How to convert hex to binary by hand
Example 1: F0 in hex is 11110000 in binary
Hex to binary: write each digit as 4 bits
Because 16 = 2⁴, every hex digit maps to exactly 4 binary digits. Drop any leading zeros at the end.
| Hex digit | Value | 4 bits |
|---|---|---|
| F | 15 | 1111 |
| 0 | 0 | 0000 |
1111 0000 → 11110000
Example 2: 3A7 in hex is 1110100111 in binary
Hex to binary: write each digit as 4 bits
Because 16 = 2⁴, every hex digit maps to exactly 4 binary digits. Drop any leading zeros at the end.
| Hex digit | Value | 4 bits |
|---|---|---|
| 3 | 3 | 0011 |
| A | 10 | 1010 |
| 7 | 7 | 0111 |
0011 1010 0111 → 1110100111
Hex to Binary conversion table
| Hex | Binary | Decimal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 3 | 11 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| A | 1010 | 10 |
| B | 1011 | 11 |
| C | 1100 | 12 |
| D | 1101 | 13 |
| E | 1110 | 14 |
| F | 1111 | 15 |
| 10 | 10000 | 16 |
| 20 | 100000 | 32 |
| 40 | 1000000 | 64 |
| 64 | 1100100 | 100 |
| 80 | 10000000 | 128 |
| FF | 11111111 | 255 |
| 100 | 100000000 | 256 |
| 200 | 1000000000 | 512 |
| 3E8 | 1111101000 | 1000 |
| 400 | 10000000000 | 1024 |
Where this conversion comes up
- Seeing exactly which bits a mask sets: 0xF0 is 11110000, the upper four bits of a byte.
- Decoding protocol flags and register values documented in hex.
- Checking bit patterns in embedded and hardware work.
Frequently asked questions
Why does every hex digit become exactly 4 bits?
16 is 2⁴, so the 16 hex digits 0 to F match the 16 possible 4-bit patterns 0000 to 1111 one to one.
Can I convert negative numbers?
Yes. Put a minus sign in front and it is kept in the result, for example -F0 becomes -11110000. The converter does not produce two's complement.
Is there a limit on how big the number can be?
No practical limit. The conversion uses arbitrary precision integers, so long values stay exact. The step-by-step working is shown for numbers up to 24 digits.
Can I convert fractions?
Not with this tool. It converts whole hex numbers to whole binary numbers.
Other number converters
Going the other way? Use the Binary to Hex Converter. To see a number in every base at once, try the all-in-one number converter.