Base 36

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Numeral systems by culture
Hindu-Arabic numerals
Indian Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Suzhou 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
1, 3, 9, 12, 20, 24, 30, 36, 60, more…
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. 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.

1 Examples
2 Conversion
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	0.333333333333…	0.C
1/4	0.25	0.9
1/5	0.2	0.777777777777…
1/6	0.166666666666…	0.6
1/7	0.142857142857…	0.555555555555…
1/8	0.125	0.4I
1/9	0.111111111111…	0.4
1/10	0.1	0.3LLLLLLLLLLL...

[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] 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, SnipURL and tr:KolayURL 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]

Sage SalesLogix uses its own Char(12) primary key IDs for database tables that contain a Base 36 number in the following manner:

[KEY TYPE][SITE CODE][INCREMENTING BASE-36 NUMBER]

e.g. AQF8AA0006EH