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Exponent of a power of two
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
Binary_logarithm
Mathematical function, inverse of an exponential function
mathematics and physics because of its very simple derivative. The binary logarithm uses base 2 and is widely used in computer science, information theory
Logarithm
Inverse function to a tower of powers
indicate the binary iterated logarithm, which iterates the binary logarithm (with base 2 {\displaystyle 2} ) instead of the natural logarithm (with base
Iterated_logarithm
Mathematical function
the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian
Common_logarithm
Entropy of a process with only two probable values
corresponds to nats and is mathematically convenient, while base 2 (binary logarithm) corresponds to shannons and is conventional (as shown in the graph);
Binary_entropy_function
Rooted binary tree data structure
remaining tree, the lookup performance is proportional to that of binary logarithm. BSTs were devised in the 1960s for the problem of efficient storage
Binary_search_tree
Search algorithm finding the position of a target value within a sorted array
or equal to the argument, and log 2 {\textstyle \log _{2}} is the binary logarithm. This is because the worst case is reached when the search reaches
Binary_search
Mathematical constant
0.301\,029\,995\,663\,981\,195.} The inverse of this number is the binary logarithm of 10: log 2 10 = 1 log 10 2 ≈ 3.321 928 095 {\displaystyle \log
Natural_logarithm_of_2
Logarithm to the base of the mathematical constant e
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately
Natural_logarithm
Development of the mathematical function
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and
History_of_logarithms
Root-finding algorithm
{\displaystyle x} to an integer as a way to compute an approximation of the binary logarithm log 2 ( x ) {\textstyle \log _{2}(x)} Use this approximation to compute
Fast_inverse_square_root
Approximation for factorials
bound for comparison sorting, it is convenient to instead use the binary logarithm, giving the equivalent form log 2 n ! = n log 2 n − n log 2 e
Stirling's_approximation
2.71828...; base of natural logarithms
constant, approximately equal to 2.71828, that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after
E_(mathematical_constant)
Number of states of a cybernetic system
inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the same quantity. Variety is used in cybernetics as an information
Variety_(cybernetics)
Scientific study of digital information
binary logarithm. Other units include the nat, which is based on the natural logarithm, and the decimal digit, which is based on the common logarithm
Information_theory
_{b}(y)={\frac {\log(y)}{\log(b)}}={\frac {\ln(y)}{\ln(b)}}.} For example, the binary logarithm (log2), which is widely used in computer science, could be calculated
List of logarithmic identities
List_of_logarithmic_identities
law Binary logarithm Bode plot Henry Briggs Bygrave slide rule Cologarithm Common logarithm Complex logarithm Discrete logarithm Discrete logarithm records
Index_of_logarithm_articles
Approach to public-key cryptography
2} for a binary field) for sufficiently small B are vulnerable to Menezes–Okamoto–Vanstone (MOV) attack which applies usual discrete logarithm problem
Elliptic-curve_cryptography
– binary logarithm (log2). (Also written as lb.) lsc – lower semi-continuity. lerp – linear interpolation. lg – common logarithm (log10) or binary logarithm
List of mathematical abbreviations
List_of_mathematical_abbreviations
Arithmetic operation
numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential
Exponentiation
Average uncertainty in variable's states
for the logarithm. Thus, entropy is characterized by the above four properties. The different units of information (bits for the binary logarithm log2,
Entropy_(information_theory)
functions. Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials. Natural logarithm Common logarithm Binary logarithm
List of mathematical functions
List_of_mathematical_functions
Musical interval unit
binary logarithms for music in a letter to Athanasius Kircher in 1647; this usage often is attributed to Leonhard Euler in 1739 (see Binary logarithm)
Cent_(music)
Best results achieved to date
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions
Discrete_logarithm_records
Two raised to an integer power
are all negative powers of two. Fermi–Dirac prime Gould's sequence Binary logarithm Power of three Power of 10 Lipschutz, Seymour (1982). Schaum's Outline
Power_of_two
Product of numbers from 1 to n
been developed, by Srinivasa Ramanujan, Bill Gosper, and others. The binary logarithm of the factorial, used to analyze comparison sorting, can be very accurately
Factorial
Concise notation for large or small numbers
be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative
