Ternary numeral system
The Ternärsystem, also called triple system is a place value system to the base 3 It comes in two varieties, than ordinary Ternärsystem with the digits 0, 1 and 2 as well as balanced Ternärsystem with the digits 0, 1 and -1.
A ternary figure is also referred to as a trit ( in analogy to the bit). In 1958, the Zeitun computer was developed in the Soviet Union, the calculated ternary numbers.
The ordinary Ternärsystem
A number is represented by a combination of the digits 0, 1 and 2 in the ordinary Ternärsystem. Since confusion with other representations of numbers, can occur particularly with the decimal system, a Ternärzahl is characterized by an attached subscript 3. The Ternärzahl a decimal equivalent can be calculated as in the following example:
Solving the powers on, then the equation looks like this:
The corresponding general formula is
Here, the Ternärziffer is at the point (either 0, 1 or 2 ), the number of decimal places and the number of the highest point. is the result, so the value of the Ternärzahl. This formula is the same as the first and second linear formula in the article, but just presented differently.
Other examples of numbers in Ternärsystem and their equivalent in the decimal system:
You can numbers in ordinary ternary system, such as numbers in other important systems also represent good for understanding in a table. The number in a box indicates how many times the number of the column name is counted. If, for example, in a field of the " 3" "2", so you have to " 3 3 " or "2 ∙ 3" expect, with "1 " in " 27" easy " 1 ∙ 27". At the end you count up all the individual results of intermediate calculations ("2 ∙ 3", " 1 ∙ 27") and receives the decimal number. Zeros the left of the first 1 or 2 ( leading zeros) in the usual notation ( composite column Ternärzahl ) are not written down.
The balanced Ternärsystem
A number in the balanced Ternärsystem is represented by a combination of the digits 0, 1 and -1. The number -1 is reproduced in this article by one, another can playback a vertically mirrored in 1 case confusion will occur in a balanced Ternärzahl with a trailing subscript " 3bal ".
Examples of numbers in balanced Ternärsystem and their equivalent in the decimal system:
In balanced Ternärsystem you do not need a sign. To go to the negative number, you swapped all of the digits 1 to 1 and all of the digits 1 to 1
Again you can, as shown for the ordinary Ternärsystem, calculate the decimal equivalent:
Powers dissolved: