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Ternary is a term for base-three arithmetic. A ternary number system can contain a total of three digits, such as 0, 1 and 2 (as opposed to something like binary code, which is often expressed through ones and zeros). Base-three number systems have many different applications, particularly in computer science and programming.
Ternary is also known as trinary.
A good way of understanding base-three math is by comparing it to the common decimal (or denary) system, which consists of a total of ten digits (0 through 9). When ascending the decimal system in numerical order and the final digit (9) is surpassed, digits are added to the left, which in turn ascend in numerical order as required.
Since ternary numbers can only incorporate three different digits, their symbolic representations extend in length at a faster rate than in the standard decimal system. In other words, ten is symbolized as "10" in decimal but as "101" ternary. Ternary systems (as well as binary, for that matter) are useful in computing because each digit can be defined by a given state of some computer component that may only exist in and toggle between three different single states.
Although not quite as omnipresent as its binary counterpart, ternary systems exist all across computer science and electronic media, such as in ternary trees, ternary signals, ternary operators and ternary search algorithms.