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Numeral systems |
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List of numeral systems |
There are many different numeral systems, that is, writing systems for expressing numbers.
Name | Base | Sample | Approx. First Appearance | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Proto-cuneiform numerals | 10&60 | c. 3500–2000 BCE | ||||||||||
Indus numerals | c. 3500–1900 BCE | |||||||||||
Proto-Elamite numerals | 10&60 | 3,100 BCE | ||||||||||
Sumerian numerals | 10&60 | 3,100 BCE | ||||||||||
Egyptian numerals | 10 | 3,000 BCE | ||||||||||
Babylonian numerals | 10&60 | 2,000 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 ( ) | 1,500 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) | 1,300 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 | 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 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 [1] | <250 BCE [2] | |||||||||
Chinese rod numerals | 10 | 𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨 𝍩 | 1st Century | |||||||||
Coptic numerals | 10 | Ⲁ Ⲃ Ⲅ Ⲇ Ⲉ Ⲋ Ⲍ Ⲏ Ⲑ | 2nd 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) [3] | |||||||||
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 [4] | |||||||||
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 | |||||||||
Vietnamese numerals (Chữ Nôm) | 10 | 𠬠 𠄩 𠀧 𦊚 𠄼 𦒹 𦉱 𠔭 𠃩 | <9th Century | |||||||||
Western Arabic numerals | 10 | 0 1 2 3 4 5 6 7 8 9 | 9th Century | |||||||||
Glagolitic numerals | 10 | Ⰰ Ⰱ Ⰲ Ⰳ Ⰴ Ⰵ Ⰶ Ⰷ Ⰸ ... | 9th Century | |||||||||
Cyrillic numerals | 10 | а в г д е ѕ з и ѳ і ... | 10th Century | |||||||||
Rumi numerals | 10 | 10th Century | ||||||||||
Burmese numerals | 10 | ၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉ | 11th Century [5] | |||||||||
Tangut numerals | 10 | 𘈩 𗍫 𘕕 𗥃 𗏁 𗤁 𗒹 𘉋 𗢭 𗰗 | 11th Century (1036) | |||||||||
Cistercian numerals | 10 | 13th Century | ||||||||||
Maya numerals | 5&20 | <15th Century | ||||||||||
Muisca numerals | 20 | <15th Century | ||||||||||
Korean numerals (Hangul) | 10 | 영 일 이 삼 사 오 육 칠 팔 구 | 15th Century (1443) | |||||||||
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 | |||||||||
Pentadic runes | 10 | 19th Century | ||||||||||
Cherokee numerals | 10 | 19th Century (1820s) | ||||||||||
Osmanya numerals | 10 | 𐒠 𐒡 𐒢 𐒣 𐒤 𐒥 𐒦 𐒧 𐒨 𐒩 | 20th Century (1920s) | |||||||||
Hmong numerals | 10 | 𖭐 𖭑 𖭒 𖭓 𖭔 𖭕 𖭖 𖭗 𖭘 𖭙 | 20th Century (1959) | |||||||||
Kaktovik numerals | 5&20 | 20th Century (1994) |
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.
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. [6] There have been some proposals for standardisation. [7]
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 | 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, seximal | Diceware, Ndom, Kanum, and Proto-Uralic language (suspected) |
7 | Septimal, Septenary [8] | Weeks timekeeping, Western music letter notation |
8 | Octal | Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, Yuki, Pame, compact notation for binary numbers, Xiantian (I Ching, China) |
9 | Nonary, nonal | Compact notation for ternary |
10 | Decimal, denary | Most widely used by contemporary societies [9] [10] [11] |
11 | Undecimal, unodecimal, undenary | A base-11 number system was attributed to the Māori (New Zealand) in the 19th century [12] and the Pangwa (Tanzania) in the 20th century. [13] 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. [14] [15] [16] Featured in popular fiction. |
12 | Duodecimal, dozenal | 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; penny and shilling |
13 | Tredecimal, tridecimal [17] [18] | Conway base 13 function. |
14 | Quattuordecimal, quadrodecimal [17] [18] | Programming for the HP 9100A/B calculator [19] and image processing applications; [20] pound and stone. |
15 | Quindecimal, pentadecimal [21] [18] | Telephony routing over IP, and the Huli language. |
16 | Hexadecimal, sexadecimal, sedecimal | Compact notation for binary data; tonal system; ounce and pound. |
17 | Septendecimal, heptadecimal [21] [18] | |
18 | Octodecimal [21] [18] | A base in which 7n is palindromic for n = 3, 4, 6, 9. |
19 | Undevicesimal, nonadecimal [21] [18] | |
20 | Vigesimal | Basque, Celtic, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages; shilling and pound |
5&20 | Quinary-vigesimal [22] [23] [24] | Greenlandic, 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" [22] |
21 | The smallest base in which all fractions 1/2 to 1/18 have periods of 4 or shorter. | |
23 | Kalam language, [25] Kobon language [ citation needed ] | |
24 | Quadravigesimal [26] | 24-hour clock timekeeping; Greek alphabet; Kaugel language. |
25 | Sometimes used as compact notation for quinary. | |
26 | Hexavigesimal [26] [27] | Sometimes used for encryption or ciphering, [28] using all letters in the English alphabet |
