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Quater-imaginary base

The Quater-imaginary numeral system was first proposed by Donald Knuth in 1955, in a submission to a high-school science talent search. It is a positional system which uses the complex number 2i as base. By analogy with the quaternary numeral system, it is able to represent every complex number using only the digits 0, 1, 2, and 3, without a sign. For example: