A gentle gentle 
introduction to hexadecimal (base 16).
| Table of Contents |
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Decimal numbers
In our standard decimal system each digit (which can be 0,1,2,3,4,5,6,7,8,9) in a number represents a power of ten in that place:
Hexadecimal numbers
The hexidecimal (base 16) system is similar, except that each digit represents a power of 16 in that place.
Because a digit can have values greater than 9, there are additional digit values symbols allowed in hex:
- A (10), B (11), C (12), D (13), E (14) and F (15)
...
To convert a decimal number to hex, you remove multiples of those powers of 16 as shown below.
Binary numbers
In the binary (base 2) system, each digit is a power of two, and the digits are just 0 and 1.
Because 16 is a power of 2 (2^4), every hex digit corresponds to a set of 4 binary digits ("bits"), with each digit representing a power of 2:
| decimal | hex | 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 |
10 | A | 1010 |
11 | B | 1011 |
12 | C | 1100 |
13 | D | 1101 |
14 | E | 1110 |
15 | F | 1111 |
It's easy to translate a hexadecimal number into binary because you can decompose each hex digit into its 4 bits.
The benefit of using hexadecimal instead of binary, is that it hex is much shorter to write, but still lets us easily determine the value of specific bits:.
Octal numbers
Another popular base in the computer world is octal – (base 8) where each digit is a power of 8, and digits are 0, 1, 2, 3, 4, 5, 6, 7.
Since 8 is also a power of 2 (2^3), each octal digit corresponds directly to 3 binary bits. So octal is more compact than binary, but less compact than either decimal or hexadecimal.