Any method of expressing a number is called a number system. The numbers are made up of different passers-by. For example, the number 123 is made up of three distinct digits: 1, 2, and 3. In the number system, various numbers are obtained by arranging certain numbers in a regular manner. These numbers are processed through various mathematical processes (such as addition, subtraction, multiplication, division, etc.). Every number is divided into integer and fraction by radix point (.). For example: 768. 653. Here are 768 complete. Point(.) radix point and o.653 fractions.
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To calculate the value of a number, three data points are needed, such as:
1. The digits used in the number are their own values
2. The base of the number system used
3. The position or local value of the digits used in the number
In mathematics, there are several kinds of number systems. These are the four most prevalent types of number systems:
- Decimal number system
- Binary number system
- Octal number system
- Hexadecimal number system
Decimal number system :
The most widely used numeral system in the world is the decimal number system, or base-10. Every digit in a decimal number represents a power of ten, and it is based on the number ten.
Ten digits make up the decimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. any number can be represented by these digits, whose placements correspond to the values of each place.
Consider the number 4567, for instance:
In the “ones” place, the number 7 stands for 7X100=7X1=7
In the “tens” place, the number 6 stands for 6X101=6X10=60
In the “hundreds “place, the number 5 stands for 5X102=5X100=500
In the “thousand “place, the number 4 stands for 4X103=4X1000=4000
When these values are added together (4000+500+60+7), we get the total value of 4567.
Numerous fields in daily life, such as mathematics, finance, science, and technology, rely heavily on the decimal system.
Binary number system :
The number system with two digits 0 and 1 is called binary number system. Binary is the simplest number system. Its base is 2. These symbols 0 and 1 are called numbers or digits in the language of mathematics. This method of writing numbers with only two symbols or digits. Therefore, these two numbers are called binary numbers or binary digits. The computer does all kinds of calculations or any work with the help of these binary numbers. The computer language made of binary numbers is called binary language. And the various mathematical processes of binary numbers are called binary mathematics or computer mathematics.
Usually, the number we use has ten units. From o to nine can be expressed by a unit (10). But whenever the number is more than 9 then one number has to be increased on the left side.
Where is enough in the decade from 10 to 99? But if it is more than that, the percentage of the century has to be used. In this way, if the limit from 0 to 9 is more than this in each cell, the space on the left has to be used.
| Decimal System | Binary System | Value |
| 0 | 0 | zero |
| 1 | 1 | One |
| 2 | 10 | Two |
| 3 | 11 | Three |
| 4 | 100 | Four |
| 5 | 101 | Five |
| 6 | 110 | Six |
| 7 | 111 | Seven |
| 8 | 1000 | Eight |
| 9 | 1001 | Nine |
| 10 | 1010 | Ten |
As a decimal system has 10 units, a binary system has two units. 0 and 1, respectively. Like in an ordinary number, if it is more than 9, then it has to be increased to the left; similarly, in a binary system, if it is more than 1, then it has to be increased to the left.
Octal number system
Since binary numbers are quite long, the octal number system was developed to represent them in simpler and smaller form. This number system is used because of the binary number process inside and outside the computer. The base of the octal number system is eight. The octal number system has eight digits. These are 0, 1, 2, 3, 4, 5, 6, and 7. The largest number here is 7. And to form a number larger than this, two or more numbers have to be arranged. The table below shows the decimal numbers as well as their binary equivalents:
| Decimal System | Octal | Value |
| 0 | 0 | zero |
| 1 | 1 | One |
| 2 | 2 | Two |
| 3 | 3 | Three |
| 4 | 4 | Four |
| 5 | 5 | Five |
| 6 | 6 | Six |
| 7 | 7 | Seven |
| 8 | 10 | Eight |
| 9 | 11 | Nine |
| 10 | 12 | Ten |
| 11 | 13 | Eleven |
Hexadecimal number system
Another number system used in computers is called hexadecimal system. This number system is also used because of the computer’s internal binary number process. Hexadecimal is a 16-based number system. In this method, there are 16 symbols, signs, or numbers which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B,C,D,E and F. The table below shows the decimal numbers as well as their hexadecimal equivalents:
| Decimal System | Hexadecimal | Value |
| 0 | 0 | zero |
| 1 | 1 | One |
| 2 | 2 | Two |
| 3 | 3 | Three |
| 4 | 4 | Four |
| 5 | 5 | Five |
| 6 | 6 | Six |
| 7 | 7 | Seven |
| 8 | 8 | Eight |
| 9 | 9 | Nine |
| 10 | A | Ten |
| 11 | B | Eleven |
| 12 | C | Twelve |
| 13 | D | Thirteen |
| 14 | E | Fourteen |
| 15 | F | Fifteen |
| 16 | 10 | Sixteen |
| 17 | 11 | Seventeen |
| 18 | 12 | Eighteen |
| 19 | 13 | Nineteen |
| 20 | 14 | Twenty |
In view of the above discussion, it can be easily said that we actually we have got the origin of the computer based on the number system. If you review the history of the computer, it can be easily understood.
