Don't you mean on an even number? Or just a power of 2? Or are you talking about a base 10 number that's composed of all 1's and 0's? (All natural numbers are base 2 numbers...)
It's very interesting to watch in binary, actually.
You first check if the LSB is 1. If not, you right shift it until it is. Once the LSB is 1, you add it to itself shifted left by one bit, then increment.
Watching the bits go by and shrink over time reminds me of cellular automata in a way.
Also related: http://xkcd.com/710/