Ternary logic

Base 3

Compared to Analog

Compared to Base 10 and 2

Compared to Base e

Base 9 and 27

Basic Ternary Algebra: Unary Functions

Constant Functions

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

One-to-One Functions

 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

Unbalanced Arithmetic

Negation: 3's complement

Addition / Subtraction

Balanced Arithmetic

Negation: Inversion

Addition / Subtraction

Unknown-State Logic

NOT: Inversion

AND, XOR, OR, XNOR, NAND

Existing Computers

• Setun

• 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)
• Trivalent Logic in the Language of Aymara (http://www.aymara.org/biblio/igr/igr3)

See also: Digital circuit