Hexadecimal Notation
Hexadecimal number is a notation system for numbers.
In hexadecimal numbering system, we represent numbers using 16 symbols. Each digit is any 0 to 9 and A to F (sometimes lowercase).
Here's examples:
| decimal | Binary | hexadecimal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 3 | 11 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| 10 | 1010 | a |
| 11 | 1011 | b |
| 12 | 1100 | c |
| 13 | 1101 | d |
| 14 | 1110 | e |
| 15 | 1111 | f |
| 16 | 10000 | 10 |
| 17 | 10001 | 11 |
| 18 | 10010 | 12 |
| 19 | 10011 | 13 |
| 20 | 10100 | 14 |
| 21 | 10101 | 15 |
| 22 | 10110 | 16 |
| 23 | 10111 | 17 |
| 24 | 11000 | 18 |
| 25 | 11001 | 19 |
| 26 | 11010 | 1a |
| 27 | 11011 | 1b |
| 28 | 11100 | 1c |
| 29 | 11101 | 1d |
| 30 | 11110 | 1e |
| 31 | 11111 | 1f |
Hexadecimal is used often in computing, because each hexadecimal digit is equivalent to 4 Binary digits, so is compact and more readable.
- 1 hexadecimal digit has the same number of possible values as 4 bits.
- 2 hexadecimal digit has the same number of possible values as 8 bits.
- 3 hexadecimal digit has the same number of possible values as 12 bits.
- 4 hexadecimal digit has the same number of possible values as 16 bits.
So, 4 bits can be written as 1 hexadecimal. 8 bits can be written as 2 hexadecimal, etc.
Possible Size in Hexadecimal Number
If a hexadecimal number has n digits, it has 16^n possible values.
| number of digits | possible distinct values |
|---|---|
| 1 | 16 |
| 2 | 256 |
| 3 | 4096 |
| 4 | 65536 |