- Quaternary numeral system
It shares with all fixed-
radixnumeral 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 decimaland binary for a discussion of these properties.
Relation to binary
As with the
octaland hexadecimalnumeral systems, quaternary has a special relation to the binary numeral system. Each radix4, 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 computingand programmingin the discussion and analysis of binary arithmetic and logic, quaternary does not enjoy the same status.
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 languagesoriginally 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 of Ventureño languagenumber 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.]
Parallels can be drawn between quaternary numerals and the way
genetic codeis 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 complementarydigit 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).
line codes have been used for transmission, from the invention of the telegraph to the 2B1Qcode used in modern ISDNcircuits.
* Conversion between bases
* [http://www.mathsisfun.com/numbers/convert-base.php?to=quaternary Quaternary Base Conversion] , includes fractional part, from
Math 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