Editing Quater-imaginary base (section)

{{short description|Non-standard numeral system}}
{{numeral systems}}
{{Technical|date=January 2023}}
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 [[radix|bases]], it uses the [[imaginary number]] <math>2i</math> (such that <math>(2i)^2=-4</math>) as its base. It is able to ([[#Converting into quater-imaginary|almost]]) uniquely represent every [[complex number]] using only the digits 0, 1, 2, and 3.<ref name="knuth1960">{{cite journal|title=An imaginary number system|journal=Communications of the ACM|volume=3|issue=4|pages=245–247|date=April 1960|author=Donald Knuth|authorlink1=Donald Knuth | doi = 10.1145/367177.367233 |s2cid=16513137 |doi-access=free}}</ref> 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.