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The strange connection between ternary system and computers: why is it so important in certain circuits?
The ternary, or base 3, number system has unique properties and advantages over the traditional binary system. Each ternary digit is called a "trit", and the amount of information in a trit is equivalent to about 1.58496 binary bits, which makes the ternary system very important in certain digital computing applications.
Basic concepts of ternary system
The ternary system consists of 0, 1, and 2. Compared to binary, integer representation does not become verbose quickly. For example, the decimal number 365 corresponds to the binary number 101101101 (9 bits long), and the ternary number 111112 (6 bits long). This shows a certain compactness of ternary number representation.
"Although the ternary system may not be as good at compressing numbers as the decimal system, it may perform better than the binary system in some circumstances."
Advantages and applications of ternary system
Ternary provides a convenient way to represent rational numbers. For example, 1/3 can avoid the trouble of using infinite repeating decimals in ternary system. However, the ternary system still has its limitations in some cases. For example, it cannot finitely represent numbers such as 1/2, 1/4, and 1/8. This is because the cardinality of three does not include the prime factor 2.
"The ternary system is particularly useful in defining Cantor sets and related point sets, because the structure of the Cantor set is exactly suitable for expression in ternary system."
Practical application of ternary system in computers
In some analog logics, the states of a circuit are often expressed in ternary form. This phenomenon is particularly prevalent in CMOS circuits and transistor-transistor logic with totem-pole outputs. In such a configuration, the output state of the circuit can be defined as low (ground), high, or on (high impedance), which allows for flexible operation in the circuit.
The three-in-one system is also used in American baseball statistics: every three outs are counted as a complete defensive inning, which makes the records appear concise.
Choice and efficiency of ternary system
Ternary is considered the integer radix with the lowest radix economy, followed by binary and quaternary, making this mathematical system favored for efficiency. Ternary can also be used to encode a three-choice tree structure, such as a telephone menu system, thus simplifying the query path for any branch.
"Ternary encoding has become popular in some digital computing systems because it can improve the efficiency of calculations."
Ternary Coding and Future Prospects
For compatibility with binary computers, ternary computers sometimes use binary coded ternary (BCT) numbers, a technique that makes it possible to convert data between different systems. Advances in this type of technology will help promote the application of the ternary system in a wider range of fields.
ConclusionFrom computing speed to storage efficiency, the ternary system has undoubtedly demonstrated its potential in the field of computing. However, with the advancement of technology and changes in demand, will ternary system have a place in mainstream computers in the future?
