I taught my wife to count this way. She is a teacher and 31 is about as big as a class gets at her school, so she can count her kids as they come in and still carry her books or her laptop etc. Its quite a simple pattern once you get then hang of it. She can just advance the count without thinking and then look at her hand and work out what she is up to.

I'd suggest inverting the numbers so that your thumb is 1, your index finger 2, you middle 4, etc. That way your more dexterous fingers do the fast movements of 1's, and 2s and 4s while your slower ring and pinky count up in 8 and 16s.

It really can be rather handy.

I find the most useful times is when you think of your hands as two five bit registers... when you need to count two things at once.