Quater-imaginary base

Non-standard numeral system

The quater-imaginary numeral system is a numeral system, first proposed by Donald Knuth in 1960. Unlike standard numeral systems, which use an integer as their bases, it uses the imaginary number 2i as its base. It is able to uniquely represent every complex number using only the digits 0, 1, 2, and 3. 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.

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