Number Classification

The term “number system” refers to a method of representing numbers in a consistent manner. The number system is a mathematical notation for describing the number classification of a particular set by utilizing a set of digits or symbols in a logical manner. The Number System is a useful tool for learning the fundamentals of mathematics.

A number’s digit value can be calculated using

• It’s the actual number.
• Its occurrence in the sequence.
• This is where all numbers begin.

Number classification

Numerals can be broken down into the following categories:

• Natural numbers

Natural numbers are those numbers that can be used to count things. The letter N is used to designate a natural number.

Example: N = 1,2,3,…..

• Whole numbers

The set of numbers that includes zero as well as the natural numbers are referred to as “whole numbers.” W is the abbreviation for the total number of digits.

Example : W = 0,1,2,3….

• Integers

Integers include not just zero and negative numbers, but also all the other natural numbers. I and Z are used to represent integers.

Example : I = ……,-2,-1,0,1,2……..

• Rational numbers

P/q is a way to express rational numbers, where q is an integer greater than zero and p is an integer less than zero. A Q identifies them.

Example : Q = 6/7 , 5/9

• Irrational number

The numbers cannot be expressed in the form of p/q where ‘p’ & ‘q’ are integers and q≠0.

Example : π = 3.141592653589793238….

• Prime number

It is a natural number that can only be divided by itself and 1. It is always greater than zero.

Example: 2,3,5…

• Composite number

This includes all numbers that are not prime numbers (save 1), and they are known as composite numbers.

Example : 4,8,22

• Co -prime

Only one common factor (HCF) is required for a set of integers to be called Co-Prime Numbers.

Example: 4 and 7

• Even number

‘Even’ numbers are those that divide evenly by two.

Example: 2,4,6…..

• Odd number

Odd numbers are any numbers that are not divisible by two.

Example: 1,3,5…

• Real number

To be a real number, a continuous quantity must have at least one value that can represent the distance between two points on a line. An infinite number of possibilities. An actual number, fifty (50) exists. This is a very large real number, one billion (1,000,000,000). There are three types of real numbers, and we’ll discuss them in a moment. No matter what kind of number classification you’re dealing with: whole, rational or irrational.

• Imaginary number

Number classification made up in one’s head is not real. A real number is multiplied by an imaginary unit to create a complex number (i). For example, the imaginary number I is “1” and “25” is “5”. In spite of the fact that imaginary numbers are not “real numbers,” they have value. There are imaginary numbers used in electrical engineering when dealing with currents and voltage. In complex calculus computations, imaginary numbers are also used. Because they are referred to as “imaginary,” these numbers aren’t necessarily useless.

Number system 

There are several number systems in which numbers are classified :

• Binary number system (Base – 2)
• Octal number system (Base – 8)
• Decimal number system (Base – 10)
• Hexadecimal number system (Base – 16)

Binary Number System

Only 0 and 1 digits are used in the binary number system. This system uses a two-digit number basis. Bits are the digits 0 and 1, and a byte is the sum of all eight bits. Bits and bytes are the units of measurement used by computers to store their data. There are no other numbers in the binary number system, such as 2,3,4,5,7,8 and so on. The binary number system includes numbers like 100012, 1111012, and 10101012.

Octal Number System

The octal number system is made up of eight digits: 0,1,2,3,4,5,6,7, with a base number of 8. This system’s advantage is that it has fewer digits than some other systems, reducing the likelihood of computing errors. The octal number system does not include digits 8 and 9. Minicomputers employ the octal number system, which uses digits 0 to 7 instead of the binary system. The octal number system includes numbers such as 358, 238, and 1418.

Decimal Number System

Ten digits are used in the decimal number system: 0,1,2,3,4,5,6,7,8 and 9 with the base number being 10 Real-world numbers are typically expressed using the decimal number system. The base of any integer is 10 if it is represented without a base. Some instances of decimal numerals include 72310, 3210, and 425710.

Hexadecimal Number System

The base number for the hexadecimal number system is 16 digits/alphabets: 0, 1, 2, 3, 5, 6, 7, 8, 9 and A, B, C, D, E, F. The hexadecimal numerals A-F correspond to the decimal numbers 10-15 in this case. For computers, the binary system uses this method to reduce its large-scale strings. Hexadecimal numbers include those beginning with 7B316, 6F16, and 4B2A16.

Conclusion

When moving to the right, a place becomes smaller while a place becomes larger when moving to the left. The place value pattern continues in both directions. We are able to represent both infinitely large and infinitely small number classification with simple symbols. It’s all a part of mathematics’s lovely order. Understanding the digital system’s operations requires a firm grasp of number classification. Binary, octal, and hexadecimal numbers are all accepted as inputs by digital systems, which then process and output the results.