In ancient times, humans relied on counting with their fingers. With the development of human settlements and the establishment of towns and villages, there was a pressing need for other methods of counting and calculation.

Thus, different number systems emerged, developed by civilizations that existed more than a thousand years before the Common Era.

This article introduces number systems and their four main types, shedding light on each in detail regarding their nature and uses.

Number Systems

A number system is a structured way of representing numbers through specific symbols, which are digits and letters.

Repeating and combining these symbols allows us to express larger numbers. Each number system consists of three key components: the digit, its type, and its base.

Types of Number Systems

Given the diverse applications and fields, it became essential to represent all numbers and use them to solve mathematical problems.

Thus, various types of number systems have been developed:

Decimal System

The decimal system is the system we use daily for transactions and calculations. It is based on the number 10, with digits ranging from 0 to 9.

In the decimal system, two numbers may share the same digits but differ in their arrangement (place value), giving them distinct values, such as 243 and 342.

The decimal system is one of the embedded number systems used in computers, relying on microprocessors or precise control of devices and software.

Binary System

The binary system is based on the number 2, using only two digits: 0 and 1.

It is used for storing and processing all digital data in computers, including numbers, words, files, graphics, and videos.

It is also used for storing passwords and user data, making websites more secure because hackers find it challenging to read these binary codes. Hackers need to convert binary symbols to text, which is time-consuming.

In reality, any binary number stored is converted into a series of binary numbers for processing. The binary system is also used in electrical circuits because it consists of only two symbols: 0 and 1.

These symbols represent an open or closed circuit, respectively, with 0 representing an open circuit and 1 representing a closed circuit.

The binary system benefits computers, which operate on low voltage passing through electrical circuits.

Octal System

The octal system is based on the number 8, with digits ranging from 0 to 7.

Although the octal system is less commonly used than other systems, it is simpler for handling inputs and outputs and is used in computer applications within digital and computing systems.

Hexadecimal System

The hexadecimal system is based on the number 16, using symbols representing numbers from 0 to 9 and letters A, B, C, D, E, and F.

These letters correspond to the numbers 10, 11, 12, 13, 14, and 15, respectively.

The hexadecimal system is used for data compression because it represents values from 0 to 15 with a single digit, making it useful for converting bits to bytes.

It also enhances web security because it is difficult for humans to read and write.

Programmers often convert numbers from the decimal to the hexadecimal system and store them in a database.

The hexadecimal system improves computer processor speed and is useful for identifying and correcting errors on websites.

Sometimes, it is necessary to convert from one number system to another for specific purposes, and each conversion has its own rules. We will discuss this in another article.

Each number system has a role in life. People use the decimal system for everyday life, commercial transactions, and mathematical problem-solving, while electronic and digital devices rely on the binary, hexadecimal, and octal systems.

Author: Abdul Hamid Al-Deiban, Mathematics Teacher, Masarat Initiative