Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...
36 is the natural number following 35 and preceding 37.- In mathematics :36 is both the square of 6 and a triangular number, making it a square triangular number...
In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...
. The choice of 36 is convenient in that the digits can be represented using the Arabic numerals 0-9 and the Latin letters
Latin alphabet
The Latin alphabet, also called the Roman alphabet, is the most recognized alphabet used in the world today. It evolved from a western variety of the Greek alphabet called the Cumaean alphabet, which was adopted and modified by the Etruscans who ruled early Rome...
A-Z (the Basic Latin alphabet). Base 36 is therefore the most compact case-insensitive alphanumeric
Alphanumeric
Alphanumeric is a combination of alphabetic and numeric characters, and is used to describe the collection of Latin letters and Arabic digits or a text constructed from this collection. There are either 36 or 62 alphanumeric characters. The alphanumeric character set consists of the numbers 0 to...
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...
Various proposals have been made to quantify the relative costs between using different radices in representing numbers, especially in computer systems.-Definition:...
A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....
s, 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
Senary
In mathematics, a senary numeral system is a base- numeral system.Senary may be considered useful in the study of prime numbers since all primes other than 2 and 3, when expressed in base-six, have 1 or 5 as the final digit...
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
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.
0.C
1/4
0.25
0.9
1/5
0.2
0.
1/6
0.1
0.6
1/7
0.
0.
1/8
0.125
0.4I
1/9
0.
0.4
1/10
0.1
0.3
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
GNU Multi-Precision Library
The GNU Multiple Precision Arithmetic Library, also known as GMP, is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers...
arbitrary-precision math library. For floating-point numbers the corresponding functions are called mpf_set_str and mpf_get_str.
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);
}
}
PHP implementation
The decimal value of 12abcxyz is
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.
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
The Remote Imaging Protocol Scripting Language, more commonly known as the Remote Imaging Protocol or RIPscrip, is a scripting language created by Jeff Reeder, Jim Bergman, and Mark Hayton to enhance bulletin board systems and other applications.RIPscrip was introduced in 1993 and consisted of...
A Bulletin Board System, or BBS, is a computer system running software that allows users to connect and log in to the system using a terminal program. Once logged in, a user can perform functions such as uploading and downloading software and data, reading news and bulletins, and exchanging...
s used base 36 notation for transmitting coordinates in a compact form.
Siebel CRM Systems, Inc. was a software company principally engaged in the design, development, marketing, and support of customer relationship management applications. The company was founded by Thomas Siebel in 1993. At first known mainly for its sales force automation products, the company...
Customer relationship management is a widely implemented strategy for managing a company’s interactions with customers, clients and sales prospects. It involves using technology to organize, automate, and synchronize business processes—principally sales activities, but also those for marketing,...
application uses base 36 as the unique identifier generator for all the entities in its model (e.g., 1-8GH4DX).
URL redirection, also called URL forwarding and the very similar technique domain redirection also called domain forwarding, are techniques on the World Wide Web for making a web page available under many URLs.- Similar domain names :...
TinyURL is a URL shortening service, a web service that provides short aliases for redirection of long URLs. Kevin Gilbertson, a web developer, launched the service in January 2002 so that he would be able to link directly to newsgroup postings that frequently had long and cumbersome addresses.-...
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
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
dates in file names, using one digit each for the day and the month.
Dell, Inc. is an American multinational information technology corporation based in 1 Dell Way, Round Rock, Texas, United States, that develops, sells and supports computers and related products and services. Bearing the name of its founder, Michael Dell, the company is one of the largest...
uses a 5 or 7 digit base 36 number (Service Tag) as a compact version of their Express Service Codes.
The Sage Group plc , commonly known as Sage, is a global enterprise software company headquartered in Newcastle upon Tyne, United Kingdom. It is the world's third-largest supplier of enterprise resource planning software , the largest supplier to small businesses, and has 6.1 million customers...
TreasuryDirect is a website run by the United States Treasury that allows US individual investors to purchase Treasury securities such as T-Bills and others directly from the U.S. government...
website, which allows individuals to buy and redeem securities directly from the U.S. Department of the Treasury in paperless electronic form, serializes security purchases in an account using a 4 digit base 36 number. However, the Latin letters A-Z are used before the Arabic numerals 0-9, so that the purchases are listed as AAAA, AAAB... AAAZ, AAA0, AAA1... AAA9, AABA...
An email client, email reader, or more formally mail user agent , is a computer program used to manage a user's email.The term can refer to any system capable of accessing the user's email mailbox, regardless of it being a mail user agent, a relaying server, or a human typing on a terminal...
Unix time, or POSIX time, is a system for describing instants in time, defined as the number of seconds elapsed since midnight Coordinated Universal Time of Thursday, January 1, 1970 , not counting leap seconds, which are declared by the International Earth Rotation and Reference Systems Service...
of the email's arrival and uses this for the first six characters of the message's filename.
MediaWiki stores uploaded files in directories with names derived from the base-36 representation of a uploaded file's checksum .
Siteswap is a notation used to describe juggling patterns. It encodes the number of beats of each throw, which is related to their height, and the hand to which the throw is to be made...
, a type of juggling notation, frequently employs 0-9 and a-z to signify the dwell time of a toss (which may roughly be thought of as the height of the throw). Throws higher than 'z' may be made but no notation has widespread acceptance for these throws.
Minecraft is a sandbox-building independent video game written in Java originally by Swedish creator Markus "Notch" Persson and now by his company, Mojang, formed from the proceeds of the game. It was released as an alpha on May 17, 2009, with a beta version on December 20, 2010...
stores level chunk files in directories with names derived from the base-36 representation of a chunk's position.
SEDOL stands for Stock Exchange Daily Official List, a list of security identifiers used in the United Kingdom and Ireland for clearing purposes. The numbers are assigned by the London Stock Exchange, on request by the security issuer...
securities identifiers, the check digit is computed from a weighted sum of the first six characters, each character interpreted in base-36.
In the International Securities Identification Number (ISIN), the check digit is computed by first taking the value of each character in base-36, concatenating the numbers together, then doing a weighted sum.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
PHP is a general-purpose server-side scripting language originally designed for web development to produce dynamic web pages. For this purpose, PHP code is embedded into the HTML source document and interpreted by a web server with a PHP processor module, which generates the web page document...
