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There are many different numeral systems, that is, writing systems for expressing numbers.
By culture / time period
[edit]"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system."[1]:โ38โ The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers.[1] Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base).
| Name | Base | Sample | Approx. First Appearance | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Proto-cuneiform numerals | 10&60 | c. 3500โ2000 BCE | ||||||||||
| Indus numerals | unknown[2] | c. 3500โ1900 BCE[2] | ||||||||||
| Proto-Elamite numerals | 10&60 | 3100 BCE | ||||||||||
| Sumerian numerals | 10&60 | 3100 BCE | ||||||||||
| Egyptian numerals | 10 |
|
3000 BCE | |||||||||
| Babylonian numerals | 10&60 | ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image |
2000 BCE | |||||||||
| Aegean numerals | 10 | ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ( ๐ 1 ๐ 2 ๐ 3 ๐ 4 ๐ 5 ๐ 6 ๐ 7 ๐ 8 ๐ 9 ) ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ( ๐ 10 ๐ 20 ๐ 30 ๐ 40 ๐ 50 ๐ 60 ๐ 70 ๐ 80 ๐ 90 ) ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ก ( ๐ 100 ๐ 200 ๐ 300 ๐ 400 ๐ 500 ๐ 600 ๐ 700 ๐ 800 ๐ 900 ) ๐ข ๐ฃ ๐ค ๐ฅ ๐ฆ ๐ง ๐จ ๐ฉ ๐ช ( ๐ 1000 ๐ 2000 ๐ 3000 ๐ 4000 ๐ 5000 ๐ 6000 ๐ 7000 ๐ 8000 ๐ 9000 ) ๐ซ ๐ฌ ๐ญ ๐ฎ ๐ฏ ๐ฐ ๐ฑ ๐ฒ ๐ณ ( ๐ 10000 ๐ 20000 ๐ 30000 ๐ 40000 ๐ 50000 ๐ 60000 ๐ 70000 ๐ 80000 ๐ 90000 ) |
1500 BCE | |||||||||
| Chinese numerals Japanese numerals Korean numerals (Sino-Korean) Vietnamese numerals (Sino-Vietnamese) |
10 |
้ถไธไบไธๅไบๅ
ญไธๅ
ซไนๅ็พๅ่ฌๅ (Default, Traditional Chinese) |
1300 BCE | |||||||||
| Roman numerals | 5&10 | I V X L C D M | 1000 BCE[1] | |||||||||
| Hebrew numerals | 10 | ื ื ื ื ื ื ื ื ื ื ื ื ื ื ืก ืข ืค ืฆ ืง ืจ ืฉ ืช ื ื ื ืฃ ืฅ |
800 BCE | |||||||||
| Indian numerals | 10 |
Bengali เงฆ เงง เงจ เงฉ เงช เงซ เงฌ เงญ เงฎ เงฏ Devanagari เฅฆ เฅง เฅจ เฅฉ เฅช เฅซ เฅฌ เฅญ เฅฎ เฅฏ Gujarati เซฆ เซง เซจ เซฉ เซช เซซ เซฌ เซญ เซฎ เซฏ Kannada เณฆ เณง เณจ เณฉ เณช เณซ เณฌ เณญ เณฎ เณฏ Malayalam เตฆ เตง เตจ เตฉ เตช เตซ เตฌ เตญ เตฎ เตฏ Odia เญฆ เญง เญจ เญฉ เญช เญซ เญฌ เญญ เญฎ เญฏ Punjabi เฉฆ เฉง เฉจ เฉฉ เฉช เฉซ เฉฌ เฉญ เฉฎ เฉฏ Tamil เฏฆ เฏง เฏจ เฏฉ เฏช เฏซ เฏฌ เฏญ เฏฎ เฏฏ Telugu เฑฆ เฑง เฑจ เฑฉ เฑช เฑซ เฑฌ เฑญ เฑฎ เฑฏ |
