Meaning of binary system (what is it, concept and definition)

What is Binary System:

The binary system is a numbering system that uses 2 symbols 0 (zero) and 1 (one), called binary digits. The binary system, also known as the digital system, is used for the representation of texts, data and executable programs on computing devices.

In computer science, the binary system is a language that uses 2 binary digits, 0 and 1, where each symbol constitutes a bit, called in English as binary bit or binary bit. 8 bits make up a byte and each byte contains a character, letter or number.

Binary system and decimal system

Binary systems are number systems used in the area of ​​computing. The numerical system that we usually use is decimal numbering, that is, it consists of 10 numbers, counting from 0 to number 9. In addition, unlike the binary system, the position that a number occupies gives it different values, such as, at number 23, 22 represents 20 and 3 is only 3.

It is important to emphasize that the binary system is a base 2 numbering system and the decimal system is base 10.

Binary to decimal system

To transform a number from one numbering system from one base to another, in this case from binary (base 2) to decimal (base 10), each digit (0 or 1) of the binary number must be multiplied, for example, 1011 by the power of 2 raised to the position corresponding to each digit starting with position 0 counting from right to left. The result is obtained by adding each multiplication.

Following the previous steps to solve this exercise, the steps to convert the binary code 1011 to decimal system would be:

The 1 in position 3 means: multiply 1 by 2 ³ whose result is 8

The 0 in position 2 means multiplying 0 by 2 ² whose result is 0

The 1 in position 1 means multiplying 1 by 2 ¹ whose result is 2

The 1 in position 0 means multiplying 1 by 2 ⁰ whose result is 1

We add the results 8 + 0 + 2 + 1 = 11

The binary code 1011 is translated into the decimal system as the number 11.

To check the result, the process is reversed to transform the number 11 in base 10 to the binary system in base 2. To do this, divide the number 11 by 2 until it is indivisible. Then the remainders of each quotient of the division will form the binary code.