Converting denary (base-10) numbers to hexadecimal (base-16) is an essential skill, and a guaranteed exam question!
Denary numbers are 0 – 9.
Hexadecimal numbers are 0 – 15, with numbers after 9 represented by letters A – F.
The easiest method is to use binary as a middle step. Let's go through the process and convert this decimal number to hexadecimal…
| 132 |
Step 1: Convert Denary to Binary
Convert the denary number 132 into an 8-bit binary number.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
132 = 128 + 4
Step 2: Split into Nibbles
Split the 8-bit binary number into two 4-bit binary numbers.
Remember to re-number the binary columns for the first nibble.
| 8 | 4 | 2 | 1 | 8 | 4 | 2 | 1 | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
Step 4: Convert each Nibble to Denary
Convert each binary nibble into denary.
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
= 8
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 0 | 1 | 0 | 0 |
= 4
Step 5: Convert each Denary Digit to Hexadecimal
Convert each denary number to its hexadecimal equivalient.
Denary numbers 10–15 are equivalent to hexadecimal numbers A–F.
| 8 | = | 8 |
8 less than 10, so it is the same in hexadecimal and denary.
| 4 | = | 4 |
4 less than 10, so it is the same in hexadecimal and denary.
Step 6: Combine the Digits
Bring the two separate hexadecimal values together, and the conversion is complete!
| 8 | 4 |
| 8 | 4 |
The answer
We have now converted 13210 to 8416.