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are symbols that represent numbers such as “4, 5, 6.” It is impossible to count anything without numbers; date, time, money, and so on; these numbers are also employed for measurement and labelling. Numbers are useful for conducting arithmetic operations because of their qualities. These numbers can be written in both numeric & word form.
Number System
A number system is a representation system for numbers. It’s also known as the numeration system, and it specifies a set of values to describe a quantity. These numbers are often used as digits, and the most popular ones are 0 & 1, which are binary numbers. Other forms of number systems are represented by digits ranging from 0 to 9.
A number system can be defined as the consistent representation of numbers using the digits or other symbols. A digit, position of the digit in the number, and base of the number system can all be used to determine the value of any digit in a number. The numbers are defined in a distinct way, allowing us to perform arithmetic operations such as subtraction, addition, and division.
Types of Number System
Binary Number System (Base 2)
In Binary, “bi” signifies “two.” As a result, the line is reduced to a depiction of a number using only the numbers 0 & 1. It is simple to convert decimal numbers to a binary number system. The notations of decimal and binary numerals are different. A base of 10 is used to represent a decimal number, while a base of 2 is used to represent a binary number.
Decimal Number | Binary Number |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
Octal Number System
The Octal Number System is a number system with an eight-digit base with digits ranging from 0 to 7. Numbers having eight-digit base are referred to as octal. Octal numbers have a wide range of uses and significance, including in the computers & the digital numbering systems. Octal number is converted to binary numbers as well as the binary numbers to octal numbers in the number system by 1st converting the binary number to a decimal number and then translating a decimal number to an octal number.
For example:
347=3×82+4×81+7×80
Decimal Number System (Base 10)
A Decimal number system is a number system having a base value of ten. It generates numbers using ten digits (from 0 to 9). Each digit in number has its own place value, which is a product of distinct powers of ten. From right to left, the place value is referred to as units, then tens, hundreds, thousands, and so on. Units have a place value of 100, tens have a place value of 101, hundreds have a place value of 102, thousands have a place value of 103, and so on.
For Example
10264
1×104+0×103+2×102+6×101+4×100
1000+0+200+60+4
10264
Hexadecimal Number System (Base 16)
Hexadecimal Number System is a number system having a base value of 16. The Hexadecimal Number System produces numbers of 16 digits. The numerals 0-9 are represented as they are in the decimal number system, but the digits 10 through 15 are represented as given below in the table. Memory address locations can be handled using hexadecimal numbers.
For example:
25510 is written as (FF)16
Decimal number | Hexadecimal Number |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
8 | 8 |
9 | 9 |
10 | A |
11 | B |
12 | C |
13 | D |
14 | E |
15 | F |
Conclusion
Number systems are mathematical systems which are used to represent numbers in various formats and that computers can understand. A number is a numerical value which can be used to count, measure, and do arithmetic calculations. Natural numbers, rational irrational numbers, and so on are all types of numbers. Similarly, other types of number systems, such as decimal number system, octal number system, binary number system, & hexadecimal number system, have different qualities.
