Quaternary is the base-4 numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.
Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number (the other being 36), making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary. However, it fares no better in the localization of prime numbers (the smallest better base being the primorial base six, senary).
Quaternary 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
Parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in alphabetical order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0, 1, 2, and 3. With this encoding, the complementary digit pairs 0↔3, and 1↔2 (binary 00↔11 and 01↔10) match the complementation of the base pairs: A↔T and C↔G and can be stored as data in DNA sequence.[2]
For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010 😊 decimal 9156 or binary 10 00 11 11 00 01 00).
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