Alutor language facts for kids

By culture / time period

Name	Base	Sample	Approx. First Appearance
Alutor Numerals			-35000 !35,000 BCE
Babylonian numerals	60		-3100 !3,100 BCE
Egyptian numerals	10		-3000 !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)	-1600 !1,600 BCE
Aegean numerals	10	𐄇 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 !1,500 BCE
Roman numerals		I V X L C D M	-1000 !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 !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 !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 !<400 BCE
Phoenician numerals	10	𐤙 𐤘 𐤗 𐤛𐤛𐤛 𐤛𐤛𐤚 𐤛𐤛𐤖 𐤛𐤛 𐤛𐤚 𐤛𐤖 𐤛 𐤚 𐤖	-250 !<250 BCE
Chinese rod numerals	10	𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨 𝍩	1 !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	200 !3rd – 4th Century, 15th Century (Modern Style)
Armenian numerals	10	Ա Բ Գ Դ Ե Զ Է Ը Թ Ժ	400 !Early 5th Century
Khmer numerals	10	០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩	600 !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	700 !<8th Century
Eastern Arabic numerals	10	٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠	701 !8th Century
Western Arabic numerals	10	0 1 2 3 4 5 6 7 8 9	800 !9th Century
Cyrillic numerals	10	А҃ В҃ Г҃ Д҃ Е҃ Ѕ҃ З҃ И҃ Ѳ҃ І҃ ...	900 !10th Century
Tangut numerals	10	Template:Tangut	1036 !1036
Burmese numerals	10	၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉	1000 !11th Century
Maya numerals	20		1400 !<15th Century
Muisca numerals	20		1400 !<15th Century
Aztec numerals	20		1500 !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	1700 !<18th Century
Kaktovik Inupiaq numerals	20		1994

By type of notation

Not to be confused with Algerian Saharan Arabic.

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 Semitic Central Semitic Arabic Maghrebi Arabic Algerian Arabic
Writing system	Arabic script

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

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code: ja is deprecated ). 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

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

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	pè	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	dʒ
𞤕	𞤷	c	tchi	tʃ
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