Conversion of
Number Systems

toc Table of Contents

What are Number Systems?

Number systems are a fundamental concept in mathematics and computer science. There are several popular numeral systems used around the world, including the decimal, binary, octal and hexadecimal. Understanding these systems is important for a variety of purposes, including digital electronics, computer programming, and cultural studies.

Number systems play a crucial role in mathematics and computer science, as they provide a way to represent numerical values in a structured and systematic way. By using different sets of symbols and rules, each numeral system allows for the representation of numbers in a unique way, making them useful for different applications.

The decimal system, for example, is the most commonly used system worldwide, using ten digits (0-9) to represent numbers based on the powers of ten. On the other hand, the binary system uses only two digits (0 and 1) to represent numbers based on the powers of two, and is essential in computing and digital electronics.

The octal and hexadecimal systems are also widely used in computer programming and networking, with the octal system using eight digits (0-7) and the hexadecimal system using sixteen digits (0-9 and A-F) to represent numbers based on the powers of eight and sixteen, respectively.

Understanding the different numeral systems and their applications is important for a variety of purposes, including mathematics, computer science, and cultural studies.

Popular Number Systems

Let's take a brief look at each of the popular numeral systems. The following table provides an idea of the digits used in each system.

Binary (Base 2) Number System

A binary number system represents a number in terms of only two numerals, i.e., 0 (zero) and 1 (one). In the word "binary", "bi" means "two". Binary numbers are represented with 2 at their base, for example 1010101₂.

Octal (Base 8) Number System

Octal number system(Oct) has a base of eight and uses combinations of numerals 0 to 7 to represent any number. 12₈ is an example of Octal number equal to decimal 10.

Decimal (Base 10) Number System

Decimal number is the most commonly used number system. It is a base 10 number system, uses combinations of numerals 0 to 9 to represent any number. It is widely used in everyday life for representing and manipulating numbers in many cultures and scientific applications.

Hexadecimal (Base 16) Number System

Hexadecimal Number System is a base 16 number system, uses combinations of numerals 0 to 9 and alphabetic characters A to F to represent any number. Hexadecimal numbers are represented with 16 at their base, for example 1AF₁₆.

Decimal, Octal, Hexadecimal, Binary Conversion Chart Table