Converting hexadecimal (base-16) numbers to denary (base-10) 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 hexadecimal number to denary…
| B | 0 |
Step 1: Split the Bits
Split the two hexadecimal numbers into single digits.
| B | 0 |
| B | 0 |
Step 2: Convert Digits to Denary
Convert each digit to denary.
For numbers 0 – 9, it will be the same. For numbers A – F, use 10 – 15.
| B | = | 11 |
B in hex is equivalent to 11 in denary.
| 0 | = | 0 |
0 less than 10, so it is the same in hexadecimal and denary.
Step 3: Convert to Binary Nibbles
Convert each denary digit into a nibble (a four-bit binary number).
11 =
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 1 | 0 | 1 | 1 |
0 =
| 8 | 4 | 2 | 1 |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
Step 4: Join into a Byte
Put our two binary nibbles together to create one byte.
Remember to re-number the binary columns for the first nibble.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
Step 5: Convert Binary to Denary
Finally, convert the whole binary byte into a decimal number.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
128 + 32 + 16 = 176
The answer
We have now converted B016 to 17610.