## What is binary system:

The binary system is a **number 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 in computing devices.

In computing, the binary system is a language that uses 2 binary digits, 0 and 1, where each symbol constitutes a bit, known 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, this means that 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 , in the number 23, the 22 represents 20 and the 3 is just 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 in a numbering system from one base to another, in this case from binary (base 2) to decimal (base 10), you must multiply each digit (0 or 1) of the binary number, for example, 1011 by the power of 2 raised to the position that corresponds 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 the 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 multiply 0 by 2^{two} whose result is 0

The 1 in position 1 means multiply 1 by 2^{1} whose result is 2

The 1 in position 0 means multiply 1 by 2^{0} whose result is 1

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

The binary code 1011 translates to the decimal system as the number 11.

See also binary code.

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