Binary is such an obvious system. If you do decide to use it, note that you should only go up to 2^4, reserving one bit (thumb or pinkie) for sign.

Try using base 3 instead of base 2, it's slightly more obscure, and you can use no finger for 0, just a nub for 1, curled for 2, extended for 3.

It will be more subtle and more obscure.