- Quaternary numeral system
**Quaternary**is the base-num|4numeral system . It uses the digits 0, 1, 2 and 3 to represent anyreal 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 ofrational number s andirrational number s. Seedecimal and binary for a discussion of these properties.**Relation to binary**As with the

octal andhexadecimal numeral systems, quaternary has a special relation to thebinary numeral system . Eachradix 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, orbit s. For example, in base 4,:30210_{4}= 11 00 10 01 00_{2}.Although octal and hexadecimal are widely used incomputing andprogramming in the discussion and analysis of binary arithmetic and logic, quaternary does not enjoy the same status.**Hilbert curves**Quaternary numbers are however used in the representation of 2D Hilbert-curves. Here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected.

**Occurrence in human languages**Many or all of the

Chumashan languages originally used a base 4 counting system, in which the names for numbers were structured according to multiples of 4 and 16 (not 10). There is a surviving list ofVentureño language number words up to 32 written down by a Spanish priest ca. 1819. [*"Chumashan Numerals" by Madison S. Beeler, in "Native American Mathematics", edited by Michael P. Closs (1986), ISBN 0-292-75531-7.*]**Genetics**Parallels can be drawn between quaternary numerals and the way

genetic code is represented byDNA . The four DNAnucleotide s inalphabetical 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, thecomplementary digit pairs 0↔3, and 1↔2 (binary 00↔11 and 01↔10) match the complementation of thebase pair s: A↔T and C↔G.For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010 (= decimal 9156).

**Data transmission**Quaternary

line code s have been used for transmission, from the invention of the telegraph to the2B1Q code used in modernISDN circuits.**References****ee also*** Conversion between bases

**External links*** [

*http://www.mathsisfun.com/numbers/convert-base.php?to=quaternary Quaternary Base Conversion*] , includes fractional part, fromMath Is Fun

* [*http://hauptmech.com/base42/wiki/index.php?title=Base4 Base42*] Proposes unique symbols for Quaternary and Hexadecimal digits

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**List of numeral system topics**— Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese … Wikipedia**Quaternary (disambiguation)**— Quaternary (from Latin quaternarius ) is an adjective meaning consisting of or containing four each , but sometimes (as in geology) taken to mean fourth or fourth hand , where it is used in place of quartary to continue the sequence Primary,… … Wikipedia**Numeral (linguistics)**— This article is about the linguistic concept of words that represent numbers. For the mathematical notation for representing numbers of a given set, see Numeral system. In linguistics, number names (or numerals) are specific words in a natural… … Wikipedia**Quater-imaginary base**— The quater imaginary numeral system was first proposed by Donald Knuth in 1955, in a submission to a high school science talent search. It is a non standard positional numeral system which uses the imaginary number, 2 i , as its base. By analogy… … Wikipedia**Quartal**— may refer to:*Quartal harmony, music featuring chords built from fourths *Quaternary numeral system, a system for representing numbers based on powers of four … Wikipedia**Quarternary (disambiguation)**— Quarternary may refer to: *Quarternary, a geological period *Quaternary numeral system, a numerical system that uses base 4 … Wikipedia**List of mathematics articles (Q)**— NOTOC Q Q analog Q analysis Q derivative Q difference polynomial Q exponential Q factor Q Pochhammer symbol Q Q plot Q statistic Q systems Q test Q theta function Q Vandermonde identity Q.E.D. QED project QR algorithm QR decomposition Quadratic… … Wikipedia**Positional notation**— Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese … Wikipedia**Nonary**— Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese … Wikipedia**7 (number)**— Seven redirects here. For other uses, see Seven (disambiguation). 7 −1 0 1 2 3 4 5 6 7 8 9 → List of numbers Integers … Wikipedia