Perhaps counting on your fingers conjures up images of a little kid in preschool using his fingers to count to 10? But, why couldn't such a little kid count to 1023 with those same fingers?

Treat each digit (err, finger) as a bit. If the finger is sticking up, it's a one. Else, it's a zero. Unless your parents were cousins or you lost an argument with a tablesaw, you should have 10 bits with which to count.

The range of unsigned integer values that is representable with 10 bits is 0 to 1023.