Editing Ternary numeral system (section)

==Practical usage==
[[File:fewest_weights_balance_puzzle.svg|thumb|Use of ternary numbers to balance an unknown integer weight from 1 to 40&nbsp;kg with weights of 1, 3, 9 and 27&nbsp;kg (4 ternary digits actually gives 3<sup>4</sup> = 81 possible combinations: &minus;40 to +40, but only the positive values are useful)]]






In certain analog logic, the state of the circuit is often expressed ternary. This is most commonly seen in [[CMOS]] circuits, and also in [[transistor–transistor logic]] with [[Push–pull output|totem-pole output]]. The output is said to either be low ([[Ground (electricity)|grounded]]), high, or open ([[High impedance|high-''Z'']]). In this configuration the output of the circuit is actually not connected to any [[voltage]] reference at all. Where the signal is usually grounded to a certain reference, or at a certain voltage level, the state is said to be high [[Electrical impedance|impedance]] because it is open and serves its own reference. Thus, the actual voltage level is sometimes unpredictable.

A rare "ternary point" in common use is for defensive statistics in American [[baseball]] (usually just for [[Pitcher|pitchers]]), to denote fractional parts of an inning. Since the team on offense is allowed three [[Out (baseball)|outs]], each out is considered one third of a defensive inning and is denoted as '''.1'''. For example, if a player pitched all of the 4th, 5th and 6th innings, plus achieving 2 outs in the 7th inning, his [[innings pitched]] column for that game would be listed as '''3.2''', the equivalent of {{frac|3|2|3}} (which is sometimes used as an alternative by some record keepers). In this usage, only the fractional part of the number is written in ternary form.<ref>{{cite web |url=https://www.blessyouboys.com/2019/1/9/18172095/baseball-stats-for-beginners-earned-run-average-field-independent-pitching-explained |title=A complete beginner's guide to baseball stats: Pitching statistics, and what they mean |author= Ashley MacLennan |date=Jan 9, 2019 |work=Bless You Boys |access-date=July 30, 2020}}</ref><ref>{{cite web |url=https://www.mlb.com/stats/team/pitching/innings-pitched?split=rp |title=Stats - Team - Pitching |publisher=MLB (Major League Baseball) |access-date=July 30, 2020}}</ref>

Ternary numbers can be used to convey self-similar structures like the [[Sierpiński triangle|Sierpinski triangle]] or the [[Cantor set]] conveniently. Additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have a ternary expression that does not contain any instance of the digit 1.<ref name="Soltanifar_2006_1"/><ref name="Soltanifar_2006_2"/> Any terminating expansion in the ternary system is equivalent to the expression that is identical up to the term preceding the last non-zero term followed by the term one less than the last non-zero term of the first expression, followed by an infinite tail of twos. For example: 0.1020 is equivalent to 0.1012222... because the expansions are the same until the "two" of the first expression, the two was decremented in the second expansion, and trailing zeros were replaced with trailing twos in the second expression.

Ternary is the integer base with the lowest [[radix economy]], followed closely by [[Binary numeral system|binary]] and [[Quaternary numeral system|quaternary]]. This is due to its proximity to the [[mathematical constant]] [[e (mathematical constant)|''e'']]. It has been used for some computing systems because of this efficiency. It is also used to represent three-option ''trees'', such as phone menu systems, which allow a simple path to any branch.

A form of [[redundant binary representation]] called a binary signed-digit number system, a form of [[signed-digit representation]], is sometimes used in low-level software and hardware to accomplish fast addition of integers because it can eliminate [[Carry (arithmetic)|carries]].<ref name="Phatak_1994"/>

===Binary-coded ternary===
Simulation of ternary computers using binary computers, or interfacing between ternary and binary computers, can involve use of binary-coded ternary (BCT) numbers, with two or three bits used to encode each trit.<ref name="Frieder_1975"/><ref name="Parhami_2013"/> BCT encoding is analogous to [[binary-coded decimal]] (BCD) encoding. If the trit values 0, 1 and 2 are encoded 00, 01 and 10, conversion in either direction between binary-coded ternary and binary can be done in [[Time complexity#Logarithmic time|logarithmic time]].<ref name="Jones_2016_1"/> A library of [[C (programming language)|C code]] supporting BCT arithmetic is available.<ref name="Jones_2016_2"/>

===Tryte===
Some [[ternary computer]]s such as the [[Setun]] defined a '''tryte''' to be six trits<ref name="Impagliazzo_2006"/> or approximately 9.5 [[bit]]s (holding more information than the ''de facto'' [[Binary number|binary]] [[byte]]).<ref name="Brousentsov_2010"/>