In Mathematics, one of the most important concepts which are used in our daily life is the โ€œNumber System and its Conversionโ€. One such important application of the number system is the computer architecture. We usually communicate with each other using a particular language using different words. But computers do not understand words or letters. Generally, we type letters through the keyboard. But those letters or words are converted to the machine understandable language. That means the letters are translated to the numbers. It can be done with the help of a number system and different conversion methods. Thus, the number system is a technique to represent the numbers in the computer architecture. The different types of number system are:

  • Binary (Base 2) Number System
  • Octal (Base 8) Number System
  • Decimal (Base 10) Number System
  • Hexadecimal (Base 16) Number System


As computers and other electronic gadgets support the number system, it is essential to know about the number system conversion methods. Now, let us discuss the different number systems and their applications.

Binary Number System

The binary number system is also called the base 2 number system, which consists of only two digits such a 0 and 1. An important application of the binary number system is found in computer architecture. The base 2 number system simplifies computer design and its related technologies. The binary numbers are used in the electronic gates, as there are only two options available, such as true or false. In this case, 1 represents true, and 0 represents false.

Octal Number System

The octal number system consists of eight digits from 0 to 7. It is also known as the base 8 number system. It requires only 3 bits to represent the value of any digit. Like other number systems, the octal number system is also used in the IT industry. It is also widely employed in providing file permission on UNIX systems, such as read access, write access, read and write access, and so on. Since the octal numbers use fewer digits than the decimal and hexadecimal numbers, it is easier to handle the data in the octal form.

Decimal Number System

The decimal number system is also called the base 10 number system, which consists of 10 digits that ranges from 0 to 9. The decimal number system has a vital role in the development of science and technology. It can be easily readable and used by humans, and it is easy to manipulate. Initially, all computer architecture uses the decimal number system. As the base 10 number system consumes more space and time, it is replaced by the base 2 number system. Thus, the conversion from decimal to hex or decimal to binary is preferred as it is more suitable for storage and other criteria.

Hexadecimal Number System

The hexadecimal number system (base 16 number system), consists of alphanumeric values from 0-9 and A-F. The programmers often prefer the base 16 number system. The hexadecimal numbers are used to display the error message, to define the colour on the webpage, to specify the memory location, and so on.


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