Convert hexadecimal to octal
FF in hexadecimal
377
How it gets there
- Each digit carries its place
- 15 × 16¹ + 15 × 16⁰
- Which is
- 240 + 15 = 255
- Divide by 8, keeping the remainders
- 255 ÷ 8 = 31 remainder 7 31 ÷ 8 = 3 remainder 7 3 ÷ 8 = 0 remainder 3
- 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.