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The amazing secret of ternary: Why is it more efficient than binary?
In the digital world, base 3 (or trinary) has its own unique wonders compared to the binary system we use in daily life. Ternary uses three symbols (usually 0, 1, and 2) to represent numbers. Its basic unit is called a "trit", and each trit can carry about 1.58 bits of binary information. As computer technology continues to advance, more and more researchers are exploring the potential of ternary computing, especially in comparison with binary efficiency.
The properties of the ternary system make it excellent for representing large amounts of information.
When converting integers to base ternary, fewer digits are required than in the binary system. For example, the decimal number 365 requires nine bits to represent in binary (101101101), but only six bits in ternary (111112). This conversion effect makes ternary system very effective in some applications.
Ternary system also shows its advantages in representing rational numbers. For example, one third can be represented by a simple number in the ternary system, but in the decimal system, it often requires repeating decimals. Although the ternary system cannot represent certain numbers (such as half) using a finite number of digits, the way it processes information gives the user flexibility.
The ternary form is particularly convenient for representing self-similar structures like the Sierpinski triangle or the Cantor set.
In the world of mathematics, ternary representation also has an important influence on the definition of the Cantor set. The Cantor set consists of ternary representations that do not contain the number 1, which makes the study of this set more efficient. This relationship also leads to the connection between ternary and the mathematical constant e. Surprisingly, ternary is the integer system with the least cardinality economy.
In practical applications, ternary system also appears in analogical logic. For example, in CMOS circuits, the state of the circuit is often expressed in ternary form. These circuits often have output states of low (ground), high, or on (high impedance). In this configuration, the output of the circuit is not actually connected to any voltage reference, so the true voltage level of the signal is sometimes unpredictable.
Interestingly, the three-point system is also used in defensive statistics in American baseball, particularly for evaluating pitchers' performance.
In baseball records, each out is counted as one-third of a fielding inning, and this is often expressed as a decimal point, so that a pitcher who pitched a full inning with two outs would be counted as 3.2, which means 3 and two-thirds innings. This expression makes the interpretation of data more convenient and intuitive.
In addition to practical applications, ternary system also shows its potential value in computing systems. Some ternary computers, such as Setun, define six trits as a tryte. This structure can carry more information than binary bytes, which means greater data processing capabilities. In some cases, system compatibility can be further improved by converting ternary to binary-coded ternary (BCT), which facilitates data conversion between different bases.
Ternary has also been found to work well in multiple-choice tree structures, such as mobile phone menu systems, which give users a simple path to the options they need. This feature strongly supports the application of ternary system in intelligent system design.
As our understanding of digital systems deepens, can ternary system become the new cornerstone of the future computing revolution?