27 | Septemvigesimal | Telefol, [29] Oksapmin, [30] Wambon, [31] and Hewa [32] 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, [33] to provide a concise encoding of alphabetic strings, [34] or as the basis for a form of gematria. [35] Compact notation for ternary. |
28 | Months timekeeping. | |
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. |
32 | Duotrigesimal | Found in the Ngiti language. |
33 | Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong. | |
34 | Using 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. | |
35 | Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O. | |
36 | Hexatrigesimal [36] [37] | Covers the ten decimal digits and all letters of the English alphabet. |
37 | Covers the ten decimal digits and all letters of the Spanish alphabet. | |
38 | Covers the duodecimal digits and all letters of the English alphabet. | |
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 | Largest base for which all minimal primes are known. | |
47 | Smallest base for which no generalized Wieferich primes are known. | |
49 | Compact notation for septenary. | |
50 | Quinquagesimal | 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 | Covers the digits and letters assigned to base 62 apart from the basic vowel letters; [38] similar to base 26 but distinguishing upper- and lower-case letters. | |
56 | A variant of base 58.[ clarification needed ] [39] | |
57 | Covers base 62 apart from I, O, l, U, and u, [40] or I, 1, l, 0, and O. [41] | |
58 | Covers base 62 apart from 0 (zero), I (capital i), O (capital o) and l (lower case L). [42] | |
60 | Sexagesimal | Babylonian 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). [43] |
62 | Can be notated with the digits 0–9 and the cased letters A–Z and a–z of the English alphabet. | |
64 | Tetrasexagesimal | 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 (+ and /). |
72 | The smallest base greater than binary such that no three-digit narcissistic number exists. | |
80 | Octogesimal | Used as a sub-base in Supyire. |
85 | 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. | |
89 | Largest base for which all left-truncatable primes are known. | |
90 | Nonagesimal | Related to Goormaghtigh conjecture for the generalized repunit numbers (111 in base 90 = 1111111111111 in base 2). |
95 | Number of printable ASCII characters. [44] | |
96 | Total number of character codes in the (six) ASCII sticks containing printable characters. | |
97 | Smallest base which is not perfect odd power (where generalized Wagstaff numbers can be factored algebraically) for which no generalized Wagstaff primes are known. | |
100 | Centesimal | As 100=102, these are two decimal digits. |
121 | Number expressible with two undecimal digits. | |
125 | Number expressible with three quinary digits. | |
128 | Using as 128=27.[ clarification needed ] | |
144 | Number expressible with two duodecimal digits. | |
169 | Number expressible with two tridecimal digits. | |
185 | Smallest base which is not a perfect power (where generalized repunits can be factored algebraically) for which no generalized repunit primes are known. | |
196 | Number expressible with two tetradecimal digits. | |
210 | Smallest base such that all fractions 1/2 to 1/10 terminate. | |
225 | Number expressible with two pentadecimal digits. | |
256 | Number expressible with eight binary digits. | |
360 | Degrees of angle. |
Base | Name | Usage |
---|---|---|
1 | Unary (Bijective base‑1) | Tally marks, Counting |
10 | Bijective base-10 | To avoid zero |
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. [45] |
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 |
Base | Name | Usage |
---|---|---|
2i | Quater-imaginary base | related to base −4 and base 16 |
Base | related to base −2 and base 4 | |
Base | related to base 2 | |
Base | related to base 8 | |
Base | related to base 2 | |
−1 ± i | Twindragon base | Twindragon fractal shape, related to base −4 and base 16 |
1 ± i | Negatwindragon base | related to base −4 and base 16 |
Base | Name | Usage |
---|---|---|
Base | a rational non-integer base | |
Base | related to duodecimal | |
Base | related to decimal | |
Base | related to base 2 | |
Base | related to base 3 | |
Base | ||
Base | ||
Base | usage in 12-tone equal temperament musical system | |
Base | ||
Base | a negative rational non-integer base | |
Base | a negative non-integer base, related to base 2 | |
Base | related to decimal | |
Base | related to duodecimal | |
φ | Golden ratio base | Early Beta encoder [46] |
ρ | Plastic number base | |
ψ | Supergolden ratio base | |
Silver ratio base | ||
e | Base | Lowest radix economy |
π | Base | |
e π | Base | |
Base |
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 |
All known numeral systems developed before the Babylonian numerals are non-positional, [47] as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.
