Quaternary System

The quaternary system is the Numbering system basic 4. It uses the Chiffre S 0,1,2 and 3 to represent any Real number.

It divides with all the numbering systems to radical fixed several properties, such as the capacity to represent any real number with a canonical representation (almost single) and the characteristics of the representations of the rational numbers and irrational numbers. See the Decimal system and the Binary system for a discussion of these properties.

Like the octal system and the Hexadecimal system , the quaternary system has a special relation with the Binary system. Each bases 4, 8 and 16 is a power of 2, therefore conversion of and towards the binary one is implemented while coinciding each figure with 2,3 or 4 binary digits, or bits. For example, bases 4,

30210₄ of it = 11 00 10 01 00₂

Although the octal one and the hexadecimal one are largely used in Calcul and Programmation in the analyzes and the discussions of arithmetic and logical binary, the quaternary system did not have the same statute.

In an interesting way, parallels can be made between the quaternary system and the way in which the genetic Code is represented by DNA. The four Nucleotide S of the DNA in the Alphabetical order, in summary has, C, G and T, can be taken to represent the quaternary figures in the numerical Ordre 0,1,2, and 3. With this code, the pairs of figures Complementary S 0<->3, and 1<->2 (binary 00<->11 and 01<->10) coîncident with the complementarity of the even bases: A<->T and C<->G.

For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010₄ (= 9156₁₀).

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