# Quaternary numeral system

numeral system with four as its base

A quaternary numeral system uses the digits 0, 1, 2, and 3 to represent any real number. It is a base-4 system, which means it works in a similar way to how we count in regular decimal numbers, but with only four possible digits. Converting from binary (a base-2 system) to quaternary is easy.

The number four is a useful choice for a base in counting because it is the highest number that can be quickly recognized without counting each item one by one (subitizing). It is also both a square number and a highly composite number (in the same way 36 is), making it quite easy. Despite being twice as large as binary, it has the same radix economy for counting. However, it is not the best choice for identifying prime numbers (the smallest better choice being the primorial base six, or senary).

Quaternary is like other numeral systems with a fixed-radix in that it has certain properties, such as the capability to represent any real number using a standard representation that is almost unique. Additionally, it has similar characteristics for the representation of irrational and rational numbers as systems like decimal or binary. See discussions on binary and decimal for more information on these properties.