Mathematical Tutorial
How to Convert Hex to Binary.
Learn the standard digit expansion method to turn base-16 hexadecimal codes into base-2 binary strings.
Try it: Hex to Binary mini-calculator
Binary Result: 00101010
Digit expansion method.
Hexadecimal is a base-16 system, while binary is base-2. Since 24 = 16, each hexadecimal digit corresponds to exactly four bits (binary digits).
To convert hex to binary, simply write down each hex character separately and write its 4-digit binary code, padding with leading zeros where necessary.
Step-by-step example.
Convert the hex value 2A into binary:
- Separate the digits: 2 and A.
- Convert the digit 2 to 4-bit binary: 0010.
- Convert the digit A (which equals decimal 10) to 4-bit binary: 1010.
- Concatenate the groups: 0010 + 1010 = 00101010 (or 101010).
Hex mapping reference
| Hex | 4-Bit Binary |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 9 | 1001 |
| A | 1010 |
| F | 1111 |