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trinary

Trinary logic is three-level digital logic, with states represented by the numbers -1, 0, and 1. Alternatively, the three states can be represented by the numbers 0, 1, and 2. The smallest number corresponds to logical falsity, the highest number to logical truth, and the middle value to logical neutrality (neither truth nor falsity). Trinary logic is not often used. Binary logic, in which there are only two states represented by 0 and 1, is the most common in computer science and electronics.

In the trinary number system, each individual digit can have one of only three values: 0, 1, or 2. Whole numbers in this system count upwards as follows: 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, ..., 220, 221, 222, 1000, 1001, 1002, ..., 2221, 2222, 10000, 10001, 10002, ... . The trinary number system is rarely used. In computer applications, the binary system is almost universal. Some computer applications use octal and hexadecimal number systems. The decimal number system is used in lay documentation and in general scientific work.

This was last updated in September 2005

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I'm curious as to why the Trinary Number system is limited to those numbers, instead of every number countable on a base 3 system. I understand that at this point most computers are limited to storing information in on/off positions, which limits them to binary. But why would a theoretical computer able to operate on a trinary system be limited to those numbers? One that operates on ON/Neutral/OFF positions.

How I was looking at it is like this. 
ON = 1
NEU = base number * 2
OFF = 0

Let 1 = ON, X = Base * 2, and 0 = OFF

On a 4 bit system you'd be able to represent up to 80 vs. 15 on binary.

0001 = 1
000X = 2
0010 = 3
0011 = 4
001X = 5
00X0 = 6
00X1 = 7
00XX = 8
0100 = 9
0X00 = 18
1000 = 27
X000 = 54
XXXX = 80
 
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Imagine these hypothetical trinary points on a 3D (x,y,z) plane as 3 separate matricies of 9 points each The 3rd dimension "depth" is going to be represented by different "( [ {brackets} ] )"

Variable X coordinates: Variable Y: Variable Z:
(0,0,0)(1,0,0)(2,0,0) [0,2,0][0,2,0][0,2,0] {0,0,0}{0,0,1}{0,0,2}
(0,0,0)(1,0,0)(2,0,0) [0,1,0][0,1,0][0,1,0] {0,0,1}{0,0,1}{0,0,2}
(0,0,0)(1,0,0)(2,0,0) [0,0,0][0,0,0][0,0,0] {0,0,2}{0,0,2}{0,0,2}

The problem with variable Z is it's on this third plane that I personally am not very used to visualizing things. But in a matrix like this it doesn't give the information of which direction to view it from if we're not also using negative numbers. But if we're still talking about a physical object how do you represent a negative number? A void. As I understand it trinary is going to be more useful at assessing the overall manipulating factors in systems with more than 2 variables, but hopefully less than 3. because if it's more than 3 you're getting into 4D and the aspect of time comes into play while trying to visualize.

If anyone thinks I'm talking out my a**, let me know because I could be completely wrong since I've tried to learn all of this from extensive google searching and connecting dots.
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