Ternary numeral system
The ternary numeral system (also called base 3) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log23 (about 1.58496) bits of information.
Although ternary most often refers to a system in which the three digits 0, 1, and 2 are all non-negative numbers, the adjective also lends its name to the balanced ternary system, used in comparison logic and ternary computers.
Comparison to other radices
Representations of integer numbers 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 as decimal — see below for a compact way to codify ternary using nonary and septemvigesimal.
As for rational numbers, ternary offers a convenient way to represent one third (as opposed to its cumbersome representation as an infinite string of recurring digits in decimal); but a major drawback is that, in turn, ternary does not offer a finite representation for one half (neither for one quarter, one sixth, one eighth, one tenth, etc.), because 2 is not a prime factor of the base.
Numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
The number the numeral represents is called its value.
Ideally, a numeral system will:
For example, the usual decimal representation of whole numbers gives every non zero whole number a unique representation as a finite sequence of digits, beginning by a non-zero digit. However, when decimal representation is used for the rational or real numbers, such numbers in general have an infinite number of representations, for example 2.31 can also be written as 2.310, 2.3100000, 2.309999999..., etc., all of which have the same meaning except for some scientific and other contexts where greater precision is implied by a larger number of figures shown.
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