Counting in binary
Instead of counting up to five on each hand, a binary system can be used to count up to 31 on one hand, and up to 1023 on two hands. This is done by using your fingers to represent increasing numbers, multiplying by two each time.
Once the numbers 1, 2, 4, 8 and 16 are assigned to the fingers, as above, different numbers can be represented by raising or tucking in the fingers. A raised finger represents its number being “on”, whereas a lowered finger represents its number being “off”.
For example, raising the thumb (1), the index finger (2) and the ring finger (8) shows a total of 1 + 2 + 8 = 11.
For higher numbers, exactly the same principle is used, by continuing to double the numbers used on the first hand: 32, 64, 128, 256, 512.
Alternatively, by placing your hand above a surface like a table, pressing the fingertip to the surface can be counted as “on”, which is useful both for the less dexterous and for avoiding having the number 4 misinterpreted by somebody else.