In arithmetic, a complex base system is a positional numeral system whose radix is an imaginary or complex number.
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Examples
In either of these systems, all Gaussian integers can be represented without sign.
Quater-imaginary base
Quater-imaginary base, proposed by Donald Knuth in 1955, uses the radix 2i and the digits 0,1,2,3.[1]
Base −1±i
Base −1±i, using digits 0 and 1, was proposed by Walter F. Penney in 1965.[2][3] The rounding region of an integer – i.e., a set of complex (non-integer) numbers that share the integer part of their representation in this system – has a fractal shape, the twindragon.
References
- ^ Knuth, Donald (1998). "Positional Number Systems". The art of computer programming. Volume 2 (3rd ed.). Boston: Addison-Wesley. pp. 205. ISBN 0-201-89684-2. OCLC 48246681.
- ^ Jamil, T. (2002). "The complex binary number system". IEEE Potentials 20: 39–41. doi:.
- ^ Duda, Jarek (2008-02-24). Complex base numeral systems. http://arxiv.org/pdf/0712.1309. Retrieved 2008-09-23.
See also
External links
- "Number Systems Using a Complex Base" by Jarek Duda, the Wolfram Demonstrations Project
- "The Boundary of Periodic Iterated Function Systems" by Jarek Duda, the Wolfram Demonstrations Project
- "Number Systems in 3D" by Jarek Duda, the Wolfram Demonstrations Project
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