Scientific_notation
Property of a thermodynamic system
_{i=1}^{n}{p(x_{i})\log {p(x_{i})}}} where the base of the logarithm determines the units (for example, the binary logarithm corresponds to bits). In the case of transmitted
Entropy
Convention to identify bit positions
LSb 0 numbering. ARINC 429 Binary numeral system Signed number representations Two's complement Endianness Binary logarithm Unit in the last place (ULP)
Bit_numbering
Function in statistics
this, the logit is also called the log-odds since it is equal to the logarithm of the odds p 1 − p {\textstyle {\frac {p}{1-p}}} where p is a probability
Logit
Shift-and-add algorithm
0.5; } return y; } Logarithms for bases other than e can be calculated with similar effort. Example program for binary logarithm in C++ (see A_2 for
BKM_algorithm
Family of related bitwise operations on machine words
significant set bit is log base 2, so called because it computes the binary logarithm ⌊log2(x)⌋. This is closely related to count leading zeros (clz) or
Find_first_set
Swiss mathematician (1707–1783)
approach is mainly mathematical, for instance, his introduction of binary logarithms as a way of numerically describing the subdivision of octaves into
Leonhard_Euler
Algorithm checking for prime numbers
Here ordr(n) is the multiplicative order of n modulo r, log2 is the binary logarithm, and φ ( r ) {\displaystyle \varphi (r)} is Euler's totient function
AKS_primality_test
Indian inventions
coincides with the binary logarithm on the powers of two, but it is different for other integers, giving the 2-adic order rather than the logarithm. Kuṭṭaka –
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
Random search tree data structure
probability distribution as a random binary tree; in particular, with high probability its height is proportional to the logarithm of the number of keys, so that
Treap
Topics referred to by the same term
methods for fluid simulation Liberty BASIC, a programming language Binary logarithm, lb(n) = log2(n) Lower bound, a mathematical concept in order theory
LB
Computer approximation for real numbers
applications. Logarithmic number systems (LNSs) represent a real number by the logarithm of its absolute value and a sign bit. The value distribution is similar
Floating-point_arithmetic
Statistical model for a binary dependent variable
the inverse of the natural logarithm – the exponential function. Thus, although the observed dependent variable in binary logistic regression is a 0-or-1
Logistic_regression
Device that converts a digital signal into an analog signal
This is usually stated as the number of bits it uses, which is the binary logarithm of the number of levels. For instance, a 1-bit DAC is designed to reproduce
Digital-to-analog_converter
Computing concept
\log _{2}(n+1)\rceil } where log 2 {\displaystyle \log _{2}} is the binary logarithm and ⌈ ⋅ ⌉ {\displaystyle \lceil \cdot \rceil } is the ceiling function
Bit-length
Index to measure economic inequality
Index). In information theory, when information is given in binary digits, the binary logarithm is used (with a {\displaystyle a} equal to 2). In physics
Theil_index
Non-eliminating tournament format, without playing every competitor
same number of rounds as that of a knockout tournament, which is the binary logarithm of the number of players rounded up. Thus, three rounds can handle
Swiss-system_tournament
computer word is 1 or 0, especially for floating point operations and binary logarithms. Abed, K.H.; Siferd, R.E. (2006). "VLSI Implementations of Low-Power
Leading-one_detector
Substitution cipher based on linear algebra
of possible keys. The effective key size, in number of bits, is the binary logarithm of the key space size. There are 26 n 2 {\displaystyle 26^{n^{2}}}
Hill_cipher
Greatest integer less than or equal to square root
the algorithm. When a fast computation for the integer part of the binary logarithm or for the bit-length is available (like e.g. n.bit_length() in Python)
Integer_square_root
C standard library header file
natural logarithm (to base e) log2 computes binary logarithm (to base 2) log10 computes common logarithm (to base 10) log1p computes natural logarithm (to
C_mathematical_functions
Statistical distance measure
two discrete probability distributions, given that one uses the base 2 logarithm: 0 ≤ J S D ( P ∥ Q ) ≤ 1 {\displaystyle 0\leq {\rm {JSD}}(P\parallel Q)\leq
Jensen–Shannon_divergence
Relative unit corresponding to doubling of frequency
ratios. A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio: number of octaves = log 2 ( f 2 f 1 ) {\displaystyle
Octave_(electronics)
Problem of sorting pairs of numbers by their sum
two, sorting requires a number of comparisons at least equal to the binary logarithm of the factorial, which is n log 2 n − O ( n ) {\displaystyle n\log
X_+_Y_sorting
Topics referred to by the same term
