Convert binary to decimal
1011 in binary is 11 in decimal. 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
11
How it gets there
- Each digit carries its place
- 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰
- Which is
- 8 + 0 + 2 + 1 = 11
binary to decimal, at a glance
The conversion every other one is defined against. Each binary place is a power of two, so the value is a sum: 1011 is 8 + 0 + 2 + 1. Going back is repeated division by two, reading the remainders upwards.
| binary | decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
| 10000 | 16 |
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.