and image processing applications; pound and stone
15 Pentadecimal Telephony routing over IP, and the Huli language
16 Hexadecimal Base16 encoding; compact notation for binary data; tonal system; ounce and pound
17 Heptadecimal Base17 encoding
18 Octodecimal Base18 encoding
19 Enneadecimal Base19 encoding
20 Vigesimal Basque, Celtic, Maya, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages
21 Unvigesimal Base21 encoding
22 Duovigesimal Base22 encoding
23 Trivigesimal Kalam language, Kobon language
24 Tetravigesimal 24-hour clock timekeeping; Kaugel language
25 Pentavigesimal Base25 encoding
26 Hexavigesimal Base26 encoding; sometimes used for encryption or ciphering, using all letters
27 Heptavigesimal Septemvigesimal Telefol and Oksapmin 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, to provide a concise encoding of alphabetic strings, or as the basis for a form of gematria. Compact notation for ternary.
28 Octovigesimal Base28 encoding; months timekeeping
29 Enneavigesimal Base29
30 Trigesimal The 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
31 Untrigesimal Base31
32 Duotrigesimal Base32 encoding and the Ngiti language
33 Tritrigesimal Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong
34 Tetratrigesimal Using all numbers and all letters except I and O
35 Pentatrigesimal Using all numbers and all letters except O
36 Hexatrigesimal Base36 encoding; use of letters with digits
37 Heptatrigesimal Base37; using all numbers and all letters of the Spanish alphabet
38 Octotrigesimal Base38 encoding; use all duodecimal digits and all letters
40 Quadragesimal DEC 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.
42 Duoquadragesimal Base42 encoding
45 Pentaquadragesimal Base45 encoding
48 Octoquadragesimal Base48 encoding
49 Enneaquadragesimal Compact notation for septenary
50 Quinquagesimal Base50 encoding; SQUOZE encoding used to compactly represent file names and other symbols on some IBM computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits.
52 Duoquinquagesimal Base52 encoding, a variant of Base62 without vowels or a variant of Base26 using all lower and upper case letters.
54 Tetraquinquagesimal Base54 encoding
56 Hexaquinquagesimal Base56 encoding, a variant of Base58
57 Heptaquinquagesimal Base57 encoding, a variant of Base62 excluding I, O, l, U, and u or I, 1, l, 0, and O
58 Octoquinquagesimal Base58 encoding, a variant of Base62 excluding 0 (zero), I (capital i), O (capital o) and l (lower case L).
60 Sexagesimal Babylonian numerals; NewBase60 encoding, similar to Base62, excluding I, O, and l, but including _(underscore); degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari and Sumerian languages
62 Duosexagesimal Base62 encoding, using 0–9, A–Z, and a–z
64 Tetrasexagesimal Base64 encoding; I 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 (for example, YouTube video codes use the hyphen and underscore characters, - and _ to total 64).
72 Duoseptuagesimal Base72 encoding
80 Octogesimal Base80 encoding
81 Unoctogesimal Base81 encoding, using as 81=34 is related to ternary
85 Pentoctogesimal Ascii85 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.
90 Nonagesimal Related to Goormaghtigh conjecture for the generalized repunit numbers.
91 Unnonagesimal Base91 encoding, using all ASCII except "-" (0x2D), "\" (0x5C), and " (0x27); one variant uses "\" (0x5C) in place of """ (0x22).
92 Duononagesimal Base92 encoding, using all of ASCII except for "`" (0x60) and """ (0x22) due to confusability.
93 Trinonagesimal Base93 encoding, using all of ASCII printable characters except for "," (0x27) and "-" (0x3D) as well as the Space character. "," is reserved for delimiter and "-" is reserved for negation.
94 Tetranonagesimal Base94 encoding, using all of ASCII printable characters.
95 Pentanonagesimal Base95 encoding, a variant of Base94 with the addition of the Space character.
96 Hexanonagesimal Base96 encoding, using all of ASCII printable characters as well as the two extra duodecimal digits
100 Centesimal As 100=102, these are two decimal digits
120 Centevigesimal Base120 encoding
121 Centeunvigesimal Related to base 11
125 Centepentavigesimal Related to base 5
128 Centeoctovigesimal Using as 128=27
144 Centetetraquadragesimal Two duodecimal digits
256 Duocentehexaquinquagesimal Base256 encoding, as 256=28
360 Trecentosexagesimal Degrees for angle

Non-standard positional numeral systems

Bijective numeration

Base Name Usage
1 Unary (Bijective base-1) Tally marks
2 Bijective base-2
3 Bijective base-3
4 Bijective base-4
5 Bijective base-5
6 Bijective base-6
8 Bijective base-8
10 Bijective base-10
12 Bijective base-12
16 Bijective base-16
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.

