How do you convert a fraction to binary?

Question

1/10(decimal) = 0.0001100110011... (binary)

How do I do that? Am I supposed to convert to binary and then divide? Could someone show me?

Answer 1

In university I learned it this way:

1. Multiply by two
2. take decimal as the digit
3. take the fraction as the starting point for the next step
4. repeat until you either get to 0 or a periodic number
5. read the number starting from the top - the first result is the first digit after the comma

Example:

0.1 * 2 = 0.2 -> 0
0.2 * 2 = 0.4 -> 0
0.4 * 2 = 0.8 -> 0
0.8 * 2 = 1.6 -> 1
0.6 * 2 = 1.2 -> 1
0.2 * 2 = 0.4 -> 0
0.4 * 2 = 0.8 -> 0
0.8 * 2 = 1.6 -> 1
0.6 * 2 = 1.2 -> 1
Result: 0.00011(0011) periodic.