Convert hexadecimal to binary
FF in hexadecimal
11111111
How it gets there
- Each digit carries its place
- 15 × 16¹ + 15 × 16⁰
- Which is
- 240 + 15 = 255
- Divide by 2, keeping the remainders
- 255 ÷ 2 = 127 remainder 1 127 ÷ 2 = 63 remainder 1 63 ÷ 2 = 31 remainder 1 31 ÷ 2 = 15 remainder 1 15 ÷ 2 = 7 remainder 1 7 ÷ 2 = 3 remainder 1 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 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.