750โ500 BCE | |||||||||
| Greek numerals | 10 | ล ฮฑ ฮฒ ฮณ ฮด ฮต ฯ ฮถ ฮท ฮธ ฮน ฮฟ ฮสน ฮสน ฮสน ฮสน ฮสน ฯสน ฮสน ฮสน ฮสน |
<400 BCE | |||||||||
| Kharosthi numerals | 4&10 | ๐ฉ ๐ฉ ๐ฉ ๐ฉ ๐ฉ ๐ฉ ๐ฉ ๐ฉ | <400โ250 BCE[3] | |||||||||
| Phoenician numerals | 10 | ๐ค ๐ค ๐ค ๐ค๐ค๐ค ๐ค๐ค๐ค ๐ค๐ค๐ค ๐ค๐ค ๐ค๐ค ๐ค๐ค ๐ค ๐ค ๐ค [4] | <250 BCE[5] | |||||||||
| Chinese rod numerals | 10 | ๐ ๐ก ๐ข ๐ฃ ๐ค ๐ฅ ๐ฆ ๐ง ๐จ ๐ฉ | 1st century | |||||||||
| Coptic numerals | 10 | โฒ โฒ โฒ โฒ โฒ โฒ โฒ โฒ โฒ | 2nd century | |||||||||
| Ge'ez numerals | 10 | แฉ แช แซ แฌ แญ แฎ แฏ แฐ แฑ แฒ แณ แด แต แถ แท แธ แน แบ แป แผ [6] |
3rdโ4th century 15th century (Modern Style)[7]:โ135โ136โ | |||||||||
| Armenian numerals | 10 | ิฑ ิฒ ิณ ิด ิต ิถ ิท ิธ ิน ิบ | Early 5th century | |||||||||
| Khmer numerals | 10 | แ แก แข แฃ แค แฅ แฆ แง แจ แฉ | Early 7th century | |||||||||
| Thai numerals | 10 | เน เน เน เน เน เน เน เน เน เน | 7th century[8] | |||||||||
| Abjad numerals | 10 | ุบ ุธ ุถ ุฐ ุฎ ุซ ุช ุด ุฑ ู ุต ู ุน ุณ ู ู ู ู ู ุท ุญ ุฒ ู ูู ุฏ ุฌ ุจ ุง | <8th century | |||||||||
| Chinese numerals (financial) | 10 | ้ถๅฃน่ฒณๅ่ไผ้ธๆๆ็ๆพไฝฐไป่ฌๅ (T. Chinese) ้ถๅฃน่ดฐๅ่ไผ้ๆๆ็ๆพไฝฐไป่ฌๅ (S. Chinese) |
late 7th/early 8th century[9] | |||||||||
| Eastern Arabic numerals | 10 | ูฉ ูจ ูง ูฆ ูฅ ูค ูฃ ูข ูก ู | 8th century | |||||||||
| Vietnamese numerals (Chแปฏ Nรดm) | 10 | ๐ ฌ ๐ ฉ ๐ ง ๐ฆ ๐ ผ ๐ฆน ๐ฆฑ ๐ ญ ๐ ฉ | <9th century | |||||||||
| Western Arabic numerals | 10 | 0 1 2 3 4 5 6 7 8 9 | 9th century | |||||||||
| Glagolitic numerals | 10 | โฐ โฐ โฐ โฐ โฐ โฐ โฐ โฐ โฐ ... | 9th century | |||||||||
| Cyrillic numerals | 10 | ะฐ ะฒ ะณ ะด ะต ั ะท ะธ ัณ ั ... | 10th century | |||||||||
| Rumi numerals | 10 | 10th century | ||||||||||
| Burmese numerals | 10 | แ แ แ แ แ แ แ แ แ แ | 11th century[10] | |||||||||
| Tangut numerals | 10 | ๐ฉ ๐ซ ๐ ๐ฅ ๐ ๐ค ๐น ๐ ๐ขญ ๐ฐ | 11th century (1036) | |||||||||
