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Quater-imaginary base

The Quater-imaginary number system was first proposed by Donald Knuth in 1955, in a submission to a high-school science talent search. Quater-imaginary (by analogy with quaternary) is able to represent every complex number with only digits 0, 1, 2, and 3, without a sign. For example:

(11210.31)2i = 1(16) + 1(-18i) + 2(-4) + 1(2i) + 3(-1/2i) + 1(-1/4) = 7 3/4 - 7 1/2i


  • D. Knuth. The Art of Computer Programming. Volume 2, 3rd Ed. Addison-Wesley. pp.205, "Positional Number Systems"

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