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Encyclopedia > Base 36
Numeral systems by culture
Hindu-Arabic numerals
Indian
Eastern Arabic
Khmer
Indian family
Brahmi
Thai
East Asian numerals
Chinese
Counting rods
Japanese
Korean 
Alphabetic numerals
Abjad
Armenian
Cyrillic
Ge'ez
Hebrew
Greek (Ionian)
Āryabhaṭa
 
Other systems
Attic
Babylonian
Egyptian
Etruscan
Mayan
Roman
Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
3, 9, 12, 20, 24, 30, 36, 60, more…
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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.) This article is about different methods of expressing numbers with symbols. ... I like cream cheese, it tastes good on toast. ... The Eastern Arabic numerals (also called Eastern Arabic numerals, 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, Pakistan and parts of India, and also in the no longer used Ottoman Turkish... Khmer numerals are the numerals used in the Khmer language of Cambodia. ... India has produced many numeral systems. ... The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ... The counting rods (Traditional Chinese: , Simplified Chinese: , pinyin: chou2) were used by ancient Chinese before the invention of the abacus. ... The 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. ... Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. ... Note: This article contains special characters. ... The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. ... 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. ... 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. ... The Etruscan numerals were used by the ancient Etruscans. ... Mayan numerals. ... Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. ... During the beginning of the Urnfield culture, around 1200 BC, a series of votive sickles of bronze with marks that have been interpreted as a numeral system, appeared in Central Europe. ... This is a list of numeral system topics, by Wikipedia page. ... 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. ... The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... For other uses, see Decimal (disambiguation). ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... Quaternary is the base four numeral system. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. ... Base32 is a derivation of Base64 with the following additional properties: The resulting character set is all uppercase, which can often be beneficial when using a case-sensitive filesystem. ... In computing, base64 is a data encoding scheme whereby binary-encoded data is converted to printable ASCII characters. ... Ternary or trinary is the base-3 numeral system. ... Nonary is a base 9 numeral system, typically using the digits 0-8, but not the digit 9. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). ... As there are 24 hours in a day a numbering system based upon 24, and as the base 12 is convenient here some examples of the base 24 (quadrovigesimal) system. ... Base 30 or trigesimal is a positional numeral system using 30 as the radix. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... 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. ... 36 (thirty-six) is the natural number following 35 and preceding 37. ... The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... Numerals sans-serif 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. ... Abcdefghijklmnopqrstuvwxyz redirects here. ... Text sometimes exhibits case sensitivity, that is, words can differ in meaning based on the differing use of uppercase and lowercase letters. ... Generally speaking, the term alphanumeric refers to anything that consists of only letters and numbers. ... This article is about different methods of expressing numbers with symbols. ... Image:ASCII fullsvg There are 95 printable ASCII characters, numbered 32 to 126. ... In mathematics, hexadecimal or simply hex is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ... In computing, base64 is a data encoding scheme whereby binary-encoded data is converted to printable ASCII characters. ...


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. Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... A senary numeral system is a base-six numeral system. ...


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. Latin is the language originally spoken in the region around Rome called Latium. ... In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. ... A neologism is a word, term, or phrase which has been recently created (or coined), often to apply to new concepts, to synthesize pre-existing concepts, or to make older terminology sound more contemporary. ...

Contents

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
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:

Decimal Base 36
1 1
10 A
100 2S
1,000 RS
10,000 7PS
100,000 255S
1,000,000 LFLS
1,000,000,000 GJDGXS
1,000,000,000,000 CRE66I9S
Base 36 Decimal
1 1
10 36
100 1296
1,000 46656
10,000 1679616
100,000 60466176
1,000,000 2176782336
10,000,000 78364164096
100,000,000 2821109907456
Decimal Base 36
1/2 0.I
1/3 0.C
1/4 0.9
1/5 0.777777777777...
1/6 0.6
1/7 0.555555555555...
1/8 0.4I
1/9 0.4
1/10 0.3LLLLLLLLLLL...

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. The GNU Multiple-Precision Library, also known as GMP, is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. ...


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. The Remote Imaging Protocol (RIP), also referred to as RIPscrip (and frequently, yet incorrectly as RIPscript), was an early vector graphics protocol, created by Jeff Reeder, a founder of TeleGrafix Communications. ... BBS redirects here. ... URL redirection, also called URL forwarding, domain redirection and domain forwarding, is a technique on the World Wide Web for making a web page available under many URLs. ... TinyURL (tinyurl. ... RickDate is a compressed date format using a base 36 numeral system to represent a date using a minimal amount of characters. ... For the calendar of religious holidays and periods, see liturgical year. ...


Dell also uses Base-36 to obtain its Express Service Code from the Service Tag.[1]


References

  1. ^ [1]

External links

In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ... For other uses, see PHP (disambiguation). ...

 
 

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