Ternary Logic from Binary Logic

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This will go over how to adapt NOT, AND, and OR from binary logic into one kind of ternary logic.
Note for exercise: There are a lot of possible connectives for ternary logic, consider finding symmetries.

0:00 Opening
0:07 Two-Value to Three Values
0:22 What is Other?
0:32 What will we be doing?
0:40 Logical NOT
1:01 Filling in NOT
1:18 Logical AND
1:43 Filling in AND
2:10 Logical OR
2:35 Filling in OR
2:58 Exercise

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Yes you can, it can be constructed with a finite number of one gate, the nand or nor gate. All the O shenenigans will come out naturally if you have negation and some symmetric operator.

NieLękajcieSię·PrawdaJestJedna

If you use balanced ternary as [-1, 0, 1] then the AND gate can be thought of as a LEAST gate and an OR gate can be a GREATEST gate. This is kinda how they work in binary anyway. Zero can not be thought of as sign-less, so it can not be inverted with the NOT gate... I'm not sure, mathematically, if negative zero and positive zero have any repercussions.

peterweston

If I were doing unbalanced ternary logic, then the NOT gate flips the sequence of numbers, OR gives me the higher number and AND gives the the lower number

epicmidtoker

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