Converting Between Hexadecimal & Binary (Cambridge (CIE) IGCSE Computer Science): Revision Note
Binary to Hexadecimal Conversion
How do you convert from binary to hexadecimal?
Examiner Tips and Tricks
Cambridge IGCSE 0478 expects all conversions to use 8-bit binary and 2-digit hex where possible. These examples follow the exam format exactly—so you’re revising the right way.
It is important before revising how to convert from binary to hexadecimal and vice versa that you fully understand the binary and hexadecimal number systems.
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
Example 1
To convert the binary number 10110111 to hexadecimal, first split the 8 bit number into 2 binary nibbles
8 | 4 | 2 | 1 |
| 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|---|
1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
For each nibble, convert the binary to it’s denary value
(1 x 8) + (1 x 2) + (1 x 1) = 11 (B)
(1 x 4) + (1 x 2) + (1 x 1) = 7
Join them together to make a 2 digit hexadecimal number
Binary 10110111 is B7 in hexadecimal
Example 2
To convert the binary number 00111001 to hexadecimal, first split the 8 bit number into 2 binary nibbles
8 | 4 | 2 | 1 |
| 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
For each nibble, convert the binary to it’s denary value
(1 x 2) + (1 x 1) = 3
(1 x 8) + (1 x 1) = 9
Join them together to make a 2 digit hexadecimal number
Binary 00111001 is 39 in hexadecimal
Hexadecimal to Binary Conversion
How do you convert from hexadecimal to binary?
Example 1
To convert the hexadecimal number 5F to binary, first split the digits apart and convert each to a binary nibble
8 | 4 | 2 | 1 |
|
|---|---|---|---|---|
0 | 1 | 0 | 1 | = 5 |
8 | 4 | 2 | 1 |
|
|---|---|---|---|---|
1 | 1 | 1 | 1 | = 15 (F) |
Join the 2 binary nibbles together to create an 8 bit binary number
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
Hexadecimal 5F is 01011111 in binary
Examiner Tips and Tricks
You might see methods that skip writing out the full 8-bit binary number—especially in textbooks. In this course, we stick to examiner-approved formatting, so your answers never fall short.
Example 2
To convert the hexadecimal number 26 to binary, first split the digits apart and convert each to a binary nibble
8 | 4 | 2 | 1 |
|
|---|---|---|---|---|
0 | 0 | 1 | 0 | = 2 |
8 | 4 | 2 | 1 |
|
|---|---|---|---|---|
0 | 1 | 1 | 0 | = 6 |
Join the 2 binary nibbles together to create an 8 bit binary number
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
Hexadecimal 26 is 00100110 in binary
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