1011 0110₂ → decimal — number base conversion
intropositional expansion
Answer
182
Why this example is worth doing
The reverse direction, and the one where the working matters most: each 1 contributes its place value, and the sum of the contributing powers is the answer. The tool lays out all eight positions with their weights, including the zeros, because a student who only writes the contributing terms loses track of which column they are in. This byte reappears throughout the site as the running example for masking, complementing and hex conversion.
Try your own input in the Binary ⇄ decimal ⇄ hex ⇄ octal. Convert between any two bases, integers and fractions, with the positional working.
How the answer is reached
Base 2 to base 10
Convert 10110110 from base 2 to base 10. The sign is carried across unchanged; only the magnitude is converted.
| digit | value | weight | weight (base 10) | digit x weight |
|---|---|---|---|---|
| 1 | 1 | 2^7 | 128 | 128 |
| 0 | 0 | 2^6 | 64 | 0 |
| 1 | 1 | 2^5 | 32 | 32 |
| 1 | 1 | 2^4 | 16 | 16 |
| 0 | 0 | 2^3 | 8 | 0 |
| 1 | 1 | 2^2 | 4 | 4 |
| 1 | 1 | 2^1 | 2 | 2 |
| 0 | 0 | 2^0 | 1 | 0 |
| total | 182 |
Integer part: divide by 10 and read the remainders bottom to top.
| n | divide by | quotient | remainder |
|---|---|---|---|
| 182 | 182 ÷ 10 | 18 | 2 |
| 18 | 18 ÷ 10 | 1 | 8 |
| 1 | 1 ÷ 10 | 0 | 1 |
10110110 (base 2)182 (base 10)