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Mathematics# Numeral systems

## What are numeral systems?

## What are the numeral systems for?

## Characteristics of numeral systems

## Origin

## History

## Types of numeral systems

## Application of numeral systems

## Operations

## Importance

## Examples

Just as the first forms of writing appeared sometime after speech development, the first efforts to create a graphical **representation** of **numbers** came a long time after people learned to count. Probably the oldest way to keep track of a count was through a **counting system** that included the use of a series of physical objects such as **pebbles** or **sticks**. Judging by the habits of today's indigenous peoples, as well as by the earliest findings of written or sculpted records, the **first** **numbers** were simple and **stick-shaped**, with **signs** or **marks** on one or a **piece of pottery**. Having no fixed units of measurement, no coins, and no trade beyond barter, people did not need written numbers until the beginning of so-called **historical times**.

**Related topics**

**Numeral systems** are a group of **rules, norms and conventions** that allow us to make a representation of all **natural numbers,** through a wide group of basic **symbols** that is defined by the **base** it uses.

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

Among the main characteristics we can mention the following:

- Each numeral system is characterized by its base.
- The numeral systems have a base or set of symbols that allow to represent the different numeral quantities.
- They have a number or quantity that is formed by the juxtaposition of the different elements.
- Each element within the numeral system has a weighted value.
- The number 0 expresses or denotes the absence of a given quantity.
- It is a positional system.
- They are composed of digits.

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

Since antiquity, man has found himself in the need to count things in order to achieve adequate **control**. This was one of the main reasons why man invented a **numbering system**. Throughout **history**, the **base 10** was the most used, however, there was also the Babylonian numeration that used a range between 10 and 60, and the Mayas, who used numbers between 20 and 5. It has been approximately 5000 years since civilizations began to count and use **units, hundreds, tens**, etc., varying the way of writing numbers.

The oldest numbering systems are Greek, Ionic, ancient Slavic, Cyrillic, Hebrew, Arabic, Georgian, etc. The step from counting manually to **writing numbers** took place 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 numeral figures in history. The birth of the **Egyptian numeration** was based on the repetition of symbols and the succession of these in ascending or descending order and had a base of 10, tens, hundreds, thousands.

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

**Positional**: it is the type of numeral system in which the value that has a**number**changes according to the**position**in which it is, inside the figure of the number. The positional system is also subdivided into various types, for example:**Binary system**: it only has two numeric values, the 0 and the number 1.**Decimal system**: it is the system that has a base of 10 and ten digits that go from the number 0 to 9.**Hexadecimal system**: this system requires 16 different digits to express or represent a number.**Octal system**: it is the system that has eight digits to express different quantities.**Non-positional**: This is the numeral system in which the number**does not depend**on the**position**within the number. For example, we can mention the Roman numerals.

Numeral systems have the following uses:

- To
**count**and**express**the results of a measurement and to perform different calculations. - They can be used to
**codify 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
**computation**to group bits. - The binary system is also used in
**computing**and**electronic devices**.

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

The numeral system is of great 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 day by day. It is important in the field of **computation**, **electric** and **metric**, for the realization of measurements.

**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

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Numeral systems*. Recovered on 9 March, 2023, de Euston96: https://www.euston96.com/en/numeral-systems/