Binary numbers are numbers from the binary number system that has base 2. It is directly implemented in digital electronics, used in most modern computing devices, including computers, mobile phones and various sensors. We can say that all the technologies of our time are built on binary numbers.
Writing numbers
Any number, no matter how large it may be, is written in the binary system using two characters: 0 and 1. For example, the number 5 from the familiar decimal system in binary will be represented as 101. Binary numbers can be denoted by the prefix 0b or ampersand (&), for example: &101. In all number systems, excluding decimal, characters are read one by one, that is, taken as an example, 101 is read as "one zero one".
Transfer from one system to another
Programmers who constantly work with the binary number system can convert a binary number to decimal on the go. This can really be done without any formulas, especially if a person has an idea of how the smallest part of the computer "brain" - the bit - works.
The number zero also means 0, and the number one in the binary systemwill also be a unit, but what to do next when the numbers are over? The decimal system would "suggest" in this case to enter the term "ten", and in the binary system it would be called "two".
If 0 is &0 (ampersand is binary notation), 1=&1, then 2 will be denoted as &10. A triple can also be written in two digits, it will look like &11, that is, one two and one unit. The possible combinations have been exhausted, and in the decimal system, hundreds are entered at this stage, and in the binary system, "fours". Four is &100, five is &101, six is &110, seven is &111. The next larger counting unit is the figure eight.
You can notice a feature: if in the decimal system the digits are multiplied by ten (1, 10, 100, 1000 and so on), then in the binary system, respectively, by two: 2, 4, 8, 16, 32. This corresponds to the size of flash cards and other storage devices used in computers and other devices.
What is a binary code
Numbers represented in the binary system are called binary, but non-numerical values (letters and symbols) can also be represented in this form. Thus, words and texts can be encoded in numbers, although they will not look so concise, because it will take several zeros and ones to write just one letter.
But how do computers manage to read so much information? In fact, everything is easier than it seems. People who are accustomed to the decimal number system first translate binarynumbers into more familiar ones, and only then they perform any manipulations with them, and the basis of computer logic is initially a binary system of numbers. A unit in technology corresponds to a high voltage, and zero to a low voltage, or there is a voltage for a unit, but no voltage for a zero.
Binary numbers in culture
It would be a mistake to assume that the binary number system is the merit of modern mathematicians. Although binary numbers are fundamental in the technologies of our time, they have been used for a very long time, and in different parts of the world. A long line (one) and a broken line (zero) are used, encoding eight characters, meaning eight elements: sky, earth, thunder, water, mountains, wind, fire and a reservoir (mass of water). This analogue of 3-bit numbers was described in the classic text of the Book of Changes. Trigrams were 64 hexagrams (6-bit digits), the order of which in the Book of Changes was arranged in accordance with binary digits from 0 to 63.
This order was compiled in the eleventh century by the Chinese scholar Shao Yong, although there is no evidence that he actually understood the binary system in general.
In India, even before our era, binary numbers were also used in the mathematical basis to describe poetry, compiled by the mathematician Pingala.
Inca nodular writing (quipu) is considered the prototype of modern databases. It was they who first used not only the binary code of a number, but also non-numeric entries in the binary system. Kipu knot writing is characteristic not only of primary andadditional keys, but also the use of positional numbers, coding using color and a series of data repetitions (cycles). The Incas pioneered a method of bookkeeping called double entry.
First of the programmers
The binary number system based on the numbers 0 and 1 was also described by the famous scientist, physicist and mathematician, Gottfried Wilhelm Leibniz. He was fond of ancient Chinese culture and, studying the traditional texts of the Book of Changes, noticed the correspondence of hexagrams to binary numbers from 0 to 111111. He admired the evidence of such achievements in philosophy and mathematics for that time. Leibniz can be called the first of the programmers and information theorists. It was he who discovered that if you write groups of binary numbers vertically (one below the other), then zeros and ones will regularly repeat in the resulting vertical columns of numbers. This called him to suggest that entirely new mathematical laws might exist.
Leibniz also understood that binary numbers are optimal for use in mechanics, the basis of which should be the change of passive and active cycles. It was the 17th century, and this great scientist invented on paper a computing machine that worked on the basis of his new discoveries, but quickly realized that civilization had not yet reached such technological development, and in his time the creation of such a machine would be impossible.
