Tutorial
How to Convert Hex to Binary by Hand
The one conversion with no arithmetic at all. Learn sixteen patterns and you are done.
The converters on this site will always be faster. The point of working through it manually is that afterwards you can read a hex value without a tool at all — which is what you need when you are looking at a stack trace or a datasheet rather than a browser tab.
The method
- Take each hex digit in turn, left to right.
- Write its four-bit pattern, including leading zeros.
- Join the groups in the same order. Nothing is reversed and nothing carries.
That is genuinely all of it. There is no multiplication, no division and no borrowing, because sixteen is 24 and each digit maps onto its own four bit positions independently.
The sixteen patterns
This is the only thing to memorise. Everything else is substitution.
| Hex | Decimal | Binary | Octal |
|---|---|---|---|
| 0 | 0 | 0000 | 0 |
| 1 | 1 | 0001 | 1 |
| 2 | 2 | 0010 | 2 |
| 3 | 3 | 0011 | 3 |
| 4 | 4 | 0100 | 4 |
| 5 | 5 | 0101 | 5 |
| 6 | 6 | 0110 | 6 |
| 7 | 7 | 0111 | 7 |
| 8 | 8 | 1000 | 10 |
| 9 | 9 | 1001 | 11 |
| A | 10 | 1010 | 12 |
| B | 11 | 1011 | 13 |
| C | 12 | 1100 | 14 |
| D | 13 | 1101 | 15 |
| E | 14 | 1110 | 16 |
| F | 15 | 1111 | 17 |
Each pattern is just the number in binary, padded to four places. If you know that 8 is 1000 and 4 is 0100 and 2 is 0010 and 1 is 0001, you can build any of the sixteen by adding: B is 11, which is 8 + 2 + 1, so 1000 + 0010 + 0001 = 1011.
Worked example: C0DE
C → 1100 0 → 0000 D → 1101 E → 1110 join → 1100 0000 1101 1110
Worked example: 3F
3 → 0011 F → 1111 join → 0011 1111 (63 in decimal)
Leading zeros: the one real trap
Every digit contributes four bits. Drop a leading zero inside the number and everything to its right shifts, giving a completely different value.
correct C0DE → 1100 0000 1101 1110 16 bits wrong C0DE → 1100 0 1101 1110 13 bits, wrong number
The only zeros you may drop are at the very front of the whole result, where they change nothing — the same way 007 equals 7 in decimal.
Going back: binary to hex
- Group the bits into fours, starting from the right.
- Pad the leftmost group with zeros on the left if it is short.
- Convert each group to its hex digit.
110111 (6 bits) group from the right: 11 | 0111 pad the left: 0011 | 0111 convert: 3 7 result → 37 (55 in decimal)
Group from the right, always. The rightmost bit is the ones place and the grouping has to stay anchored to it.
Practice problems
Convert these to binary, then convert your answers back to check.
- A9
- FF
- 10
- 7E
- BEEF
- 0F0F
1. A9 → 1010 1001 2. FF → 1111 1111 3. 10 → 0001 0000 4. 7E → 0111 1110 5. BEEF → 1011 1110 1110 1111 6. 0F0F → 0000 1111 0000 1111
Reading bits back without converting
Once the patterns are fluent, you can answer bit questions straight from the hex. These come up constantly.
| Question | Look at | Because |
|---|---|---|
| Is the top bit set? | The first digit | 8 or above means the high bit is 1 |
| Is the value even? | The last digit | Even digit means bit 0 is 0 |
| Is the low nibble empty? | The last digit | A 0 there means all four low bits are clear |
| Is it a power of two? | The digit pattern | One digit of 1, 2, 4 or 8, rest zeros |
Check your work
The hex to binary converter shows the expansion digit by digit, and the reference table lists every byte.
Frequently asked questions
How do I convert hex to binary by hand?
Replace each hex digit with its four-bit pattern and join them in order. No arithmetic is involved.
Why is hex to binary so much easier than hex to decimal?
Because 16 is 2 to the fourth power, so each hex digit maps onto exactly four bits with no interference between digits. Ten is not a power of two, so decimal has no such shortcut.
What is A9 in binary?
1010 1001. A is 1010 and 9 is 1001.
Do I have to keep the leading zeros?
Inside the number, yes. Every digit must contribute four bits. Only zeros at the very front of the whole result can be dropped.
How do I convert binary back to hex?
Group the bits into fours from the right, pad the leftmost group with zeros if short, then convert each group to a hex digit.
How can I tell if a hex value is even?
Look at the last digit. If it is even, the lowest bit is 0 and so is the number.