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.

History

Immediately after conquering Ryūkyū, Satsuma conducted a land survey in Okinawa in 1609 and in Yaeyama in 1611. By doing so, Satsuma decided the amount of tribute to be paid annually by Ryūkyū. Following that, Ryūkyū imposed a poll tax on Yaeyama in 1640. A fixed quota was allocated to each island and then was broken up into each community. Finally, quotas were set for the individual islanders, adjusted only by age and gender. Community leaders were notified of quotas in the government office on Ishigaki. They checked the calculation using warazan (barazan in Yaeyama), a straw-based method of calculation and recording numerals that was reminiscent of Incan Quipu. After that, the quota for each household was written on a wooden plate called itafuda or hansatsu (板札 ). That was where Kaidā glyphs were used. Although sōrō-style Written Japanese had the status of administrative language, the remote islands had to rely on pictograms to notify illiterate peasants. According to a 19th-century document cited by the Yaeyama rekishi (1954), an official named Ōhama Seiki designed "perfect ideographs" for itafuda in the early 19th century although it suggests the existence of earlier, "imperfect" ideographs. Sudō (1944) recorded an oral history on Yonaguni: 9 generations ago, an ancestor of the Kedagusuku lineage named Mase taught Kaidā glyphs and warazan to the public. Sudō dated the event to the second half of the 17th century.

According to Ikema (1959), Kaidā glyphs and warazan were evidently accurate enough to make corrections to official announcements. The poll tax was finally abolished in 1903. They were used until the introduction of the nationwide primary education system rapidly lowered the illiteracy rate during the Meiji period. They are currently used on Yonaguni and Taketomi for folk art, T-shirts, and other products, more for their artistic value than as a record-keeping system.

Non-standard positional numeral systems

Bijective numeration

Base Name Usage
1 Unary (Bijective base-1) Tally marks
2 Bijective base-2
3 Bijective base-3
4 Bijective base-4
5 Bijective base-5
6 Bijective base-6
8 Bijective base-8
10 Bijective base-10
12 Bijective base-12
16 Bijective base-16
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.

Negative bases

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

Base Name Usage
−2 Negabinary
−3 Negaternary
−4 Negaquaternary
−5 Negaquinary
−6 Negasenary
−8 Negaoctal
−10 Negadecimal
−12 Negaduodecimal
−16 Negahexadecimal

By type of notation

Binary clock
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. There have been some proposals for standardisation.

