Converting Between Binary & Hexadecimal (OCR GCSE Computer Science)
Revision Note
Written by: Robert Hampton
Reviewed by: James Woodhouse
Binary to Hexadecimal Conversion
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.
How do you convert from binary to hexadecimal?
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
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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