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 "C"<nowiki>'</nowiki>, since they have the same largest part 9, but the next largest part 6 of "C" is less than the next largest part 7 of "C"<nowiki>'</nowiki>; the sequences compared lexicographically are (9,6,4,3,0) and (9,7,3,1,0). Another way to describe this ordering is view combinations as describing the "k" raised bits in the binary representation of a number, so that "C" = {"c"...,"c"} describes the number (this associates distinct numbers to "all" finite sets of natural numbers); then comparison of "k"-combinations can be done by comparing the associated binary numbers. In the example "C" and "C"<nowiki>'</nowiki> correspond to numbers 1001011001 =