It is known that for many years, ancient civilizations used different methods of counting. These were the settlements of the **numbering systems** that are known today, since many of these counted in units, tens, hundreds, only that the writing of the numbers was different from the one used today.

## Definition

**It can be defined as an aggregate of symbols and generation rules**, which supports the creation of valid digits in the system. The numbering systems are **made up of various elements**, which are governed by a series of rules that allow the establishment of operations and relationships between the different elements.

When these two definitions are combined, the conclusion is then reached that the numbering systems are a **set of compendiums**, whether they are symbols or digits, as well as operations, as well as relationships that those already assigned numbers can carry out.

## Classification of numbering systems

These numbering systems can be classified into 3 different groups, which are:

•** Non-positional numbering systems:** these are based on the numbers that have the value of the symbol used. That is, they do not take into account the column they invade in the number. An example of this group can be the Egyptian numbering system.

This system is the most archaic known, since they **basically used the fingers of the hands.**

They used knotted ropes to represent the quantity of numbers and they used a lot the ability to coordinate between the elements.

•** Semi-positional systems:** a system born in ancient Rome and that is flexibly considered positional. This meant that it was much more complex to develop the algorithms for addition, subtraction, multiplication, and division. An example of this is Roman numerals, which from the beginning to the end of the digit have the same value.

• **Positional numbering:** also called as the weighted numbering system, it is when the value of a number has to do with the symbols used. In other words, what matters is the position that element occupies in the digit. In this system the amount of elements that are allowed are called as base.

Within this type of system others can be known, one of them is the binary system, as well as the decimal, even the octal and hexadecimal systems. The positional decimal system is **the one used in most of the countries of the world**, except in languages such as computer science, where systems such as hexadecimal and binary are used.

**Binary system:** the digits that are used only with the numbers zero and one are represented here. Normally it is only used in computers, since they work internally with 2 voltage levels. This is basically its on that they identify it with the number 1 and with the off that is represented by the number 0.

**Hexadecimal system:** in positional numbering systems, this is base 16, which means that it is based on 16 symbols. Its use today also leans towards computing. Since these sciences use bytes and bytes as a basic memory device.

## Fundamental numbering theorem

**It institutes the ordinary way of constructing digits in positional numbering systems**, as long as the basic denominations of the valid number, the base, the various symbols, the numbers of the whole part, and the digits that make up the number are established and clear. decimal part. All of these applied to a specific formula.

The importance of numbering systems is based on the fact that all natural digits can be stated in a unique way, as a linear combination.

Number systems are a fundamental part of science, while science is the foundation of society and the world as we know it therefore it is important to know and study number systems.