Binary system

The binary system or base 2 system is a numerical system that only uses two digits: 0 and 1. Computers work by means of a binary system, which means that they can store data and perform calculations using only zeros and ones . The term is also used to refer to any digital encoding and decoding system in which there are two exact possible states. In digital data memory, storage, processing and communications, the values ​​0, which is referred to as low; and 1 which can also be called or known as “high”. One bit, Which is the name that is given to the abbreviation of a bit is the unit ‘s small of data that can be found in a computer; each bit has a unique value of 1 or 0. Executable programs are often identified as binary files and are given a file name extension of “.bin”.  Programmers often call binary executable files .

What is the binary system for?

At present, it is binary system is one of the most important because its popularity lies in the use that is given in the computers or computer . As these equipments, internally, work with two different degrees of voltage, the binary system is used to indicate the shutdown, the low power, “zero volts” or the inhibit stage. The binary number system has different uses today ranging from programming microprocessors , the data transfer , the encryption information , to digital communication , electronics and other areas related to computer. It is also important in the field of electronics and current technology , since they are present in most of the appliances that we use daily.

features

The main characteristics of the binary system are the following:

• Use only two digits, zero and one .
• Each digit has a different value that depends on the position it occupies.
• The value of each position is the same as a power of base 2.
• It is used in all types of computers because they work with internal voltage unevenness.

History

The Indian-born mathematician Pingala was the one who first presented a description of a binary numbering system in the 3rd century BC in which he represented the numbers from 1 to 8 with a sequence, consisting of 8 trigrams and 64 hexagrams , analogous to binary numbers with a precision of 3 and 6 bits . The binary system was modernized by Gottfried Leibniz , in the 17th century, through his written work known as Explication de l’Arithmétique Binaire . This modernized Leibniz system used the 0 and 1, as it remains today. In 1854, George Boole, a British mathematician, detailed a logical system that would later be called Boolean algebra which was essential for the development of the binary system, mainly in its application to electronic circuits .

How the binary system works

The binary system is based on the representation of quantities using the numbers 1 and 0 . Therefore its base is 2, which is the number of digits that a system has. Each digit in this system is called a bit . These numbers start with 0 and then 1 and now we would have to move on to the next number, which would already be two digits because there are no more single digit binary numbers. The next binary number, therefore, would be to combine 1 with 0 , that is, 10, the next would be the number 11. Once all possible combinations of 2-digit binary numbers have been made, we no longer have any more combinations so we build the 3-digit ones, and so on.

Applications

The uses and applications that can be given to the binary system are:

• Computing
• electronics
• Electricity

Converting from binary to decimal system

To be able to convert a binary number into a decimal one, we need to multiply the first binary term by the number two and to the result of that multiplication we must add 1, later, that result must be multiplied by two and add the next binary and so on until that we have one digit which must only be added and not multiplied.

Examples

• 0: 0
• eleven
• 10: 2
• 11: 3
• 100: 4
• 101: 5
• 110: 6
• 111: 7