The undecimal positional notation

Positional notation

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...

 system is based on the number eleven, rather than ten as in decimal

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 or eight in octal

Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

 and so on. It is not a commonly used system. Undecimal requires eleven symbols representing the decimal numbers 0 through 10. For example, if the symbol for 10 were 'A', the decimal numbers 0 to 24 in undecimal would be: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 20, 21, 22. The undecimal number 1A3 would be 234 in decimal.

Base 11 in fiction

Base 11 systems appear in several science fiction

Science fiction

Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...

 stories: Carl Sagan

Carl Sagan

Carl Edward Sagan was an American astronomer, astrophysicist, cosmologist, author, science popularizer and science communicator in astronomy and natural sciences. He published more than 600 scientific papers and articles and was author, co-author or editor of more than 20 books...

's novel Contact

Contact (novel)

Contact is a science fiction novel written by Carl Sagan and published in 1985. It deals with the theme of contact between humanity and a more technologically advanced, extraterrestrial life form. It ranked No. 7 on the 1985 U.S. bestseller list....

references a message "hidden" inside pi

Pi

' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

 that is most striking in base 11, as that permits it to be displayed in binary code

Binary code

A binary code is a way of representing text or computer processor instructions by the use of the binary number system's two-binary digits 0 and 1. This is accomplished by assigning a bit string to each particular symbol or instruction...

. Also the fictional Psychlos (in L. Ron Hubbard

L. Ron Hubbard

Lafayette Ronald Hubbard , better known as L. Ron Hubbard , was an American pulp fiction author and religious leader who founded the Church of Scientology...

's book Battlefield Earth

Battlefield Earth (novel)

Battlefield Earth: A Saga of the Year 3000 is a 1982 science fiction novel written by the Scientology founder L. Ron Hubbard. He composed a soundtrack to the book called Space Jazz....

) have a base-11 counting system.

In the television series Babylon 5

Babylon 5

Babylon 5 is an American science fiction television series created, produced and largely written by J. Michael Straczynski. The show centers on a space station named Babylon 5: a focal point for politics, diplomacy, and conflict during the years 2257–2262...

, the Minbari

Minbari

The Minbari are a fictional alien race featured in the television show Babylon 5. The Minbari characters of Delenn and Lennier figure prominently throughout the series; Neroon, Draal, and Dukhat are less prominent Minbari characters....

 use base-11 mathematics, according to the show's creator.

ISBN Check Digit

The check digit for ISBN is found as the result of taking modulo

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....

11. Since this could give 11 possible results, the digit "X" is used in place of "10".