Complex-base system

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In arithmetic, a complex-base system is a positional numeral system whose radix is an imaginary (proposed by Donald Knuth in 1955[1][2]) or complex number (proposed by S. Khmelnik in 1964[3] and Walter F. Penney in 1965[4][5][6]).

  1. ^ Knuth, D.E. (1960). "An Imaginary Number System". Communications of the ACM. 3 (4): 245–247. doi:10.1145/367177.367233. S2CID 16513137.
  2. ^ Knuth, Donald (1998). "Positional Number Systems". The art of computer programming. Vol. 2 (3rd ed.). Boston: Addison-Wesley. p. 205. ISBN 0-201-89684-2. OCLC 48246681.
  3. ^ Khmelnik, S.I. (1964). "Specialized digital computer for operations with complex numbers". Questions of Radio Electronics (In Russian). XII (2).
  4. ^ W. Penney, A "binary" system for complex numbers, JACM 12 (1965) 247-248.
  5. ^ Jamil, T. (2002). "The complex binary number system". IEEE Potentials. 20 (5): 39–41. doi:10.1109/45.983342.
  6. ^ Duda, Jarek (2008-02-24). "Complex base numeral systems". arXiv:0712.1309 [math.DS].