# 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 2

*i* 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:

## References

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