- Ternary numeral system
**Ternary**or**trinary**is the base-num|3numeral system . Analogous to a "bit ", a ternary digit is known as a "trit" (**tr**inary dig**it**). One trit contains about 1.58596 ($log\_2\; 3$) bit of information. Although "ternary" most often refers to a system in which the three digits, num|0, num|1, and num|2, are allnonnegative integer s, the adjective also lends its name to thebalanced ternary system, used in comparison logic andternary computer s.**Comparison to other radixes****Compared to decimal and binary**Representations of

integer number s in ternary do not get uncomfortably lengthy as quickly as in binary. For example, decimal 365 corresponds to binary 101101101 (9 digits) and to ternary 111112 (6 digits). However, they are still far less compact than the corresponding representations in bases such asdecimal — see below for a compact way to codify ternary using nonary and septemvigesimal.**Sum of the digits in trinary as opposed to binary**Where as in binary, where the sum of all previous digit values before 2

^{n}can be found using the formula 2^{n}-1, in trinary the following formula can be used: (3^{n}-1)/2.An example is where in binary the fourth digit has a value of 8, the sum of all the binary numbers before 8 can be found out using the above formula as 2

^{3}-1, which is 7. In trinary the fourth digit has a value of 27 and the sum of all previous trinary numbers can be found out using the above formula, as (3^{3}-1)/2, which is 13.The formula is 3

^{n}because we are counting to base 3 and we divide by 2 now because the maximum value of each digit is 2. The general formula for the nth digit it a base-N number is:N

^{n}and the sum of previous digits:

(N

^{n}-1)/(N-1)**Compact ternary representation: base 9 and 27**Nonary (base 9, each digit is two ternary digits) orseptemvigesimal (base 27, each digit is three ternary digits) is often used, similar to howoctal andhexadecimal systems are used in place of binary. Ternary also has a unit similar to abyte , the tryte, which is six ternary digits.**Practical usage**A base-three system is used in

Islam to keep track of countingTasbih to 99 or to 100 on a singlehand for counting prayers (as alternative for theMisbaha ). The benefit—apart from allowing a single hand to count up to 99 or to 100—is that counting doesn't distract the mind too much since the counter needs only to divideTasbih s into groups of three.A rare "ternary point" is used to denote fractional parts of an inning in

baseball . Since each inning consists of three outs, each out is considered one third of an inning and is denoted as**.1**. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, hisInnings pitched column for that game would be listed as**3.2**, meaning 3⅔. In this usage, only the fractional part of the number is written in ternary form.Ternary numbers can be used to convey self-similar structures like a

Sierpinski Triangle or aCantor set conveniently.**ee also***

Ternary logic **External links*** [

*http://www.americanscientist.org/issues/pub/third-base/ Third Base*]

* [*http://www.washingtonart.net/whealton/ternary.html Ternary Arithmetic*]

* [*http://www.mortati.com/glusker/fowler/index.htm The ternary calculating machine of Thomas Fowler*]

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

* [*http://www.americanscientist.org/issues/pub/third-base/3 Gideon Frieder's replacement ternary numeral system*]

*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**Ternary**— (from Latin ternarius ) can mean:* Ternary complex, a complex formed by the interaction of three molecules * Ternary compound, a type of chemical compound * Ternary computer, a computer using a ternary numeral system * Ternary form, a form used… … Wikipedia**Ternary computer**— Ternary computers (also sometimes referred to as trinary) use three valued logic in their calculations. History One of the earliest calculating machines, built by Thomas Fowler entirely from wood in 1840, was a ternary computer. The only modern… … Wikipedia**Ternary logic**— A ternary, three valued or trivalent logic (sometimes abbreviated 3VL) is a term to describe any of several multi valued logic systems in which there are three truth values indicating true , false and some third value. This is contrasted with the … 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**Non-standard positional numeral systems**— 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**Balanced ternary**— is a non standard positional numeral system (a balanced form), useful for comparison logic. It is a ternary system, but unlike the standard (unbalanced) ternary system, the digits have the values −1, 0, and 1. This combination is especially… … Wikipedia**0.999...**— In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0 … Wikipedia**Finger binary**— is a system for counting and displaying binary numbers on the fingers and thumbs of one or more hands. It is possible to count from 0 to 31 (25−1) using the fingers of a single hand, or from 0 through 1023 (210−1) if both hands are used. Contents … Wikipedia**Tertiary (disambiguation)**— Tertiary (from Latin tertiarius ) is an adjective meaning third or third hand . It may refer to:* The Tertiary period of the geologic time scale. * Tertiaries, members of a Third order (lay folk connected with a Mendicant Order). * Ternary… … Wikipedia