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
2 Trits, Tribbles, and Trytes
3 Basic Ternary Algebra: Unary Functions
4 Binary Functions
5 Advanced Functions
6 Implementation
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  A
102 swap 0/1     /\\'  102      ]'A  A
120 rotate up    ///  201      ]A   A
201 rotate down  \\\\\\  120      [A   A
210 swap 0/2     \\'/  210      'A   A, or A'

Many-to-One Functions

F#  ITE  Expression
001 210 \\A     A            Shift Down
002 220 ]/'A   A
010 100 \\]A    A
011 001 \\/A    A
020 120 ]/['A  A
022 002 [\\'A   A
100 010 \\'A    A
101 101 [/['A  A
110 210 [/'A   A
112 221 /\\A    A
121 121 ]\\]A   A
122 012 /A     A            Shift Up
200 020 ]/A    A
202 102 [\\]A   A
211 021 ]\\'A   A
212 112 /['A   A
220 202 [\\A    A
221 212 /'A    A

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

Magnetism

Electromechanical Relays

Rapid Single Flux Quantum

Rectifiers

External Links

See also: Digital circuit



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