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
totem-pole output. The output is said to either be low (
grounded), high, or open (
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
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
pitchers), to denote fractional parts of an inning. Since the team on offense is allowed three
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 (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. Ternary numbers can be used to convey self-similar structures like the
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. 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 and
quaternary. This is due to its proximity to the
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
carries.
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. 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
logarithmic time. A library of
C code supporting BCT arithmetic is available.
Tryte Some
ternary computers such as the
Setun defined a
tryte to be six trits or approximately 9.5
bits (holding more information than the
de facto binary byte). == See also ==