process, a widely used process in Basic oxygen steelmaking (mathematics) Binary logarithm, l d ( x ) = log 2 ( x ) {\displaystyle \mathrm {ld} (x)=\log _{2}(x)}
LD
Growth at a rate that is a logarithmic function
whose size or cost can be described as a logarithm function of some input. e.g. y = C log (x). Any logarithm base can be used, since one can be converted
Logarithmic_growth
Electronic circuit used to multiply binary numbers
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic
Binary_multiplier
Diagram in computational biology
_{2}(RG)={\frac {1}{2}}(\log _{2}(R)+\log _{2}(G))} M is, therefore, the binary logarithm of the intensity ratio (or difference between log intensities) and
MA_plot
Low-space search for a majority element
need, for instance, on a Turing machine) is higher, the sum of the binary logarithms of the input length and the size of the universe from which the elements
Boyer–Moore majority vote algorithm
Boyer–Moore_majority_vote_algorithm
32-bit computer number format
various optimisations, resulting from the easy generation of a base-2 logarithm approximation from an integer view of the raw bit pattern. Integer arithmetic
Single-precision floating-point format
Single-precision_floating-point_format
information entropy is the bit, or more correctly the shannon, based on the binary logarithm. Although bit is more frequently used in place of shannon, its name
Quantities_of_information
Time required to double a quantity
known doubling time for the following cells: Albert Allen Bartlett Binary logarithm e-folding Exponential decay Exponential growth Half-life Relative growth
Doubling_time
Indian mathematician and Jain scholar (750–825)
This coincides with the binary logarithm when applied to powers of two, but gives the 2-adic order rather than the logarithm for other integers. Virasena
Virasena
Measurement of optical density
photography, the dynamic range is often measured in "stops", which is the binary logarithm of the ratio of highest and lowest distinguishable exposures; in an
Densitometry
Data structure that acts as a priority queue
_{2}n} binomial trees, where log 2 {\displaystyle \log _{2}} is the binary logarithm. The number and orders of these trees are uniquely determined by the
Binomial_heap
Development of mathematics in South Asia
lists various rules involving this operation. This coincides with the binary logarithm when applied to powers of two, but differs on other numbers, more closely
Indian_mathematics
Block cipher
plaintext/ciphertext pairs the adversary can obtain, and lb denotes the binary logarithm. Moreover, effective key size drops to 88 bits given 232.5 known plaintext
DES-X
Study of processing speed on cognitive tasks
theory. In Hick's experiment, the RT is found to be a function of the binary logarithm of the number of available choices (n). This phenomenon is called "Hick's
Mental_chronometry
Topics referred to by the same term
Lateral giant interneuron, an interneuron in crayfish Binary logarithm, with base 2 Common logarithm, with base 10 Liouville–Green method, another name for
LG_(disambiguation)
One of the four basic arithmetic operations
integers and generalizing up through the real numbers and beyond. General binary operations that follow these patterns are studied in abstract algebra. In
Subtraction
Multivalued function in mathematics
mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation
Lambert_W_function
Type of data structure
a leaf node is a part of a given binary hash tree requires computing a number of hashes proportional to the logarithm of the number of leaf nodes in the
Merkle_tree
Complexity of sending information in a distributed algorithm
Dietzfelbinger et al.)). The nondeterministic communication complexity is the binary logarithm of the rectangle covering number of the matrix: the minimum number
Communication_complexity
Length of ciphertext needed to unambiguously break a cipher
where N is the number of characters in the alphabet and log2 is the binary logarithm. So for English each character can convey log2(26) = 4.7 bits of information
Unicity_distance
Part of a number in scientific notation
may cause the term "mantissa" to be misleading, since the mantissa of a logarithm is always its fractional part. Although the other names mentioned are
Significand
Basic unit of quantum information
a basic unit of quantum information, the quantum version of the classic binary bit. A qubit can be physically realized with a two-state (or two-level)
Qubit
Family of cryptographic hash functions
to be natural numbers, where log {\displaystyle \log } denotes the binary logarithm. The reason for w ⋅ log ( n / w ) > r {\displaystyle w\cdot \log(n/w)>r}
Fast_syndrome-based_hash
Number of arguments required by a function
the logarithm operator, the addition operator, and the division operator. Logical predicates such as OR, XOR, AND, IMP are typically used as binary operators
Arity
Computer representation of real numbers