The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared, "1000" means twelve cubed, and "0.1" means a twelfth.
In mathematics and computing, the hexadecimal numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" to represent values from ten to fifteen.
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
In linguistics, a numeral in the broadest sense is a word or phrase that describes a numerical quantity. Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the "two" in "two hats". Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an adjective. Some theories consider "numeral" to be a synonym for "number" and assign all numbers to a part of speech called "numerals". Numerals in the broad sense can also be analyzed as a noun, as a pronoun, or for a small number of words as an adverb.
1 is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0.
A senary numeral system has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime. As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary.
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times.
Babylonian cuneiform numerals, also used in Assyria and Chaldea, were written in cuneiform, using a wedge-tipped reed stylus to print a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.
A vigesimal or base-20 (base-score) numeral system is based on twenty. Vigesimal is derived from the Latin adjective vicesimus, meaning 'twentieth'.
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one).
Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same factor. Such units are common for instance in measuring time; a time of 32 weeks, 5 days, 7 hours, 45 minutes, 15 seconds, and 500 milliseconds might be expressed as a number of minutes in mixed-radix notation as:
... 32, 5, 07, 45; 15, 500 ... ∞, 7, 24, 60; 60, 1000
A numerical digit or numeral is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
Positional notation usually denotes the extension to any base of the Hindu–Arabic numeral system. More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred. In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.
Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five digits on either hand.
Non-standard positional numeral systems here designates numeral systems that may loosely be described as positional systems, but that do not entirely comply with the following description of standard positional systems:
The Kaktovik numerals or Kaktovik Iñupiaq numerals are a base-20 system of numerical digits created by Alaskan Iñupiat. They are visually iconic, with shapes that indicate the number being represented.
An alphabetic numeral system is a type of numeral system. Developed in classical antiquity, it flourished during the early Middle Ages. In alphabetic numeral systems, numbers are written using the characters of an alphabet, syllabary, or another writing system. Unlike acrophonic numeral systems, where a numeral is represented by the first letter of the lexical name of the numeral, alphabetic numeral systems can arbitrarily assign letters to numerical values. Some systems, including the Arabic, Georgian and Hebrew systems, use an already established alphabetical order. Alphabetic numeral systems originated with Greek numerals around 600 BC and became largely extinct by the 16th century. After the development of positional numeral systems like Hindu–Arabic numerals, the use of alphabetic numeral systems dwindled to predominantly ordered lists, pagination, religious functions, and divinatory magic.
Alphasyllabic numeral systems are a type of numeral systems, developed mostly in India starting around 500 AD. Based on various alphasyllabic scripts, in this type of numeral systems glyphs of the numerals are not abstract signs, but syllables of a script, and numerals are represented with these syllable-signs. On the basic principle of these systems, numeric values of the syllables are defined by the consonants and vowels which constitute them, so that consonants and vowels are - or are not in some systems in case of vowels - ordered to numeric values. While there are many hundreds of possible syllables in a script, and since in alphasyllabic numeral systems several syllables receive the same numeric value, so the mapping is not injective.
... unodecimal, duodecimal, tridecimal, quadrodecimal, pentadecimal, heptadecimal, octodecimal, nona decimal, vigesimal and further are discussed...
A student of the American Indian languages is naturally led to investigate the wide-spread use of the quinary-vigesimal system of counting which he meets in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon.
Quinary-vigesimal. This is most frequent. The Greenland Eskimo says 'other hand two' for 7, 'first foot two' for 12, 'other foot two' for 17, and similar combinations to 20, 'man ended.' The Unalit is also quinary to twenty, which is 'man completed.' ...
There's even a hexavigesimal digital code—our own twenty-six symbol variant of the ancient Latin alphabet, which the Romans derived in turn from the quadravigesimal version used by the ancient Greeks.
[…] 2) the hexadecimal output of the hash function is converted to hexavigesimal (base-26); 3) letters in the hexavigesimal number are capitalized, while all numerals are left unchanged; 4) the order of the characters is reversed so that the hexavigesimal digits appear […]
This article proposes the Unique Number Mapping as an identification scheme, that could replace the E.164 numbers, could be used both with PSTN and VoIP terminals and makes use of the elements of the ENUM technology and the hexatrigesimal number system. […] To have the shortest IDs, we should use the greatest possible number system, which is the hexatrigesimal. Here the place values correspond to powers of 36...
Concord Numbers used in the categorisation of Luganda words encoded using either Hexatrigesimal or Duotrigesimal, standard positional numbering systems. […] We propose Hexatrigesimal system to capture numeric information exceeding 10 for adaptation purposes for other Bantu languages or other agglutinative languages.
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: CS1 maint: numeric names: authors list (link)Thanks to Satoshi Nakamoto for inventing the Base58 encoding format