The technique to represent and work with numbers is called number system.
Types of Number system:
There are different types of number system such as binary number system, octal number system, hexadecimal number system, decimal number system.etc.Decimal number system is the most common number system.
Base of Number system:
| Number system | Base of Number System |
|---|---|
| Decimal | Base10 |
| Hexadecimal | Base16 |
| Binary | Base 2 |
| Octal | Base 8 |
Decimal number system is a base 10 number system having 10 digits from 0 to 9.
We generally use the decimal place-value number system. In this system, we have
235 = (2 * 100) + (3 * 10) + (5 * 1) = (2 * 10^2) + (3 * 10^1) + (5 * 10^0)
The weightage of each position can be represented as follows −
Binary Number system:
Binary describes a numbering scheme in which there are only two possible values for each digit: 0 and 1.the 0 and 1 values are sometimes called "low" and "high," respectively
Where each digit has a value expressed in powers of 2, as displayed here.
110102 = 1×24 + 1×23 + 0×22 + 1×21 + 0×20
= 16 + 8 + 0 + 2 + 0
= 2610
Atleast Remember this 2^n, this help ful to you to convert binary to any another format.this also help you for convert IP address.
| Number 2^n : 20 | Calculations 1 |
|---|---|
| 21 | 2 |
| 22 | 4 |
| 23 | 8 |
| 24 | 16 |
| 25 | 32 |
| 26 | 64 |
| 27 | 128 |
| 28 | 256 |
| 29 | 512 |
| 210 | 1024 |
| 211 | 2048 |
| 212 | 4096 |
| 213 | 8192 |
| 214 | 16,384 |
| 215 | 32,768 |
| 216 | 65,536 |
Octal Number System
Octal number system has eight digits – 0, 1, 2, 3, 4, 5, 6 and 7. Octal number system is also a positional value system with where each digit has its value expressed in powers of 8, as shown here −
Hexadecimal Number System
Octal number system has 16 symbols – 0 to 9 and A to F where A is equal to 10, B is equal to 11 and so on till F. Hexadecimal number system is also a positional value system with where each digit has its value expressed in powers of 16, as shown here −
Number System Relationship
The following table depicts the relationship between decimal, binary, octal and hexadecimal number systems.
| HEXADECIMAL | DECIMAL | OCTAL | BINARY |
|---|---|---|---|
| 0 | 0 | 0 | 0000 |
| 1 | 1 | 1 | 0001 |
| 2 | 2 | 2 | 0010 |
| 3 | 3 | 3 | 0011 |
| 4 | 4 | 4 | 0100 |
| 5 | 5 | 5 | 0101 |
| 6 | 6 | 6 | 0110 |
| 7 | 7 | 7 | 0111 |
| 8 | 8 | 10 | 1000 |
| 9 | 9 | 11 | 1001 |
| A | 10 | 12 | 1010 |
| B | 11 | 13 | 1011 |
| C | 12 | 14 | 1100 |
| D | 13 | 15 | 1101 |
| E | 14 | 16 | 1110 |
| F | 15 | 17 | 1111 |
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