Base Name Usage
2 Binary Digital computing, imperial and customary volume (bushel-kenning-peck-gallon-pottle-quart-pint-cup-gill-jack-fluid ounce-tablespoon)
3 Ternary 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 Quaternary Data transmission, DNA bases and Hilbert curves; Chumashan languages, and Kharosthi numerals
5 Quinary Gumatj, Ateso, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
6 Senary Diceware, Ndom, Kanum, and Proto-Uralic language (suspected)
7 Septenary Weeks timekeeping, Western music letter notation
8 Octal Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, compact notation for binary numbers, Xiantian (I Ching, China)
9 Nonary Base9 encoding; compact notation for ternary
10 Decimal / Denary Most widely used by modern civilizations
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; check digit in ISBN. A base-11 number system was attributed to the Māori (New Zealand) in the 19th century and the Pangwa (Tanzania) in the 20th century.
12 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; 12-hour clock and months timekeeping; years of Chinese zodiac; foot and inch; Roman fractions
13 Tridecimal Base13 encoding; Conway base 13 function
14 Tetradecimal Programming for the HP 9100A/B calculator and image processing applications; pound and stone
15 Pentadecimal Telephony routing over IP, and the Huli language
16 Hexadecimal Base16 encoding; compact notation for binary data; tonal system; ounce and pound
17 Heptadecimal Base17 encoding
18 Octodecimal Base18 encoding
19 Enneadecimal Base19 encoding
20 Vigesimal Basque, Celtic, Maya, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages
21 Unvigesimal Base21 encoding
22 Duovigesimal Base22 encoding
23 Trivigesimal Kalam language, Kobon language
24 Tetravigesimal 24-hour clock timekeeping; Kaugel language
25 Pentavigesimal Base25 encoding
26 Hexavigesimal Base26 encoding; sometimes used for encryption or ciphering, using all letters
27 Heptavigesimal Septemvigesimal Telefol and Oksapmin 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, to provide a concise encoding of alphabetic strings, or as the basis for a form of gematria. Compact notation for ternary.
28 Octovigesimal Base28 encoding; months timekeeping
29 Enneavigesimal Base29
30 Trigesimal The 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
31 Untrigesimal Base31
32 Duotrigesimal Base32 encoding and the Ngiti language
33 Tritrigesimal Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong
34 Tetratrigesimal Using all numbers and all letters except I and O
35 Pentatrigesimal Using all numbers and all letters except O
36 Hexatrigesimal Base36 encoding; use of letters with digits
37 Heptatrigesimal Base37; using all numbers and all letters of the Spanish alphabet
38 Octotrigesimal Base38 encoding; use all duodecimal digits and all letters
40 Quadragesimal DEC 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.
42 Duoquadragesimal Base42 encoding
45 Pentaquadragesimal Base45 encoding
48 Octoquadragesimal Base48 encoding
49 Enneaquadragesimal Compact notation for septenary
50 Quinquagesimal Base50 encoding; SQUOZE encoding used to compactly represent file names and other symbols on some IBM computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits.
52 Duoquinquagesimal Base52 encoding, a variant of Base62 without vowels or a variant of Base26 using all lower and upper case letters.
54 Tetraquinquagesimal Base54 encoding
56 Hexaquinquagesimal Base56 encoding, a variant of Base58
57 Heptaquinquagesimal Base57 encoding, a variant of Base62 excluding I, O, l, U, and u or I, 1, l, 0, and O
58 Octoquinquagesimal Base58 encoding, a variant of Base62 excluding 0 (zero), I (capital i), O (capital o) and l (lower case L).
60 Sexagesimal Babylonian numerals; NewBase60 encoding, similar to Base62, excluding I, O, and l, but including _(underscore); degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari and Sumerian languages
62 Duosexagesimal Base62 encoding, using 0–9, A–Z, and a–z
64 Tetrasexagesimal Base64 encoding; I 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 (for example, YouTube video codes use the hyphen and underscore characters, - and _ to total 64).
72 Duoseptuagesimal Base72 encoding
80 Octogesimal Base80 encoding
81 Unoctogesimal Base81 encoding, using as 81=34 is related to ternary
85 Pentoctogesimal Ascii85 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.
90 Nonagesimal Related to Goormaghtigh conjecture for the generalized repunit numbers.
91 Unnonagesimal Base91 encoding, using all ASCII except "-" (0x2D), "\" (0x5C), and " (0x27); one variant uses "\" (0x5C) in place of """ (0x22).
92 Duononagesimal Base92 encoding, using all of ASCII except for "`" (0x60) and """ (0x22) due to confusability.
93 Trinonagesimal Base93 encoding, using all of ASCII printable characters except for "," (0x27) and "-" (0x3D) as well as the Space character. "," is reserved for delimiter and "-" is reserved for negation.
94 Tetranonagesimal Base94 encoding, using all of ASCII printable characters.
95 Pentanonagesimal Base95 encoding, a variant of Base94 with the addition of the Space character.
96 Hexanonagesimal Base96 encoding, using all of ASCII printable characters as well as the two extra duodecimal digits
100 Centesimal As 100=102, these are two decimal digits
120 Centevigesimal Base120 encoding
121 Centeunvigesimal Related to base 11
125 Centepentavigesimal Related to base 5
128 Centeoctovigesimal Using as 128=27
144 Centetetraquadragesimal Two duodecimal digits
256 Duocentehexaquinquagesimal Base256 encoding, as 256=28
360 Trecentosexagesimal Degrees for angle

Non-standard positional numeral systems

Bijective numeration

Base Name Usage
1 Unary (Bijective base-1) Tally marks
2 Bijective base-2
3 Bijective base-3
4 Bijective base-4
5 Bijective base-5
6 Bijective base-6
8 Bijective base-8
10 Bijective base-10
12 Bijective base-12
16 Bijective base-16
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.

