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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,
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.
Interestingly, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNADeoxyribonucleic acid DNA is a nucleic acid which carries genetic instructions for the biological development of all cellular forms of life and many viruses. DNA is sometimes referred to as the molecule of heredity as it is inherited and used to propagate. The four DNA nucleotideA nucleotide is an organic molecule consisting of a nitrogenous heterocyclic base (a purine or a pyrimidine), a pentose sugar ( deoxyribose in DNA or ribose in RNA), and a phosphate or polyphosphate group. A nucleoside is similar, except that it containss in alphabetical order, abbreviated AAdenine is one of the two purine bases used in forming nucleotides of the nucleic acids DNA and RNA. In DNA, adenine (A) binds to thymine (T) to assist in stabilizing the nucleic acid structures. In RNA, adenine binds to uracil (U). Adenine forms adenosin, CCytosine is one of the 5 main nitrogenous bases used in storing and transporting genetic information within a cell. It is a pyrimidine derivative, with a heterocyclic aromatic ring and two substituents attached (an amine group at position 4 and a keto gro, GGuanine (2- amino-6- oxy purine) is one of the four main nitrogenous bases found in nucleic acids (e. DNA and RNA). Guanine is a purine derivative and in Watson-Crick base pairing forms hydrogen bonds with cytosine. The nucleoside is called guanosine. and TThymine (CHNO, 2- oxy-4- oxy-5- methyl pyrimidine, 2,4-di oxy-5- methyl pyrimidine, 5-methyluracil) is one of the bases of the nucleic acid found in DNA. It can base pair with adenine. Thymine combined with deoxyribose creates the nucleoside thymidine., 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.
For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010 (= decimal 9156).
Quaternary is the native system of the planet Quatar.
Numeration