10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCES, Kırklareli, Turkey, 6 - 08 January 2024, pp.47-53
This article is about the base complement in 𝐵3. The complement method consists of the course
of operations around the centroid. The centroid is played an important role in the encoding of
numbers. Some of the numbers are smaller than the centroid and some are larger than the
centroid. Thus subtraction of any number is implemented by adding its complement. The
concept of caryy comes into play when numbers smaller than the centroid are subtracted from
numbers larger than the centroid. The pairs of mutually additive inverse numbers are called
complements. Changing the sign of any number is encoded by generating its complement,
which can be with a very simple and useful known algorithm. This method is widely used in
digital computing.
The base complement of an 𝑛 − 𝑑𝑖𝑔𝑖𝑡 number y in base 𝑟 is defined as 𝑟
𝑛 – 𝑦. In practice,
the base complement is (𝑟
𝑛 – 1) − 𝑦.
All these calculations were made in 𝑩𝟐. The study is about the role of the centroid concept
in 𝑩𝟑. The digit value of a number in the ternary system is redefined. The new definition
radix and diminished radix complement is also updated for this definition. This situation
enriched the coding. Any number is written 𝟎 and 𝟏 in 𝑩𝟐. This number is expressed −𝟏,
𝟎 and 𝟏 in 𝑩𝟑. The expression of a number as −𝟏, 𝟎 and 𝟏 offers new gains in the coding
and processing of data. The preliminary approaches in the study are presented noteworthy
cases in the evaluation of approaches in numeric and alphanumeric expressions. Initial
statements are given on innovations in coding and operations.