Binary arithmetic | Calculus | Logarithms

Binary logarithm

In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the logarithm to the base 2 and is the inverse function of the power of two function. As well as log2, an alternative notation for the binary logarithm is lb (the notation preferred by ISO 31-11 and ISO 80000-2). 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 areasin which the binary logarithm is frequently used include combinatorics, bioinformatics, the design of sports tournaments, and photography. Binary logarithms are included in the standard C mathematical functions and other mathematical software packages.The integer part of a binary logarithm can be found using the find first set operation on an integer value, or by looking up the exponent of a floating point value.The fractional part of the logarithm can be calculated efficiently. (Wikipedia).

Binary logarithm
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List of logarithmic identities | Millioctave | Inverse function | Exponentiation | ISO 31-11 | Power set | Ratio test | Strassen algorithm | MATLAB | Ramsey's theorem | Factorization | Karatsuba algorithm | Logarithm | Dynamic range | Long double | Hypercube graph | Master theorem (analysis of algorithms) | Floor and ceiling functions | Longest increasing subsequence | Big O notation | Convergent series | Mathematical analysis | Weber–Fechner law | Calculator | Cent (music) | F-number | Negative number | Rational number | Pseudocode | Combinatorics | Find first set | Power of two | Rounding | Analysis of algorithms | Exposure value | Information theory | Binary search tree | Quicksort | Complex logarithm | Clique (graph theory) | Gilbert–Shannon–Reeds model | Euclid's Elements | Mathematics | Comparison sort | Integer | Shannon–Hartley theorem | Real number | Family of sets | Bit | Number theory | Perfect number | Independent set (graph theory) | Strahler number | Complex number | Exponentiation by squaring | Natural logarithm | Nat (unit) | Leonhard Euler | Partial cube | Algorithm | Euclid–Euler theorem | Common logarithm | Binary tree | Units of information