Binary numbers: binary number system

Binary numbers are numbers from the binary number system having the base 2. It is directly implemented in digital electronics, used in most modern computing devices, including computers, mobile phones and all sorts of sensors. We can say that all the technologies of our time are built on binary numbers.

Recording numbers

Any number, however large, is written in the binary system by two characters: 0 and 1. For example, the digit 5 from the whole familiar decimal system in binary will be represented as 101. The binary numbers can be designated by the prefix 0b or ampersand (&), For example: & 101.
In all systems, except decimal, the characters are read individually, that is, taken in example 101 is read as "one zero one".

Translation from one system to another

Programmers who constantly work with the binary number system, on the move can translate the binary number into a decimal number. This can indeed be done without any formulas, especially if a person has an idea of how the smallest part of the computer "brain" works - a bit.

The number zero also means 0, and the number one in the binary system will also be a unit, but what to do next when the numbers are over? The decimal system "suggested" in this case to introduce the term "ten", and in the binary system this will be called "deuce".

If 0 is & 0 (ampersand is the designation of the binary system), 1 = & 1, then 2 will be denoted as & 10. The triple can also be written in two places, it will have the form & 11, that is, one deuce and one unit. Possible combinations are exhausted, and in the decimal system at this stage hundreds are entered, and in the binary - the "four". Four - it's 100, five - 101, six - 110, seven - 111. The next, larger unit of account is the figure eight.

You can notice a feature: if in the decimal system the bits are multiplied by ten (1, 10, 100, 1000, and so on), then in binary, respectively, two: 2, 4, 8, 16, 32. This corresponds to the size of the flash cards And other drives used in computers and other devices.

What is a binary code

The numbers represented in the binary system are called binary, but in this form, you can also represent numeric values (letters and symbols). Thus, in the figures you can encode words and texts, though they will not look so laconic, because to write only one letter will require several zeros and ones.

But how do computers manage to read this amount of information? In fact, everything is easier than it seems. People accustomed to the decimal number system first translate binary numbers into more familiar ones, and only then perform any manipulations with them, and at the heart of computer logic is initially a binary number system. A unit in technology corresponds to a high voltage, and to zero it is low, or there is a voltage for a unit, and for zero there is no voltage at all.

Binary numbers in culture

The mistake is to assume that the binary system of numbers 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 intermittent (zero) are used, encoding eight characters meaning eight elements: sky, earth, thunder, water, mountains, wind, fire and water (mass of water). This analogue of 3-bit digits was described in the classic text of the book Changes. The trigrams were 64 hexagrams (6-bit digits), the order of which in the Change book was located in accordance with the binary digits from 0 to 63.

This order was compiled in the eleventh century by the Chinese scientist Shao Yong, although there is no evidence that he really understood the binary system of numbers in general.

In India, even before our era, binary numbers were also used mathematically to describe poetry, compiled by the mathematician Pingala.

The Inka written system of the Incas (kipu) is considered the prototype of modern databases. They first used not only a binary number code, but also not numeric entries in the binary system. The lettered letter to the bale is characterized not only by primary and additional keys, but also by the use of positional numbers, color coding and a series of repetitions of data (cycles). The Inca first applied a method of accounting, called a double entry.

The first of programmers

The binary number system, based on the numerals 0 and 1, was 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 programmers and information theorists. It was he who discovered that if you record the binary numbers vertically (one under the other), then in the resulting vertical columns of numbers, zeros and ones will be regularly repeated. This called him to assume that there could be entirely new mathematical laws.

Leibniz also realized that binary numbers are optimal for use in mechanics, the basis of which should be the replacement of passive and active cycles. In the courtyard was the 17th century, and this great scientist invented on paper a computer 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.