# Numerical systems

Just as the first forms of writing appeared long after the development of speech, the first efforts to create a graphical **representation** of **numbers** came long after people learned to count. Probably the oldest way of keeping track of a count was by means of a **counting system** that included the use of a series of physical objects such as **pebbles** or **sticks** . Judging from the habits of current indigenous peoples, as well as the earliest finds from written or sculpted records, the **earliest numbers** were **simple** and **stick-** shaped ,**marks** or **marks** on one or a **piece of ceramic** . Having no fixed units of measurement, no coins, and no trade beyond barter, people had no need for written numbers until the beginning of so-called **historical times** .

## What are number systems?

The **number systems** are a set of **rules** , **norms** and **conventions** we allow a **representation** of all **natural numbers** , by a large group of **symbols** basic and is defined by the **database** you use.

- What are number systems for?
- Characteristics of number systems
- Source
- History
- Types of number systems
- Application of number systems
- Operations
- Importance
- Examples

## What are number systems for?

The main objective of number systems is to **count** the different **elements** that a **set** has . Through them we can get to build all valid numbers within the number **system** . Its purpose is to **represent** numbers.

## Characteristics of number systems

Among the main characteristics we can mention the following:

- Each number system is characterized by its base.
- Number systems have a base or set of symbols that allow representing different numerical quantities.
- They have a figure or quantity that is formed by the juxtaposition of the different elements.
- Each element within the number system has a weighted value.
- The number 0 expresses or denotes the absence of a certain quantity.
- It is a positional system.
- They are made up of digits.

## Source

To discover the origin of the numbers we must transport ourselves to the **Egyptians** who were the first inhabitants of the earth who had a decimal system , known at that time as the **hieratic number system** .

## History

Since ancient times, man has seen the need to count things to achieve proper **control** . This was one of the main reasons why men devised a **system** of **numbering** . Throughout history , **base 10** was the most used, however there was also the Babylonian numbering that used a range between 10 and 60, and the Mayans, who used numbers between 20 and 5. About 5000 years ago civilizations began to count and use the **units** , **hundreds** , **tens**, etc., varying the way of writing the numbers. The oldest numbering systems are Greek, Ionian, Old Slavic, Cyrillic, Hebrew, Arabic, Georgian, etc. The step from manually counting to **writing numbers** occurred approximately 4000 years before Christ. A rudimentary system of **cuneiform symbols was created** to represent some numbers that were later adopted by the **Sumerians** of **Lower ****Mesopotamia** , who were responsible for creating the oldest numerical figures in history. The birth of **Egyptian numbering** it was based on the repetition of symbols and their succession in ascending or descending order and had a base 10, tens, hundreds, thousands.

## Types of number systems

There are two types or two major classifications of number systems:

**Positional**: it is the type of numerical system in which the value of a**figure**changes according to the**position**in which it is found within the figure of the number. The positional system in turn is subdivided into several types, for example:**Binary system**: it only has two numerical values, 0 and the number 1.**Decimal system**: it is the system that has a base 10 and ten digits that go from the number 0 to 9.**Hexadecimal**system: this system requires 16 different figures to express or represent a number.**Octal system**: it is the system that has eight figures to express different quantities.

**Non-positional**: This is the number system in which the figure**does not depend**on the**position**within the number. For example we can mention the Roman numerals .

## Application of number systems

Number systems have the following uses:

- To
**count**and**express**the results of a measurement and to perform different calculations. - They can be used for
**encodings**of**information**. - They are used in the
**metric system**. - They are used in the field of
**physics**to show scalar and derived magnitudes. - The octal system is used in
**computing**to group bits. - The binary system is also used in
**computers**and**electronic devices**.

## Operations

With the number system you can perform **arithmetic** , addition, subtraction, multiplication and division operations. Each number system has its own way of doing each of these operations.

## Importance

The number system is of the utmost importance for our daily life because through it we can **represent** all the **numbers** and work with them to solve a series of mathematical **problems** that may arise from day to day. It is important in the field of **computation** , **electrical** and **metric** , for the realization of measurements.

## Examples

**Binary System:**0, 1**Decimal System:**0, 1, 2, 3, 4, 5, 6, 7, 8, 9**Hexadecimal System:**0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F