Convert hexadecimal to octal
FF in hexadecimal is 377 in octal. 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
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.
hexadecimal to octal, at a glance
Neither maps onto the other in whole digits — four bits against three — so this one goes through binary in the middle. That is why it is the least used of the base conversions and the one worth showing the working for.
| hexadecimal | octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| A | 12 |
| B | 13 |
| C | 14 |
| D | 15 |
| E | 16 |
| F | 17 |
| 10 | 20 |
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.