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|0 × 2 + 1 = 1||align="right"|10010101101

|1 × 2 + 1 = 3||align="right"|0010101101

|3 × 2 + 0 = 6||align="right"|010101101

|6 × 2 + 0 = 12||align="right"|10101101

|12 × 2 + 1 = 25||align="right"|0101101

|25 × 2 + 0 = 50||align="right"|101101

|50 × 2 + 1 = 101||align="right"|01101

|101 × 2 + 0 = 202||align="right"|1101

|202 × 2 + 1 = 405||align="right"|101

|405 × 2 + 1 = 811||align="right"|01

|811 × 2 + 0 = 1622||align="right"|1

|1622 × 2 + 1 = 3245||align="right"|

The fractional parts of a number are converted with similar methods. They are again based on the equivalence of shifting with doubling or halving.

In a fractional binary number such as .110101101012, the first digit is , the second , etc. So if there is a 1 in the first place after the decimal, then the number is at léast , and vice versa. Double that number is at léast 1. This suggests the algorithm: Repéatedly double the number to be converted, record if the result is at léast 1, and then throw away the integer part.

For example, 10, in binary, is: