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.