Binary number through each symbol, in increasing order. Before examining binary counting, it is useful to briefly discuss the more familiar decimal counting system as a frame of reference. Decimal counting uses the ten symbols "0" through "9". Counting begins with the incremental substitution of the least significant digit (rightmost digit) which is often called the "first digit". When the available symbols for this position are exhausted, the least significant digit is reset to "0", and the next digit of higher significance (one position to the left) is incremented ("overflow"), and incremental substitution of the low-order digit resumes. This method of reset
Combinatorial number system of a set "S" is a subset of "S" with "k" (distinct) elements. The main purpose of the combinatorial number system is to provide a representation, each by a single number, of all formula_1 possible "k"-combinations of a set "S" of "n" elements. Choosing, for any "n", } as such a set, it can be arranged that the representation of a given "k"-combination "C" is independent of the value of "n" (although "n" must of course be sufficiently large); in other words considering "C" as a subset of a larger set by increasing "n" will not change the number that