Sunday, February 5, 2023

# What is the Purpose of a Number System?

In mathematics, a number system is defined as the way of writing technique for expressing numbers. This is also called the system of numeration, and it is a mathematical notation for denoting the given set of numbers using a specific set of digits or symbols or characters in a constant manner. Moreover, we can use the same set of characters to represent various numbers in different types of number systems. Here, the types of number systems include binary, decimal, octal and hexadecimal number systems, etc. Generally, we use a number system to count things, items, etc. Let’s briefly understand the purpose and importance of the number system in various fields.

Let us consider the four most commonly used numbering systems, binary, octal, decimal and hexadecimal. The importance of these number systems can be explained as given below.

##### Significance of Binary Number System

Binary numbers are generally used when only two options are available, so if one is false, the other is true. The binary number system is widely used to illustrate everyday situations as well. This number system represents bits in computers that can have only two values, 0 and 1. Also, in electric circuits, a switch can be represented using (1) to on and (0) to off. Besides, for electronic gates in electrical circuits, we can display the false or true statements in binary digits such that 0 means false and 1 means true. It is also possible to convert one number to another, for example, binary to decimal, decimal to binary, and so on.

##### Significance of Octal Number System

The octal number is a rarely used number system and is primarily used in graphics and text computing. The base of this number system is 8. Well-known operating systems, even UNIX, use an octal number system for their file protection system. This number system includes eight unique representations, which we can combine to create more octal number expressions. Octal numbers are complex for an ordinary person who has a limited understanding of the number system. In this type of number system, we use seven digits to represent the first seven numbers; then, it is challenging to comprehend. Here, we can also perform the conversion such as binary to octal, octal to binary, octal to decimal, etc.

##### Significance of Decimal Number System

The decimal number system is the most commonly used system to write the sequence of numbers. Interestingly, the decimal number system is that we represent integers, natural numbers, etc. For example, the digits of the decimal number system are 1, 2, 3, 4, 5, 6, etc., which also represent counting numbers or natural numbers. This system of numbers is also known as the denary number system. The decimal number system is the most frequently used one in our day-to-day activities; this includes calculation, calendar systems, accounts and financial systems or simple routine counting. This system is more comfortable to use when compared with other types of number systems. However, the conversion of this number system to others is relatively easy. For example—decimal to octal, decimal to hex conversion and so on

##### Significance of Hexadecimal Number System

Software developers and system designers use hexadecimal numbers to a great extent to deliver a human-friendly declaration of binary-coded values. The hexadecimal number system is used when more possibilities need to be defined. Also, it is the most commonly used number system in computing to describe various memory locations. This is also known as the positional number system.

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