What you should know:
In the previous lesson we showed that hexadecimal format is used whenever there is the need to represent a binary number. This is because the conversion between the two formats is very easy and, with the right training, can be performed on the fly without the need to use a calculator or a sheet of paper.
To convert an exadecimal number to binary, we just have to convert one symbol at a time, using the reference table provided in the previous lesson.
| Binary | Exadecimal |
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | A |
| 1011 | B |
| 1100 | C |
| 1101 | D |
| 1110 | E |
| 1111 | F |
For instance, if we have to convert the hexadecimal number:
AB4FThe calculation will be carried out as shown in the following table.
| A | B | 4 | F |
| 1010 | 1011 | 0100 | 1111 |
The result is obviously
1010101101001111The conversion from binary to hexadecimal works more or less in the same way. We just have to group the bits, four at a time, starting from the right. If the last group has less than four bits, it can be padded with enough zeros on the left.
Let’s convert the binary number:
10101111010001The conversion will be carried out as in the following table. The leftmost part of the sequence: 10, is made of two bits and has been rewritten as 0010.
| 0010 | 1011 | 1101 | 0001 |
| 2 | B | D | 1 |
The result is:
2BD1