Ternary logic

Ternary logic is a multi-valued logic in which there are three states, thus the ternary numeral system is used to represent ternary logic equations. This article is a work in progress.

Table of contents 1 Base 3 1.1 Compared to Analog 1.2 Compared to Base 10 and 2 1.3 Compared to Base e 1.4 Base 9 and 27 2 Trits, Tribbles, and Trytes 3 Basic Ternary Algebra: Unary Functions 3.1 Constant Functions 3.2 One-to-One Functions 3.3 Many-to-One Functions 4 Binary Functions 4.1 Commutativity 4.2 Preference Functions 4.3 Tritmasks 4.4 Named Functions 5 Advanced Functions 5.1 Unbalanced Arithmetic 5.1.1 Negation: 3's complement 5.1.2 Addition / Subtraction 5.2 Balanced Arithmetic 5.2.1 Negation: Inversion 5.2.2 Addition / Subtraction 5.3 Unknown-State Logic 5.3.1 NOT: Inversion 5.3.2 AND, XOR, OR, XNOR, NAND 6 Implementation 6.1 Existing Computers 7 Magnetism 8 Electromechanical Relays 9 Rapid Single Flux Quantum[?] 10 Rectifiers 11 External Links

Base 3

Compared to Analog

Compared to Base 10 and 2

Compared to Base e

Base 9 and 27

Trits, Tribbles, and Trytes

Basic Ternary Algebra: Unary Functions

Constant Functions

 000 clear to 0
 111 clear to 1
 222 clear to 2

One-to-One Functions

The symbols here need to be TeXified; font face Symbol is unacceptable

 F#  Name    Diff:012 Inverse   Expression
 012 buffer         012      A    A
 021 swap 1/2     '/\  021      ['A  ÈA
 102 swap 0/1     /\'  102      ]'A  ÇA
 120 rotate up    ///  201      ]A   ÇA
 201 rotate down  \\\  120      [A   ÈA
 210 swap 0/2     \'/  210      'A   A, or A'

Many-to-One Functions

 F#  ITE  Expression
 001 210 \A     æA            Shift Down
 002 220 ]/'A   ÇäA
 010 100 \]A    æÇA
 011 001 \/A    æäA
 020 120 ]/['A  ÇäÈA
 022 002 [\'A   ÈæA
 100 010 \'A    æA
 101 101 [/['A  ÈäÈA
 110 210 [/'A   ÈäA
 112 221 /\A    äæA
 121 121 ]\]A   ÇæÇA
 122 012 /A     äA            Shift Up
 200 020 ]/A    ÇäA
 202 102 [\]A   龂A
 211 021 ]\'A   ÇæA
 212 112 /['A   äÈA
 220 202 [\A    ÈæA
 221 212 /'A    äA

Binary Functions

Commutativity

Preference Functions

Tritmasks

Named Functions

Advanced Functions

Unbalanced Arithmetic

Negation: 3's complement

Addition / Subtraction

Balanced Arithmetic

Negation: Inversion

Addition / Subtraction

Unknown-State Logic

NOT: Inversion

AND, XOR, OR, XNOR, NAND

Implementation

Existing Computers

• Setun

Magnetism

Electromechanical Relays

Rapid Single Flux Quantum[?]

Rectifiers

External Links

• Steve Grub's Trinary.cc (http://www.trinary.cc/)
• Trinary Computer Systems (http://xyzzy.freeshell.org/trinary/)
• TriINTERCAL (http://www.progsoc.uts.edu.au/~sbg/intercal/ick5.html)
• Trivalent Logic in the Language of Aymara (http://www.aymara.org/biblio/igr/igr3.html)

See also: Digital circuit