Does anybody have an interesting use case for this? Just curious whether it's actually used.
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.
"No, I wasn't flipping you off with both hands, I was trying to tell you the number 132 in binary."
For example the natural response might be, "Well, I personally can count to ten" and, after you pressed about alternative schemes: "On a more theoretical level you could of course enumerate way more states than ten using your fingers. Just think of American sign language, which has 26 letters only one of which includes motion (the Z).[1] And that's on a single hand, so just counting the letters in ASL only - and no other gestures, you can count to at least 676. Add a few more static hand shapes - there are lots of shapes in ASL- maybe try to learn a hundred per hand, which is good because you can encode two digits in each hand, I could confidently count to 10,000 using just my fingers. It would probably take no more than a few days to learn."
Would I pass your interview? Probably not, because it wasn't what you were thinking of. Even though I just showed you that I could count to ten times higher than the number you were thinking of.
And I wouldn't even mention what I was REALLY thinking which is "Hmmmm, I wonder where the limit is. A human hand has about 26 degrees of freedom, so two hands have about 52, if we encode a degree using just 2 bits - one of four levels of flexion - we're at 52 * 2 = 104 bits. So something like 10^31 = what is that 'ten nonillion'. I probably shouldn't say nonillion. No, I definitely shouldn't say nonillion. Probably even a million is pushing it, I shouldn't say that. But I bet it's possible - a million is just twenty bits, that's just 10 bits per hand, or two bits per finger and it's obvious that a finger has way more than 4 positions it can take - looking at my own hand my first knuckles are independent of the crook of the finger, it doesn't take much effort at all to control them independently.... I bet I can count to a million."
[1] http://www.lifeprint.com/asl101/pages-layout/handshapes.htm
It can also be nifty for ASCII conversions, as letters A-Z and a-z are the numbers 0-26, but with different prefixes (010 and 011 accordingly). This means you can read people's binary tattoos.