The process of representing or naming numbers is termed as a number systems. Number System is also known by the term Numeral System in many fields of knowledge. We are familiar with the decimal number system in which we have to represent the numbers between 0 to 9. There are also other number systems like binary number system, octal number system and hexagonal number system which we would deal with later. But here with the use of a base, the representation of the number system changes. So, let us understand what a base is.

Definition of a Base

A base or a radix within a number system can be defined as a combination of digits or different digits and letters which are used by the system of counting for representing numbers. The decimal number system is the most common number system found till date. The base of the number system is denoted by 10 since the word ‘dec’ means 10. Thus, we know that in the decimal number system, we can use a total of 10 numbers to represent the numbers.

Moreover, there are other number systems which use different bases for representing all the numbers within the system. A few of the number systems are mentioned below.

Different Types of Number Systems

Below is a list of a few commonly used number systems in the field of mathematics.

  • Decimal Number System – This number system has a base of 10. This means to represent any number, this numeral system uses 10 digits from 0 to 9.
  • Binary Number System – This number system has a base of 2. This means to represent any number, this numeral system uses 2 digits. The digits used are 0 and 1. For instance, the number 2 in the decimal number system is represented as 0010 in the binary number system.The binary number system is mainly used by computers. This is because the computer only recognizes the binary numbers 0 and 1. Whatever we type, read, copy, cut or store within a computer is processed in a sequence of numbers with 0 and 1. The Binary Number System helps with easy calculations. This allows individuals to get rid of unnecessary circuits and provides ample amount of space, time, energy and cost.
  • Hexadecimal Number System – This number system has a base of 16. This means to represent any number, this number system uses 16 digits which consist of both numbers and letters. The numbers range from 0 to 9 whereas the letters range from A to F. For instance, the number 10 in decimal is represented as ‘A’ in the Hexadecimal number system.

The Hexadecimal Number System is mainly used for simplifying the Binary Number System and is mainly used by programmers and coders. Hexadecimal Number System is used in various computer-related projects like Memory Allocation, Color Formats, MAC address, Internet Protocol and using flags in networking. The Color Formats are mainly denoted by hex and appears in the format like #RRGGBB.

  • Octal Number System – This number system has a base of 8. Thus to represent any number, this number system uses 8 digits. The digits used are between 0 to 8. For instance, the number 11 in the decimal number system is denoted by 013 in the octal number system.

The Octal Number System has been utilized lately and is similar to the Hexadecimal Number System which is used nowadays. It has been overlooked as an abbreviation of the Binary Number System since the bit size of the computers used was 26 and 36 bits. The bit size represents the number of bits that a computer can handle in one go. Nowadays, the hexadecimal number system has become popular with the advent of modern computers around the world.

For more information about numerical systems and place value, do visit Cuemath which is available online. You can book a free session.