Signed-digit representation

Base Name Usage
2 Balanced binary (Non-adjacent form)
3 Balanced ternary Ternary computers
4 Balanced quaternary
5 Balanced quinary
6 Balanced senary
7 Balanced septenary
8 Balanced octal
9 Balanced nonary
10 Balanced decimal John Colson
Augustin Cauchy
11 Balanced undecimal
12 Balanced duodecimal

Negative bases

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

Base Name Usage
−2 Negabinary
−3 Negaternary
−4 Negaquaternary
−5 Negaquinary
−6 Negasenary
−8 Negaoctal
−10 Negadecimal
−12 Negaduodecimal
−16 Negahexadecimal

Complex bases

Base Name Usage
2i Quater-imaginary base related to base −4 and base 16
\sqrt{2}i Base \sqrt{2}i related to base −2 and base 4
\sqrt[4]{2}i Base \sqrt[4]{2}i related to base 2
2 \omega Base 2 \omega related to base 8
\sqrt[3]{2} \omega Base \sqrt[3]{2} \omega related to base 2
−1 ± i Twindragon base Twindragon fractal shape, related to base −4 and base 16
1 ± i Nega-Twindragon base related to base −4 and base 16

Non-integer bases

Base Name Usage
\frac{3}{2} Base \frac{3}{2} a rational non-integer base
\frac{4}{3} Base \frac{4}{3} related to duodecimal
\frac{5}{2} Base \frac{5}{2} related to decimal
\sqrt{2} Base \sqrt{2} related to base 2
\sqrt{3} Base \sqrt{3} related to base 3
\sqrt[3]{2} Base \sqrt[3]{2}
\sqrt[4]{2} Base \sqrt[4]{2}
\sqrt[12]{2} Base \sqrt[12]{2} using in music scale
2\sqrt{2} Base 2\sqrt{2}
-\frac{3}{2} Base -\frac{3}{2} a negative rational non-integer base
-\sqrt{2} Base -\sqrt{2} a negative non-integer base, related to base 2
\sqrt{10} Base \sqrt{10} related to decimal
2\sqrt{3} Base 2\sqrt{3} related to duodecimal
φ Golden ratio base Early Beta encoder
ρ Plastic number base
ψ Supergolden ratio base
1+\sqrt{2} Silver ratio base
e Base e Lowest radix economy
π Base \pi
e^\pi Base e^\pi

n-adic number

Base Name Usage
2 Dyadic number
3 Triadic number
4 Tetradic number the same as dyadic number
5 Pentadic number
6 Hexadic number not a field
7 Heptadic number
8 Octadic number the same as dyadic number
9 Enneadic number the same as triadic number
10 Decadic number not a field
11 Hendecadic number
12 Dodecadic number not 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, ...}
  • {60, 60, 24, 7} in timekeeping
  • {60, 60, 24, 30 (or 31 or 28 or 29), 12} 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

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.

By type of notation

Binary clock
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. There have been some proposals for standardisation.

