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Hexadecimal number system
Hexadecimal is the other main number system used in computing. It works in tandem with the binary number system and provides an easier and more accessible means of working with long sequences of binary numbers.
Hexadecimal place value
Unlike denary which uses base ten and binary which uses base two, hexadecimal uses base 16 as its place value.
Each place in a hexadecimal number represents a power of 16 and each place can be one of 16 symbols.
Hexadecimal values
The table below shows the symbols comprising hexadecimal alongside their denary and binary equivalents:
| Hexadecimal | Decimal | Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1 | 1 | 0001 |
| 2 | 2 | 0010 |
| 3 | 3 | 0011 |
| 4 | 4 | 0100 |
| 5 | 5 | 0101 |
| 6 | 6 | 0110 |
| 7 | 7 | 0111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| A | 10 | 1010 |
| B | 11 | 1011 |
| C | 12 | 1100 |
| D | 13 | 1101 |
| E | 14 | 1110 |
| F | 15 | 1111 |
This table shows the raw value of each hexadecimal place value:
16^{3} |
16^{2} |
16^{1} |
16^{0} |
|---|---|---|---|
| 4096 | 256 | 16 | 1 |
Converting hexadecimal numbers
Using the previous table we can convert hexadecimal values to decimal.
For example we can convert 1A5 as follows, working from right to left:
(5 \cdot 1 = 5) + (A \cdot 16 = 160) + (1 \cdot 256 = 256) = 421
The process is quite easy: we get the n from 16^{n} based on the position of the digit and then multiply this by the value of the symbol (1,2,...F):
16^{n} \cdot 1,2,...F
As applied to 1A5:
16^{2} |
16^{1} |
16^{0} |
|---|---|---|
1\cdot 16^{2} = 256 |
A (10)\cdot 16^{1} = 160 |
5\cdot 16^{0} = 5 |
Another example for F00F:
(15 \cdot 4096 = 61440) + (0 \cdot 256 = 0) + (0 \cdot 16 = 0) + (15 \cdot 1 = 15) = 61455
// TODO: Relation to binary and bytes