| Cistercian numerals | 10 | ๐ Image |
13th century | |||||||||
| Maya numerals | 5&20 | ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ ๐ก ๐ข ๐ฃ ๐ค ๐ฅ ๐ฆ ๐ง ๐จ ๐ฉ ๐ช ๐ซ ๐ฌ ๐ญ ๐ฎ ๐ฏ ๐ฐ ๐ฑ ๐ฒ ๐ณ |
15th century | |||||||||
| Muisca numerals | 20 | ๐ Image |
15th century | |||||||||
| Korean numerals (Hangul) | 10 | ์ ์ผ ์ด ์ผ ์ฌ ์ค ์ก ์น ํ ๊ตฌ | 15th century (1443) | |||||||||
| Aztec numerals | 20 | ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image ๐ Image (1, 5, 20, 100, 400, 800, 8000) |
16th century | |||||||||
| Sinhala numerals | 10 | เทฆ เทง เทจ เทฉ เทช เทซ เทฌ เทญ เทฎ เทฏ ๐ก ๐ข ๐ฃ ๐ค ๐ฅ ๐ฆ ๐ง ๐จ ๐ฉ ๐ช ๐ซ ๐ฌ ๐ญ ๐ฎ ๐ฏ ๐ฐ ๐ฑ ๐ฒ ๐ณ ๐ด |
18th century | |||||||||
| Pentadic runes | 10 | ๐ Image |
19th century | |||||||||
| Cherokee numerals | 10 | ๐ Image |
19th century (1820s) | |||||||||
| Vai numerals | 10 | ๊ ๊ก ๊ข ๊ฃ ๊ค ๊ฅ ๊ฆ ๊ง ๊จ ๊ฉ [11] | 19th century (1832)[12] | |||||||||
| Bamum numerals | 10 | ๊ฏ ๊ฆ ๊ง ๊จ ๊ฉ ๊ช ๊ซ ๊ฌ ๊ญ ๊ฎ [13] | 19th century (1896)[12] | |||||||||
| Mende Kikakui numerals | 10 | ๐ฃ ๐ฃ ๐ฃ ๐ฃ ๐ฃ ๐ฃ ๐ฃ ๐ฃ ๐ฃ [14] | 20th century (1917)[15] | |||||||||
| Osmanya numerals | 10 | ๐ ๐ก ๐ข ๐ฃ ๐ค ๐ฅ ๐ฆ ๐ง ๐จ ๐ฉ | 20th century (1920s) | |||||||||
| Medefaidrin numerals | 20 | ๐บ ๐บ/๐บ ๐บ/๐บ ๐บ/๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ ๐บ [16] | 20th century (1930s)[17] | |||||||||
| N'Ko numerals | 10 | ฿ ฿ ฿ ฿ ฿ ฿ ฿ ฿ ฿ ฿ [18] | 20th century (1949)[19] | |||||||||
| Hmong numerals | 10 | ๐ญ ๐ญ ๐ญ ๐ญ ๐ญ ๐ญ ๐ญ ๐ญ ๐ญ ๐ญ๐ญ | 20th century (1959) | |||||||||
| Garay numerals | 10 | ๐ Garay numbers [20] |
20th century (1961)[21] | |||||||||
| Adlam numerals | 10 | ๐ฅ ๐ฅ ๐ฅ ๐ฅ ๐ฅ ๐ฅ ๐ฅ ๐ฅ ๐ฅ ๐ฅ [22] | 20th century (1989)[23] | |||||||||
| Kaktovik numerals | 5&20 | ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ [24] |
20th century (1994)[25] | |||||||||
| Sundanese numerals | 10 | แฎฐ แฎฑ แฎฒ แฎณ แฎด แฎต แฎถ แฎท แฎธ แฎน | 20th century (1996)[26] |
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By type of notation
[edit]Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base.
