# 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.*

## 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 'AA, 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 ÈæÇA

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

## Magnetism

## Electromechanical relays

## Rapid single flux quantum

## Rectifiers

## External links

- Steve Grub's Trinary.cc
- Trinary Computer Systems
- TriINTERCAL
- Trivalent Logic in the Language of Aymara
- A brief introduction to ternary logic
- trinary operating system