Converting Between Hexadecimal & Binary (Cambridge International IGCSE Computer Science)
Exam board Cambridge International · IGCSEUpdated 2025-05-06
Binary to Hexadecimal Conversion
Spec point — b(iii) Convert between positive hexadecimal and positive binary
How do you convert from binary to hexadecimal?
Exam Hint 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
Spec point — b(iii) Convert between positive hexadecimal and positive binary
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
Exam Hint 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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