Combinatorial number system 601 and 1010001011 = 651, which again shows that "C" comes before "C"<nowiki>'</nowiki>. This number is not however the one one wants to represent the "k"-combination with, since many binary numbers have a number of raised bits different from "k"; one wants to find the relative position of "C" in the ordered list of (only) "k"-combinations. The number associated in the combinatorial number system of degree "k" to a "k"-combination "C" is the number of "k"-combinations strictly less than "C" in the given ordering. This number can be computed from "C" = { "c", ..., "c", "c" } with "c"
Binary logarithm and ISO 80000-2), and (with a prior statement that the default base is 2) . Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory. In computer science, they count the number of steps needed for binary search and related algorithms. Other