You are undoubtedly already familiar with counting on your fingers in base ten, which is also called decimal. In this manner of counting, each finger simply represents a quantity of one. Every raised finger contributes to the total sum, which is at most ten.
Counting in base six is a little different. Only six numerals (0 through 5) are needed to represent a number in base six. Thus, we let each hand represent one digit of a base-six number. The right hand can be the unit's place (60), and the left hand can be the six's place (61). In this manner of counting, it is possible to count up to 556, which is 35 in base ten.
Counting in binary (or base two) is truly a skill to master. Representing a number in binary only requires two numerals (0 and 1). Therefore, we can let each finger represent one digit of a binary number. A raised finger represents a one (1), and a lowered finger represents a zero (0). In this fashion, it is possible to count on your fingers up to 1,023 (29 + 28 + 27 + 26 + 25 + 24 + 23 + 22 + 21 + 20). However, caution is advised as the number four is prone to offend onlookers.
Binary Coded Decimal
Binary Coded Decimal (BCD) is a type of numerical representation wherein each digit of a decimal number is represented by a four-digit binary number. Four binary digits are more than sufficient for representing quantities of zero (00002) through nine (10012). So by letting four fingers on each hand represent a binary encoding of a decimal digit, it is possible to count up to 99.
Counting in base sixteen or hexadecimal is similar to counting in binary coded decimal. The only difference is that hex requires sixteen numerals. Since 24 equals 16, four binary digits are sufficient to represent quantities from zero (00002) through fifteen (11112). Therefore, we let four fingers on each hand represent a binary encoding of a hexadecimal digit. In this manner, it is possible to count up to FF16, which is 255 in base ten.