Page shown from here. Go to page 1 Zoom out
From Wikipedia, the free encyclopedia
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2008)
Numeral systems by culture
Hindu-Arabic numerals
Western Arabic (Hindu numerals)
Eastern Arabic
Indian family
Tamil
Burmese
Khmer
Lao
Mongolian
Thai
East Asian numerals
Chinese
Japanese
Suzhou
Korean
Vietnamese
Counting rods
Alphabetic numerals
Abjad
Armenian
Āryabhaṭa
Cyrillic
Ge'ez
Greek
Georgian
Hebrew
Other systems
Aegean
Attic
Babylonian
Brahmi
Egyptian
Etruscan
Inuit
Kharosthi
Mayan
Quipu
Roman
Sumerian
Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16,
20, 24, 30, 36, 60, 64
Balanced ternary
Non-positional system
Unary numeral system (Base 1)
List of numeral systems
v d e
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[1] (the ISO basic Latin alphabet). Base 36 is therefore the most compact case-insensitive alphanumeric numeral system using
ASCII characters, although its radix economy is poor.
From a mathematical viewpoint, 36, as with all highly composite numbers, 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.
Contents
1 Examples
2 Conversion
2.1 Java implementation
2.2 PHP implementation
2.3 Python implementation
2.4 Ruby implementation
3 Uses in practice
4 References
5 External links
[edit]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 1,296
1000 46,656
10000 1,679,616
100000 60,466,176
1000000 2,176,782,336
10000000 78,364,164,096
100000000 2,821,109,907,456
Fraction Decimal Base 36
1/2 0.5 0.I
1/3 0.3 0.C
1/4 0.25 0.9
1/5 0.2 0.7
1/6 0.16 0.6
1/7 0.142857 0.5
1/8 0.125 0.4I
1/9 0.1 0.4
1/10 0.1 0.3L
[edit]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.
[edit]Java implementation
public class Base36 {
public long decode(final String value) {
return Long.parseLong(value, 36);
}
public String encode(final long value) {
return Long.toString(value, 36);
}
}
[edit]PHP implementation
The decimal value of 12abcxyz is <?php print base_convert("12abcxyz",36,10); ?>
The base_convert function converts the value to a floating-point number, which loses accuracy for numbers above implementation-specific limits. For php 5.3.6 on 64-bit linux, the highest base-36 integer that can be represented accurately is 1y2p0ij32e8e7, equal to 2^63-1 or 9223372036854775807. Negative signs, decimal points and any characters outside the range 0-z are stripped prior to conversion, so -1.5 = 15 = f, rather than -1.i as might be expected.
[edit]Python implementation
def base36encode(number, alphabet='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'):
"""Convert positive integer to a base36 string."""
if not isinstance(number, (int, long)):
raise TypeError('number must be an integer')
# Special case for zero
if number == 0:
return alphabet[0]
base36
= ''
sign
= ''
if number < 0: sign
= '-'
number = - number
while number != 0: number
, i = divmod(number, len(alphabet))
base36 = alphabet[i] + base36
return sign + base36
def base36decode(number):
return int(number, 36)
print base36encode(1412823931503067241)
print base36decode('AQF8AA0006EH')
[edit]Ruby implementation
1412823931503067241.to_s(36) #=> "aqf8aa0006eh"
[edit]Uses in practice
The Remote Imaging Protocol for bulletin board systems used base 36 notation for transmitting coordinates in a compact form.
The Siebel CRM application uses base 36 as the unique identifier generator for all the entities in its model (e.g., 1-8GH4DX).
Many URL redirection systems like TinyURL or SnipURL/Snipr 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 uses a 5 or 7 digit base 36 number (Service Tag) as a compact version of their Express Service Codes.
The software package SalesLogix uses base 36 as part of its database identifiers.[2
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2008)Numeral systems by culture
Hindu-Arabic numerals
Western Arabic (Hindu numerals)
Eastern Arabic
Indian family
Tamil
Burmese
Khmer
Lao
Mongolian
Thai
East Asian numerals
Chinese
Japanese
Suzhou
Korean
Vietnamese
Counting rods
Alphabetic numerals
Abjad
Armenian
Āryabhaṭa
Cyrillic
Ge'ez
Greek
Georgian
Hebrew
Other systems
Aegean
Attic
Babylonian
Brahmi
Egyptian
Etruscan
Inuit
Kharosthi
Mayan
Quipu
Roman
Sumerian
Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16,
20, 24, 30, 36, 60, 64
Balanced ternary
Non-positional system
Unary numeral system (Base 1)
List of numeral systems
v d e
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[1] (the ISO basic Latin alphabet). Base 36 is therefore the most compact case-insensitive alphanumeric numeral system using
ASCII characters, although its radix economy is poor.
From a mathematical viewpoint, 36, as with all highly composite numbers, 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.
Contents
1 Examples
2 Conversion
2.1 Java implementation
2.2 PHP implementation
2.3 Python implementation
2.4 Ruby implementation
3 Uses in practice
4 References
5 External links
[edit]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 1,296
1000 46,656
10000 1,679,616
100000 60,466,176
1000000 2,176,782,336
10000000 78,364,164,096
100000000 2,821,109,907,456
Fraction Decimal Base 36
1/2 0.5 0.I
1/3 0.3 0.C
1/4 0.25 0.9
1/5 0.2 0.7
1/6 0.16 0.6
1/7 0.142857 0.5
1/8 0.125 0.4I
1/9 0.1 0.4
1/10 0.1 0.3L
[edit]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.
[edit]Java implementation
public class Base36 {
public long decode(final String value) {
return Long.parseLong(value, 36);
}
public String encode(final long value) {
return Long.toString(value, 36);
}
}
[edit]PHP implementation
The decimal value of 12abcxyz is <?php print base_convert("12abcxyz",36,10); ?>
The base_convert function converts the value to a floating-point number, which loses accuracy for numbers above implementation-specific limits. For php 5.3.6 on 64-bit linux, the highest base-36 integer that can be represented accurately is 1y2p0ij32e8e7, equal to 2^63-1 or 9223372036854775807. Negative signs, decimal points and any characters outside the range 0-z are stripped prior to conversion, so -1.5 = 15 = f, rather than -1.i as might be expected.
[edit]Python implementation
def base36encode(number, alphabet='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'):
"""Convert positive integer to a base36 string."""
if not isinstance(number, (int, long)):
raise TypeError('number must be an integer')
# Special case for zero
if number == 0:
return alphabet[0]
base36
= ''
sign
= ''
if number < 0: sign
= '-'
number = - number
while number != 0: number
, i = divmod(number, len(alphabet))
base36 = alphabet[i] + base36
return sign + base36
def base36decode(number):
return int(number, 36)
print base36encode(1412823931503067241)
print base36decode('AQF8AA0006EH')
[edit]Ruby implementation
1412823931503067241.to_s(36) #=> "aqf8aa0006eh"
[edit]Uses in practice
The Remote Imaging Protocol for bulletin board systems used base 36 notation for transmitting coordinates in a compact form.
The Siebel CRM application uses base 36 as the unique identifier generator for all the entities in its model (e.g., 1-8GH4DX).
Many URL redirection systems like TinyURL or SnipURL/Snipr 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 uses a 5 or 7 digit base 36 number (Service Tag) as a compact version of their Express Service Codes.
The software package SalesLogix uses base 36 as part of its database identifiers.[2