156₁₀ → binary — number base conversion
introrepeated division by 2
Answer
10011100
Why this example is worth doing
The standard decimal-to-binary conversion, done by repeated division: divide by two, record the remainder, repeat, then read the remainders bottom to top. That last instruction is where most errors happen, and the tool prints the division column with an explicit arrow rather than leaving the order implicit. The page also shows the subtract-powers-of-two method beside it, since some courses teach only that one and a student needs to recognise their own method in the working.
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 10 to base 2
Convert 156 from base 10 to base 2. The sign is carried across unchanged; only the magnitude is converted.
| digit | value | weight | weight (base 10) | digit x weight |
|---|---|---|---|---|
| 1 | 1 | 10^2 | 100 | 100 |
| 5 | 5 | 10^1 | 10 | 50 |
| 6 | 6 | 10^0 | 1 | 6 |
| total | 156 |
Integer part: divide by 2 and read the remainders bottom to top.
| n | divide by | quotient | remainder |
|---|---|---|---|
| 156 | 156 ÷ 2 | 78 | 0 |
| 78 | 78 ÷ 2 | 39 | 0 |
| 39 | 39 ÷ 2 | 19 | 1 |
| 19 | 19 ÷ 2 | 9 | 1 |
| 9 | 9 ÷ 2 | 4 | 1 |
| 4 | 4 ÷ 2 | 2 | 0 |
| 2 | 2 ÷ 2 | 1 | 0 |
| 1 | 1 ÷ 2 | 0 | 1 |
156 (base 10)10011100 (base 2)