Convert binary to octal
1011 in binary
13
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 8, keeping the remainders
- 11 ÷ 8 = 1 remainder 3 1 ÷ 8 = 0 remainder 1
- Read the remainders upwards
- The last remainder is the leading digit.
Why the working is here
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.