Convert binary to hexadecimal
1011 in binary is B in hexadecimal. Each digit is multiplied by its place value — the base raised to the digit's position, counting from zero on the right — and the products are added. The page prints every one of those products rather than only the total. The conversion is exact: bases are positional notation for the same number, so nothing is rounded and the result can be checked digit by digit.
Conversion rules checked · How we check
1011 in binary
B
How it gets there
- Each digit carries its place
- 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰
- Which is
- 8 + 0 + 2 + 1 = 11
- Divide by 16, keeping the remainders
- 11 ÷ 16 = 0 remainder B
- Read the remainders upwards
- The last remainder is the leading digit.
binary to hexadecimal, at a glance
One hexadecimal digit is exactly four binary digits, which is the entire reason hexadecimal exists. Split the binary into groups of four from the right, translate each group on its own, and the conversion needs no arithmetic — a byte is always two hex digits.
| binary | hexadecimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | A |
| 1011 | B |
| 1100 | C |
| 1101 | D |
| 1110 | E |
| 1111 | F |
| 10000 | 10 |
Why is the working shown?
Every other converter of this kind prints the answer and stops. A base is a positional system, so the answer is a sum you can check: each digit is multiplied by the base raised to its position, and the results are added. Going the other way is repeated division, reading the remainders upwards. Neither is a black box, and this page refuses to be one.