Information about Base 36
| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic Eastern Arabic Khmer | Indian family Brahmi Thai |
| East Asian numerals | |
| Chinese Chinese counting rods | Korean Japanese |
| Alphabetic numerals | |
| Abjad Armenian Cyrillic Ge'ez | Hebrew Ionian/Greek Sanskrit |
| Other systems | |
| Attic Etruscan Urnfield Roman | Babylonian Egyptian Mayan |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 4, 8, 16, 32, 64 | |
| 3, 9, 12, 24, 30, 36, 60, | |
Base 36 is a positional numeral system using 36 as the radix. The choice of 36 is convenient in that the digits can be represented using the Arabic numerals 0-9 and the Latin letters A-Z. Base 36 is therefore the most compact case-insensitive alphanumeric numeral system using ASCII characters, although its radix economy is poor. (Compare with base 16 and base 64.)
From a mathematical viewpoint, 36 is a convenient choice for a base in that it is divisible by both 2 and 3, and by their multiples 4, 6, 9, 12 and 18. Each base 36 digit can be represented as two base 6 digits.
The most common latinate name for base 36 seems to be hexatridecimal, although sexatrigesimal would arguably be more correct. The intermediate form hexatrigesimal is also sometimes used. For more background on this naming confusion, see the entry for hexadecimal. Another name occasionally seen for base 36 is alphadecimal, a neologism coined based on the fact that the system uses the decimal digits and the letters of the Latin alphabet.
Examples
Conversion table:| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Base 36 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | G | H |
| Decimal | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 align="right" ! Base 36 | I || J || K || L || M || N || O || P || Q || R || S || T || U || V || W || X || Y || Z |
Some numbers in decimal and base 36:
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Conversion
32- and 64-bit integers will only hold up to 6 or 12 base-36 digits, respectively. For numbers with more digits, one can use the functions mpz_set_str and mpz_get_str in the GMP arbitrary-precision math library. For floating-point numbers the corresponding functions are called mpf_set_str and mpf_get_str.Uses in practice
The Remote Imaging Protocol for bulletin board systems used base 36 notation for transmitting coordinates in a compact form. Many URL redirection systems like TinyURL and SnipURL also use base 36 integers as compact alphanumeric identifiers. Various systems such as RickDate use base 36 as a compact representation of Gregorian dates in file names, using one digit each for the day and the month.Dell also uses Base-36 to obtain its Express Service Code from the Service Tag.[1]
References
External links
- A discussion about the proper name for base 36 at the Wordwizard Clubhouse
- The Prime Lexicon, a list of words that are prime numbers in base 36
- A Binary-Octal-Decimal-Hexadecimal-Base36 converter written in PHP
- A website that can convert numbers between bases from 2 to 36
numeral system (or system of numeration) is a framework where a set of numbers are represented by numerals in a consistent manner. It can be seen as the context that allows the numeral "11" to be interpreted as the binary numeral for three
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Hindu-Arabic numeral system (also called Algorism) is a positional decimal numeral system documented from the 9th century.
The symbols (glyphs) used to represent the system are in principle independent of the system itself.
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The symbols (glyphs) used to represent the system are in principle independent of the system itself.
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Arabic numerals, known formally as Hindu-Arabic numerals, and also as Indian numerals, Hindu numerals, Western Arabic numerals, European numerals, or Western numerals, are the most common symbolic representation of numbers around the world.
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The Eastern Arabic numerals (also called Arabic-Indic numerals, Arabic Eastern Numerals) are the symbols (glyphs) used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in Egypt, Iran, Afghanistan, Pakistan and parts of India, and also in
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Khmer numerals are the numerals used in the Khmer language of Cambodia. In informal spoken language one can ignore the last "sep" (30 to 90) and it is still understood.
e.g.
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e.g.
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symbols used in various modern Indian scripts for the numbers from zero to nine:
Variant 0 1 2 3 4 5 6 7 8 9 Used in
Eastern Nagari numerals ০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ? Bengali language
Assamese language
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Variant 0 1 2 3 4 5 6 7 8 9 Used in
Eastern Nagari numerals ০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ? Bengali language
Assamese language
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Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indic and Hindu-Arabic numerals.
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Thai numerals (ตัวเลขไทย) are traditionally used in Thailand, although the Arabic numerals (also known as Western numerals) are more common.
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This page contains Chinese text.
Without proper rendering support, you may see question marks, boxes, or other symbols instead of Chinese characters.
Without proper rendering support, you may see question marks, boxes, or other symbols instead of Chinese characters.
Numeral systems by culture
Hindu-Arabic numerals
Western Arabic
Eastern Arabic
Khmer Indian family
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Counting rods (Traditional Chinese: 籌; Simplified Chinese: 筹; Pinyin: chou2
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- sset
- 여덟 권 yeodeolgwon (eight (books)) is pronounced like [여덜꿘] yeodeolkkwon
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Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000.
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Abjad numerals are a decimal numeral system which was used in the Arabic-speaking world prior to the use of the Hindu-Arabic numerals from the 8th century, and in parallel with the latter until Modern times.
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Armenian numerals is a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet.
There was no notation for zero in the old system, and the numeric values for individual letters were added together.
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There was no notation for zero in the old system, and the numeric values for individual letters were added together.
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Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the 1700s when Peter the Great replaced it with the Hindu-Arabic numeral system.
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Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet.
In this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit (1, 2, ...
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In this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit (1, 2, ...
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Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Milesian numerals, Alexandrian numerals, or alphabetic numerals.
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Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodian.
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Etruscan numerals were used by the ancient Etruscans. The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman numerals.
Etruscan Decimal Symbol *
θu 1 I
ma? 5 ?
śar 10 X
muval? 50
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Etruscan Decimal Symbol *
θu 1 I
ma? 5 ?
śar 10 X
muval? 50
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/» and the fifths place with a stroke from the top-left to the bottom-right «\». The numbers from 1 = / to 29 = ////\\\\\ have been found.
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Interpretation
These embossed marks, unique in objects from the Bronze Age, were introduced in cast-iron molds and were not..... Click the link for more information.
Roman numerals is a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical antiquity was slightly modified in the Middle Ages to produce the system we use today. It is based on certain letters which are given values as numerals.
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Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.
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Egyptian numerals was a numeral system used in ancient Egypt. It was a decimal system, often rounded off to the higher power, written in hieroglyphs. The hieratic form of numerals stressed an exact finite series notation, being ciphered one:one onto the Egyptian alphabet.
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Maya numerals is very simple. [1]
Addition is performed by combining the numeric symbols at each level:
If five or more dots result from the combination, five dots are removed and replaced by a bar.
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Addition is performed by combining the numeric symbols at each level:
If five or more dots result from the combination, five dots are removed and replaced by a bar.
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This is a list of numeral system topics (and "numeric representations"), by Wikipedia page. It does not systematically list computer formats for storing numbers (computer numbering formats). See also number names.
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A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base or radix of that numeral system.
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base or radix is usually the number of various unique digits, including zero, that a positional numeral system uses to represent numbers. For example, the decimal system, the most common system in use today, uses base ten, hence the maximum number a single digit will ever
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decimal (base ten or occasionally denary) numeral system has ten as its base. It is the most widely used numeral system, perhaps because humans have four fingers and a thumb on each hand, giving a total of ten digits over both hands.
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binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2.
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Quaternary is the base-4 numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.
It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the
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It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the
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Herod_Archelaus
