Binary number and overflow is repeated for each digit of significance. Counting progresses as follows: Binary counting follows the same procedure, except that only the two symbols "0" and "1" are available. Thus, after a digit reaches 1 in binary, an increment resets it to 0 but also causes an increment of the next digit to the left: In the binary system, each digit represents an increasing power of 2, with the rightmost digit representing 2, the next representing 2, then 2, and so on. The equivalent decimal representation of a binary number is sum of the powers of 2 which each
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