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# Quaternary numeral system

Quaternary is the base four numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.

It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the characteristics of the representations of rational numbers and irrational numbers. See decimal and binary for a discussion of these properties.

As with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4, 8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2, 3 or 4 binary digits, or bits. For example, in base 4,

302104 = 11 00 10 01 002
Although octal and hexadecimal are widely used in computing and programming in the discussion and analysis of binary arithmetic and logic, quaternary does not enjoy the same status.