Standard positional numeral systems
[edit]Some of this article's listed sources may not be reliable. Please help improve this article by looking for better, more reliable sources. Unreliable citations may be challenged and removed. (April 2023) (Learn how and when to remove this message) |
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.[27] There have been some proposals for standardisation.[28]
| 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, trinary[29] | 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 | Aneityum (traditional),[30] Ateso, Gumatj, Kuurn Kopan Noot, and Nunggubuyu, Saraveca languages; common count grouping e.g. tally marks |
| 6 | Senary, seximal | Diceware, Ndom, Kanum, and Proto-Uralic language (suspected) |
| 7 | Septimal, septenary | |
| 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[31][32][33] |
| 11 | Undecimal, unodecimal, undenary | A base-11 number system was mistakenly attributed to the Mฤori (New Zealand) in the 19th century[34] and one was reported to be used by the Pangwa (Tanzania) in the 20th century,[35] but was not confirmed by later research and is believed to also be an error.[36] 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.[37][38][39] |
| 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. |
| 13 | Tredecimal, tridecimal[40][41] | Conway's base 13 function. |
| 14 | Quattuordecimal, quadrodecimal[40][41] | Programming for the HP 9100A/B calculator[42] and image processing applications.[43] |
| 15 | Quindecimal, pentadecimal[44][41] | Telephony routing over IP, and the Huli language.[36] |
| 16 | Hexadecimal, sexadecimal, sedecimal | Compact notation for binary data; tonal system of Nystrom. |
| 17 | Heptadecimal, septendecimal[44][41] | |
| 18 | Octodecimal[44][41] | |
| 19 | Undevicesimal, nonadecimal[44][41] | |
| 20 | Vigesimal | Basque, Celtic, Muisca, Inuit, Yoruba, Tlingit, and Dzongkha numerals; Santali, and Ainu languages. |
| 5&20 | Quinary-vigesimal[45][46][47] | Greenlandic, Iรฑupiaq, Kaktovik, Maya, Nunivak Cupสผig, and Yupสผik numerals โ "wide-spread... in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon"[45] |
| 21 | The smallest base in which all fractions โ 1/2โ to โ 1/18โ have periods of 4 or shorter. | |
| 23 | Kalam language,[48] | |
| 24 | Quadravigesimal[49] | 24-hour clock timekeeping; Greek alphabet; Kaugel language. |
| 25 | Sometimes used as compact notation for quinary. | |
| 26 | Hexavigesimal[49][50] | Sometimes used for encryption or ciphering,[51] using all letters in the English alphabet. Used to encode SHA-256 hashes into uppercase letters in InChIKey (a standard indexing system of chemical structures)[52] and SID (sequence identification, an indexing system of PCR amplicons in forensics).[50] |
| 27 | Telefol,[48] Oksapmin,[53] Wambon,[54] and Hewa[55] 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,[56] to provide a concise encoding of alphabetic strings,[57] or as the basis for a form of gematria.[58] Compact notation for ternary. | |
| 28 | Months timekeeping. | |
| 30 | The Natural Area Code, this is the smallest base such that all of โ 1/2โ to โ 1/6โ terminate, a number n is a regular number if and only if โ 1/nโ terminates in base 30. | |
| 32 | Duotrigesimal | Found in the Ngiti language. Also used to encode computer (binary) data into an alphanumerical string without confusable characters (e.g. zero and "O", eight and "B") in RFC 4648, with each character standing for 5 bits. |
| 34 | The smallest base where โ 1/2โ terminates and all of โ 1/2โ to โ 1/18โ have periods of 4 or shorter. | |
| 36 | Hexatrigesimal[59][60] | Used to encode large numbers into an alphanumeric string (26 letters, 10 numbers). |
| 40 | 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.[citation needed] | |
| 50 | SQUOZE encoding used to compactly represent file names and other symbols on some IBM computers. Encoding using all Gurmukhi characters plus the Gurmukhi digits. | |
| 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).[61] |
| 64 | Used to encode computer (binary) data into a relatively compact string, with each character standing for 6 bits (RFC 4648). | |
| 72 | The smallest base greater than binary such that no three-digit narcissistic number exists. | |
| 80 | Used as a sub-base in Supyire. | |
| 89 | Largest base for which all left-truncatable primes are known. | |
| 90 | Related to Goormaghtigh conjecture for the generalized repunit numbers (111 in base 90 = 1111111111111 in base 2). | |
| 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. | |
| 185 | Smallest base which is not a perfect power (where generalized repunits can be factored algebraically) for which no generalized repunit primes are known. | |
| 210 | Smallest base such that all fractions โ 1/2โ to โ 1/10โ terminate. |
| Base | Name | Usage |
|---|---|---|
| 1 | Unary(Bijectivebaseโ1) | Tally marks, Counting. Unary numbering is used as part of some data compression algorithms such as Golomb coding. It also forms the basis for the Peano axioms for formalizing arithmetic within mathematical logic. A form of unary notation called Church encoding is used to represent numbers within lambda calculus.
Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the more likely the email is considered spam. |
| 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.[62] |
| 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 โ4 and base 16 |
| ๐ {\displaystyle i{\sqrt {2}}} |
Base ๐ {\displaystyle i{\sqrt {2}}} |
related to base โ2 and base 4 |
| ๐ {\displaystyle i{\sqrt[{4}]{2}}} |
Base ๐ {\displaystyle i{\sqrt[{4}]{2}}} |
related to base 2 |
| ๐ {\displaystyle 2\omega } |
Base ๐ {\displaystyle 2\omega } |
related to base 8 |
| ๐ {\displaystyle \omega {\sqrt[{3}]{2}}} |
Base ๐ {\displaystyle \omega {\sqrt[{3}]{2}}} |
related to base 2 |
| โ1 ยฑ i | Twindragon base | Twindragon fractal shape, related to base โ4 and base 16 |
| 1 ยฑ i | Negatwindragon base | related to base โ4 and base 16 |
| 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 |
- Factorial number system {1, 2, 3, 4, 5, 6, ...}
- Even double factorial number system {2, 4, 6, 8, 10, 12, ...}
- Odd double factorial number system {1, 3, 5, 7, 9, 11, ...}
- Primorial number system {2, 3, 5, 7, 11, 13, ...}
- Fibonorial number system {1, 2, 3, 5, 8, 13, ...}
- {60, 60, 24, 7} in timekeeping
- {60, 60, 24, 30 (or 31 or 28 or 29), 12, 10, 10, 10} in timekeeping
- (12, 20) traditional English monetary system (ยฃsd)
- (20, 18, 13) Maya timekeeping
Other
[edit]- Quote notation
- Redundant binary representation
- Hereditary base-n notation
- Asymmetric numeral systems optimized for non-uniform probability distribution of symbols
- Combinatorial number system
Non-positional notation
[edit]| ๐ [icon] | This section needs expansion. You can help by adding missing information. (March 2026) |
![๐ [icon]](https://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png){kind=link}
All known numeral systems developed before the Babylonian numerals are non-positional,[64] as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.
See also
[edit]- History of ancient numeral systems
- History of the HinduโArabic numeral system
- List of numeral system topics
- Numeral prefix โ Prefix derived from numerals or other numbers
- Radix โ Number of digits of a numeral system
- Radix economy โ Number of digits needed to express a number in a particular basePages displaying short descriptions of redirect targets
- Timeline of numerals and arithmetic
- List of books on history of number systems
References
[edit]- ^ a b c Chrisomalis, Stephen (2004). "A cognitive typology for numerical notation". Cambridge Archaeological Journal. 14 (1): 37โ52. doi:10.1017/S0959774304000034.
- ^ a b Chrisomalis 2010, pp. 330-333.
- ^ Glass, Andrew; Baums, Stefan; Salomon, Richard (September 18, 2003). "Proposal to Encode Kharoแนฃ แนญhฤซ in Plane 1 of ISO/IEC 10646" (PDF). Unicode.org.
- ^ Everson, Michael (July 25, 2007). "Proposal to add two numbers for the Phoenician script" (PDF). UTC Document Register. Unicode Consortium. L2/07-206 (WG2 N3284).
- ^ Cajori, Florian (September 1928). A History Of Mathematical Notations Vol I. The Open Court Company. p. 18. Retrieved June 5, 2017.
- ^ "Ethiopic (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. ISBN 978-0-521-87818-0.
- ^ Chrisomalis 2010, p. 200.
- ^ Guo, Xianghe (July 27, 2009). "ๆญฆๅๅคฉไธบๅ่ดชๅๆๆฑ่ฏญๅคงๅๆฐๅญโโไธญๆฐ็ฝ" [Wu Zetian invented Chinese capital numbers to fight corruption]. ไธญๆฐ็คพ [China News Service]. Retrieved August 15, 2024.
- ^ "Burmese/Myanmar script and pronunciation". Omniglot. Retrieved June 5, 2017.
- ^ "Vai (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ a b Kelly, Piers. "The invention, transmission and evolution of writing: Insights from the new scripts of West Africa". Open Science Framework.
- ^ "Bamum (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ "Mende Kikakui (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Everson, Michael (October 21, 2011). "Proposal for encoding the Mende script in the SMP of the UCS" (PDF). UTC Document Register. Unicode Consortium. L2/11-301R (WG2 N4133R).
- ^ "Medefaidrin (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Rovenchak, Andrij (July 17, 2015). "Preliminary proposal for encoding the Medefaidrin (Oberi Okaime) script in the SMP of the UCS (Revised)" (PDF). UTC Document Register. Unicode Consortium. L2/L2015.
- ^ "NKo (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Donaldson, Coleman (January 1, 2017). "Clear Language: Script, Register And The N'ko Movement Of Manding-Speaking West Africa" (PDF). repository.upenn.edu. UPenn.