Base Name Usage
2 Binary Digital computing, imperial and customary volume (bushel-kenning-peck-gallon-pottle-quart-pint-cup-gill-jack-fluid ounce-tablespoon)
3 Ternary 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 Quaternary Data transmission, DNA bases and Hilbert curves; Chumashan languages, and Kharosthi numerals
5 Quinary Gumatj, Ateso, Nunggubuyu, Kuurn Kopan Noot, and Saraveca languages; common count grouping e.g. tally marks
6 Senary Diceware, Ndom, Kanum, and Proto-Uralic language (suspected)
7 Septenary Weeks timekeeping, Western music letter notation
8 Octal Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, compact notation for binary numbers, Xiantian (I Ching, China)
9 Nonary Base9 encoding; compact notation for ternary
10 Decimal / Denary Most widely used by modern civilizations
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; check digit in ISBN. A base-11 number system was attributed to the Māori (New Zealand) in the 19th century and the Pangwa (Tanzania) in the 20th century.
12 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; 12-hour clock and months timekeeping; years of Chinese zodiac; foot and inch; Roman fractions
13 Tridecimal Base13 encoding; Conway base 13 function
14 Tetradecimal Programming for the HP 9100A/B calculator and image processing applications; pound and stone
15 Pentadecimal Telephony routing over IP, and the Huli language
16 Hexadecimal Base16 encoding; compact notation for binary data; tonal system; ounce and pound
17 Heptadecimal Base17 encoding
18 Octodecimal Base18 encoding
19 Enneadecimal Base19 encoding
20 Vigesimal Basque, Celtic, Maya, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages
21 Unvigesimal Base21 encoding
22 Duovigesimal Base22 encoding
23 Trivigesimal Kalam language, Kobon language
24 Tetravigesimal 24-hour clock timekeeping; Kaugel language
25 Pentavigesimal Base25 encoding
26 Hexavigesimal Base26 encoding; sometimes used for encryption or ciphering, using all letters
27 Heptavigesimal Septemvigesimal Telefol and Oksapmin 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, to provide a concise encoding of alphabetic strings, or as the basis for a form of gematria. Compact notation for ternary.
28 Octovigesimal Base28 encoding; months timekeeping
29 Enneavigesimal Base29
30 Trigesimal The 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
31 Untrigesimal Base31
32 Duotrigesimal Base32 encoding and the Ngiti language
33 Tritrigesimal Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong
34 Tetratrigesimal Using all numbers and all letters except I and O
35 Pentatrigesimal Using all numbers and all letters except O
36 Hexatrigesimal Base36 encoding; use of letters with digits
37 Heptatrigesimal Base37; using all numbers and all letters of the Spanish alphabet
38 Octotrigesimal Base38 encoding; use all duodecimal digits and all letters
40 Quadragesimal DEC 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.
42 Duoquadragesimal Base42 encoding
45 Pentaquadragesimal Base45 encoding
48 Octoquadragesimal Base48 encoding
49 Enneaquadragesimal Compact notation for septenary
50 Quinquagesimal Base50 encoding; SQUOZE encoding used to compactly represent file names and other symbols on some IBM computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits.
52 Duoquinquagesimal Base52 encoding, a variant of Base62 without vowels or a variant of Base26 using all lower and upper case letters.
54 Tetraquinquagesimal Base54 encoding
56 Hexaquinquagesimal Base56 encoding, a variant of Base58
57 Heptaquinquagesimal Base57 encoding, a variant of Base62 excluding I, O, l, U, and u or I, 1, l, 0, and O
58 Octoquinquagesimal Base58 encoding, a variant of Base62 excluding 0 (zero), I (capital i), O (capital o) and l (lower case L).
60 Sexagesimal Babylonian numerals; NewBase60 encoding, similar to Base62, excluding I, O, and l, but including _(underscore); degrees-minutes-seconds and hours-minutes-seconds measurement systems; Ekari and Sumerian languages
62 Duosexagesimal Base62 encoding, using 0–9, A–Z, and a–z
64 Tetrasexagesimal Base64 encoding; I 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 (for example, YouTube video codes use the hyphen and underscore characters, - and _ to total 64).
72 Duoseptuagesimal Base72 encoding
80 Octogesimal Base80 encoding
81 Unoctogesimal Base81 encoding, using as 81=34 is related to ternary
85 Pentoctogesimal Ascii85 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.
90 Nonagesimal Related to Goormaghtigh conjecture for the generalized repunit numbers.
91 Unnonagesimal Base91 encoding, using all ASCII except "-" (0x2D), "\" (0x5C), and " (0x27); one variant uses "\" (0x5C) in place of """ (0x22).
92 Duononagesimal Base92 encoding, using all of ASCII except for "`" (0x60) and """ (0x22) due to confusability.
93 Trinonagesimal Base93 encoding, using all of ASCII printable characters except for "," (0x27) and "-" (0x3D) as well as the Space character. "," is reserved for delimiter and "-" is reserved for negation.
94 Tetranonagesimal Base94 encoding, using all of ASCII printable characters.
95 Pentanonagesimal Base95 encoding, a variant of Base94 with the addition of the Space character.
96 Hexanonagesimal Base96 encoding, using all of ASCII printable characters as well as the two extra duodecimal digits
100 Centesimal As 100=102, these are two decimal digits
120 Centevigesimal Base120 encoding
121 Centeunvigesimal Related to base 11
125 Centepentavigesimal Related to base 5
128 Centeoctovigesimal Using as 128=27
144 Centetetraquadragesimal Two duodecimal digits
256 Duocentehexaquinquagesimal Base256 encoding, as 256=28
360 Trecentosexagesimal Degrees for angle

