Quater-imaginary base

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The quater-imaginary numeral system is a numeral system, first proposed by Donald Knuth in 1960. Unlike standard numeral systems, which use an integer (such as 10 in decimal, or 2 in binary) as their bases, it uses the imaginary number ${\displaystyle 2i}$ (equivalent to ${\displaystyle {\sqrt {-4}}}$) as its base. It is able to (almost) uniquely represent every complex number using only the digits 0, 1, 2, and 3.^[1] Numbers less than zero, which are ordinarily represented with a minus sign, are representable as digit strings in quater-imaginary; for example, the number −1 is represented as "103" in quater-imaginary notation.