- ^ "Consideration of the encoding of Garay with updated user feedback (revised)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Everson, Michael (March 22, 2016). "Proposal for encoding the Garay script in the SMP of the UCS" (PDF). UTC Document Register. Unicode Consortium. L2/L16-069 (WG2 N4709).
- ^ "Adlam (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Everson, Michael (October 28, 2014). "Revised proposal for encoding the Adlam script in the SMP of the UCS" (PDF). UTC Document Register. Unicode Consortium. L2/L14-219R (WG2 N4628R).
- ^ "Kaktovik Numerals (Unicode block)" (PDF). Unicode Character Code Charts. Unicode Consortium.
- ^ Silvia, Eduardo (February 9, 2020). "Exploratory proposal to encode the Kaktovik numerals" (PDF). UTC Document Register. Unicode Consortium. L2/20-070.
- ^ "Direktori Aksara Sunda untuk Unicode" (PDF) (in Indonesian). Pemerintah Provinsi Jawa Barat. 2008.[page needed]
- ^ For the mixed roots of the word "hexadecimal", see Epp, Susanna (2010), Discrete Mathematics with Applications (4th ed.), Cengage Learning, p. 91, ISBN 9781133168669.
- ^ Multiplication Tables of Various Bases, p. 45, Michael Thomas de Vlieger, Dozenal Society of America
- ^ Kindra, Vladimir; Rogalev, Nikolay; Osipov, Sergey; Zlyvko, Olga; Naumov, Vladimir (2022). "Research and Development of Trinary Power Cycles". Inventions. 7 (3): 56. doi:10.3390/inventions7030056. ISSN 2411-5134.
- ^ The Aneityum language of Aneityum, Vanuatu traditionally had a quinary system, although this had largely been replaced by a decimal system, based on English numbers, by the early 20th century.
- ^ The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
- ^ Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994.
- ^ The Universal History of Numbers: From prehistory to the invention of the computer, Georges Ifrah, ISBN 0-471-39340-1, John Wiley and Sons Inc., New York, 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk
- ^ Overmann, Karenleigh A (2020). "The curious idea that Mฤori once counted by elevens, and the insights it still holds for cross-cultural numerical research". Journal of the Polynesian Society. 129 (1): 59โ84. doi:10.15286/jps.129.1.59-84. Retrieved July 24, 2020.
- ^ Thomas, N.W (1920). "Duodecimal base of numeration". Man. 20 (1): 56โ60. doi:10.2307/2840036. JSTOR 2840036. Retrieved July 25, 2020.
- ^ a b Hammarstrรถm, Harald (2010). "Rarities in numeral systems". Rethinking Universals. pp. 11โ60. doi:10.1515/9783110220933.11. ISBN 9783110220933.
- ^ Ulrich, Werner (November 1957). "Non-binary error correction codes". Bell System Technical Journal. 36 (6): 1364โ1365. doi:10.1002/j.1538-7305.1957.tb01514.x.
- ^ Das, Debasis; Lanjewar, U.A. (January 2012). "Realistic Approach of Strange Number System from Unodecimal to Vigesimal" (PDF). International Journal of Computer Science and Telecommunications. 3 (1). London: Sysbase Solution Ltd.: 13.
- ^ Rawat, Saurabh; Sah, Anushree (May 2013). "Subtraction in Traditional and Strange Number System by r's and r-1's Compliments". International Journal of Computer Applications. 70 (23): 13โ17. Bibcode:2013IJCA...70w..13R. doi:10.5120/12206-7640.
... unodecimal, duodecimal, tridecimal, quadrodecimal, pentadecimal, heptadecimal, octodecimal, nona decimal, vigesimal and further are discussed...
- ^ a b Das & Lanjewar 2012, p. 13.
- ^ a b c d e f Rawat & Sah 2013.
- ^ HP 9100A/B programming, HP Museum
- ^ "Image processor and image processing method".
- ^ a b c d Das & Lanjewar 2012, p. 14.
- ^ a b Nykl, Alois Richard (September 1926). "The Quinary-Vigesimal System of Counting in Europe, Asia, and America". Language. 2 (3): 165โ173. doi:10.2307/408742. JSTOR 408742. OCLC 50709582 โ via Google Books. p. 165:
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.
- ^ Eells, Walter Crosby (October 14, 2004). "Number Systems of the North American Indians". In Anderson, Marlow; Katz, Victor; Wilson, Robin (eds.). Sherlock Holmes in Babylon: And Other Tales of Mathematical History. Mathematical Association of America. p. 89. ISBN 978-0-88385-546-1 โ via Google Books.
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.' ...
- ^ Chrisomalis 2010, p. 200: "The early origin of bar-and-dot numeration alongside the Middle Formative Mesoamerican scripts, the quinary-vigesimal structure of the system, and the general increase in the frequency and complexity of numeral expressions over time all point to its indigenous development.".
- ^ a b Laycock, Donald (1975). "Observations on Number Systems and Semantics". In Wurm, Stephen (ed.). New Guinea Area Languages and Language Study, I: Papuan Languages and the New Guinea Linguistic Scene. Pacific Linguistics C-38. Canberra: Research School of Pacific Studies, Australian National University. pp. 219โ233.
- ^ a b Dibbell, Julian (2010). "Introduction". The Best Technology Writing 2010. Yale University Press. p. 9. ISBN 978-0-300-16565-4.
There's even a hexavigesimal digital codeโour 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.
- ^ a b Young, Brian; Faris, Tom; Armogida, Luigi (2019). "A nomenclature for sequence-based forensic DNA analysis". Genetics. 42. Forensic Science International: 14โ20. doi:10.1016/j.fsigen.2019.06.001. PMID 31207427.
[โฆ] 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 [โฆ]
- ^ "Base 26 Cipher (Number โฌ Words) - Online Decoder, Encoder".
- ^ "Technical FAQ - InChI Trust". inchi-trust.org. Retrieved January 8, 2021.
- ^ Saxe, Geoffrey B.; Moylan, Thomas (1982). "The development of measurement operations among the Oksapmin of Papua New Guinea". Child Development. 53 (5): 1242โ1248. doi:10.1111/j.1467-8624.1982.tb04161.x. JSTOR 1129012..
- ^ "ะะตะทัะผัะฝะฝัะน ะฟะฐะปะตั โข ะะฐะดะฐัะธ".
- ^ Nauka i Zhizn, 1992, issue 3, p. 48.
- ^ Grannis, Shaun J.; Overhage, J. Marc; McDonald, Clement J. (2002), "Analysis of identifier performance using a deterministic linkage algorithm", Proceedings. AMIA Symposium: 305โ309, PMC 2244404, PMID 12463836.
- ^ Stephens, Kenneth Rod (1996), Visual Basic Algorithms: A Developer's Sourcebook of Ready-to-run Code, Wiley, p. 215, ISBN 9780471134183.
- ^ Sallows, Lee (1993), "Base 27: the key to a new gematria", Word Ways, 26 (2): 67โ77.
- ^ Gรณdor, Balรกzs (2006). "World-wide user identification in seven characters with unique number mapping". Networks 2006: 12th International Telecommunications Network Strategy and Planning Symposium. IEEE. pp. 1โ5. doi:10.1109/NETWKS.2006.300409. ISBN 1-4244-0952-7. S2CID 46702639.
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. [โฆ] 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...
- ^ Balagadde, Robert Ssali; Premchand, Parvataneni (2016). "The Structured Compact Tag-Set for Luganda". International Journal on Natural Language Computing. 5 (4): 01โ21. doi:10.5121/ijnlc.2016.5401.
Concord Numbers used in the categorisation of Luganda words encoded using either Hexatrigesimal or Duotrigesimal, standard positional numbering systems. [โฆ] We propose Hexatrigesimal system to capture numeric information exceeding 10 for adaptation purposes for other Bantu languages or other agglutinative languages.
- ^ "NewBase60". Retrieved January 3, 2016.
- ^ Nasar, Sylvia (2001). A Beautiful Mind. Simon and Schuster. pp. 333โ6. ISBN 0-7432-2457-4.
- ^ Ward, Rachel (2008), "On Robustness Properties of Beta Encoders and Golden Ratio Encoders", IEEE Transactions on Information Theory, 54 (9): 4324โ4334, arXiv:0806.1083, Bibcode:2008arXiv0806.1083W, doi:10.1109/TIT.2008.928235, S2CID 12926540
- ^ Chrisomalis 2010, p. 254: Chrisomalis calls the Babylonian system "the first positional system ever".
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