Hexadecimal to Binary Converter
Enter the hexadecimal number you want to convert to binary.
Table of Contents
- How does hexadecimal to binary conversion work?
- Hexadecimal to binary conversion formula
- Conversion process
- Examples
- Hexadecimal to binary conversion table
- Frequently Asked Questions
How does hexadecimal to binary conversion work?
The hexadecimal system is base 16 and the binary system is base 2. To convert a hexadecimal number to binary, replace each hexadecimal digit with its 4-bit binary equivalent. This method is straightforward because each base-16 digit corresponds exactly to a group of 4 binary digits.
Hexadecimal to binary conversion formula
For a hexadecimal number with n digits:
hnhn-1...h1h0 → (bn3bn2bn1bn0) (b(n-1)3b(n-1)2b(n-1)1b(n-1)0) ... (b13b12b11b10) (b03b02b01b00)
Each hexadecimal digit hi is converted into a 4-bit binary group, equivalent to its base-16 value (0–9 or A–F). The final binary number is obtained by concatenating all the binary groups in the same order.
Conversion process
- Write down the hexadecimal number.
- Replace each digit with its 4-bit binary equivalent (use 0–9 and A–F → 0000–1111).
- Join all the 4-bit groups together to form the complete binary number.
Examples
A₁₆ to binary| Hexadecimal digit | Binary equivalent (4 bits) |
|---|---|
| A | 1010 |
Result: A₁₆ = 1010₂.
Result: A₁₆ = 1010₂.
2F₁₆ to binary| Hexadecimal digit | Binary equivalent (4 bits) |
|---|---|
| 2 | 0010 |
| F | 1111 |
Reading the groups together: 2F₁₆ = 0010 1111₂.
Result: 2F₁₆ = 0010 1111₂.
Hexadecimal to binary conversion table
Quick reference values for short hexadecimal numbers.
| Hexadecimal | Binary |
|---|---|
0 | 0000 |
1 | 0001 |
2 | 0010 |
3 | 0011 |
4 | 0100 |
5 | 0101 |
6 | 0110 |
7 | 0111 |
8 | 1000 |
9 | 1001 |
A | 1010 |
B | 1011 |
C | 1100 |
D | 1101 |
E | 1110 |
F | 1111 |
10 | 10000 |
FF | 11111111 |
100 | 100000000 |
Frequently Asked Questions
How do you convert a hexadecimal number to binary?
To convert a hexadecimal number to binary, replace each hexadecimal digit with its 4-bit binary equivalent. For example, A₁₆ = 1010₂ and F₁₆ = 1111₂.
Why is converting from hexadecimal to binary so easy?
Because each hexadecimal digit corresponds exactly to 4 binary bits, allowing for a direct conversion without extra calculations.
Cite this page
You can use the following citation format when referencing this calculator in academic or professional work.
Ramos, J., Hexadecimal to binary converter, Available at: https://calcuclub.com/convert/hex-to-binary/ (Accessed: 2 December 2025).