Non-standard positional numeral systems

Bijective numeration

Base Name Usage
1 Unary (Bijective base-1) Tally marks
2 Bijective base-2
3 Bijective base-3
4 Bijective base-4
5 Bijective base-5
6 Bijective base-6
8 Bijective base-8
10 Bijective base-10
12 Bijective base-12
16 Bijective base-16
Other
  • Quote notation
  • Redundant binary representation
  • Hereditary base-n notation
  • Asymmetric numeral systems optimized for non-uniform probability distribution of symbols
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.

Other
  • Quote notation
  • Redundant binary representation
  • Hereditary base-n notation
  • Asymmetric numeral systems optimized for non-uniform probability distribution of symbols
Other
  • Quote notation
  • Redundant binary representation
  • Hereditary base-n notation
  • Asymmetric numeral systems optimized for non-uniform probability distribution of symbols
Other
  • Quote notation
  • Redundant binary representation
  • Hereditary base-n notation
  • Asymmetric numeral systems optimized for non-uniform probability distribution of symbols
Other
  • Quote notation
  • Redundant binary representation
  • Hereditary base-n notation
  • Asymmetric numeral systems optimized for non-uniform probability distribution of symbols

Letters

Adlam has both major and minor cases. See Omniglot in the external links for the pronunciation of the basic letters

Capital Minuscule Latin Letter Name IPA
𞤀 𞤢 a alif a
𞤁 𞤣 d dâli d
𞤂 𞤤 l lam l
𞤃 𞤥 m mim m
𞤄 𞤦 b ba b
𞤅 𞤧 s singniyhé s
𞤆 𞤨 p p
𞤇 𞤩 ɓ (bh) bhè ɓ
𞤈 𞤪 r ra r/ɾ
𞤉 𞤫 e è e
𞤊 𞤬 f fa f
𞤋 𞤭 i i i
𞤌 𞤮 o ö o
𞤍 𞤯 ɗ (dh) dha ɗ
𞤎 𞤰 ƴ (yh) yhè ʔʲ
𞤏 𞤱 w wâwou w
𞤐 𞤲 n, any syllable-final nasal noûn n
𞤑 𞤳 k kaf k
𞤒 𞤴 y ya j
𞤓 𞤵 u ou u
𞤔 𞤶 j djim
𞤕 𞤷 c tchi
𞤖 𞤸 h ha h
𞤗 𞤹 ɠ (q) ghaf q
𞤘 𞤺 g ga ɡ
𞤙 𞤻 ñ (ny) gna ɲ
𞤚 𞤼 t tou t
𞤛 𞤽 ŋ (nh) nha ŋ
Supplemental: for other languages or for loanwords
𞤜 𞤾 v va v
𞤝 𞤿 x (kh) kha x
𞤞 𞥀 ɡb gbe ɡ͡b
𞤟 𞥁 z zal z
𞤠 𞥂 kp kpo k͡p
𞤡 𞥃 sh sha ʃ

The letters are found either joined akin to Arabic or separately - the joined form is commonly used in a cursive manner, however separate or block forms are also used as primarily for educational content.

Digits

Unlike in Arabic script, Adlam digits go in the same direction (right to left) as letters.

Adlam Hindu-Arabic
𞥐 0
𞥑 1
𞥒 2
𞥓 3
𞥔 4
𞥕 5
𞥖 6
𞥗 7
𞥘 8
𞥙 9
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