represented in an LNS by two components: the logarithm ( x {\displaystyle x} ) of its absolute value (as a binary word usually in two's complement), and its
Logarithmic_number_system
Proof method
(use ln {\displaystyle \ln } for the natural logarithm and log {\displaystyle \log } for the binary logarithm). Using the incompressibility method, G. J
Incompressibility_method
Base-8 numeral representation
digit can represent the value of a 3-digit binary number (starting from the right). For example, the binary representation for decimal 74 is 1001010. Two
Octal
Base-16 numeric representation
hardware is binary in nature and that hex is power of 2, the hex representation is often used in computing as a dense representation of binary information
Hexadecimal
Topics referred to by the same term
acoustic guitar, see Gibson L Series Buick LG2, a Buick V6 engine binary logarithm (lg2) Laminin G domain 2 (LG2) Lg2, a virulent strain of the fish pathogen
LG2
Scale of numbers with a fixed ratio
the common logarithm, usually as the integer part of the logarithm, obtained by truncation. For example, the number 4000000 has a logarithm (in base 10)
Order_of_magnitude
Unit of measure for digital data
system is proportional to the logarithm of N possible states of that system, denoted logb N. Changing the base of the logarithm from b to a different number
Units_of_information
integral and derivative. The binary logarithm uses base 2 (that is b=2) and is frequently used in computer science. Logarithms are examples of concave functions
Glossary_of_engineering:_A–L
Non-standard positional numeral system
bounded by the logarithm of b {\displaystyle b} and incrementation takes constant time. Hence transforming a binary number into a skew binary number runs
Skew_binary_number_system
Floating-point number formats
that when taking base 2 logarithm of a number, the sign of the exponent of the original value becomes the sign of the logarithm, the exponent of the original
Extended_precision
Bet sizing formula for long-term growth
a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric
Kelly_criterion
Integer sequence
recognize physical processes that behave similarly to Rule 90. The binary logarithms (exponents in the powers of two) of Gould's sequence themselves form
Gould's_sequence
Branch of elementary mathematics
sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers
Arithmetic
Function used in computer cryptography
the discrete logarithm. Currently there are several popular groups for which no algorithm to calculate the underlying discrete logarithm in polynomial
One-way_function
Algorithm for computing the value of a transcendental number
illustrates the working of a spigot algorithm by calculating the binary digits of the natural logarithm of 2 (sequence A068426 in the OEIS) using the identity ln
Spigot_algorithm
Observation that in many real-life datasets, the leading digit is likely to be small
stated in a stronger form, asserting that the fractional part of the logarithm of data is typically close to uniformly distributed between 0 and 1; from
Benford's_law
Function that takes one argument
functions, logarithm with a specified base, exponentiation to a particular power or base, and hyperbolic functions. Arity Binary function Binary operation
Unary_function
Decomposition of a number into a product
ISBN 978-1-4419-5905-8 "[Cado-nfs-discuss] 795-bit factoring and discrete logarithms". Archived from the original on 2019-12-02. Kleinjung, Thorsten; Aoki
Integer_factorization
Function whose actual domain of definition may be smaller than its apparent domain
(that is, if the natural logarithm function is viewed as a function from the positive reals to the reals), then the natural logarithm is a function. Subtraction
Partial_function
Binary tree derived from a sequence of numbers
In computer science, a Cartesian tree is a binary tree derived from a sequence of distinct numbers. To construct the Cartesian tree, set its root to be
Cartesian_tree
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
functions, square roots, multiplications, divisions, exponentials, and logarithms with arbitrary base, typically converging with one digit (or bit) per
CORDIC
Symbol rate measurement in telecommunications
N}.} By taking information per pulse N in bit/pulse to be the base-2-logarithm of the number of distinct messages M that could be sent, Hartley constructed
Baud
Binary tree selected at random
random binary search tree is at most 2 log n + O ( 1 ) {\displaystyle 2\log n+O(1)} , where " log {\displaystyle \log } " denotes the natural logarithm function
Random_binary_tree
Binary elastic collision between two charged particles
A Coulomb collision is a binary elastic collision between two charged particles interacting through their own electric field. As with any inverse-square
Coulomb_collision
Algebraic structure with a binary operation
structure. Specifically, a magma consists of a set equipped with a single binary operation that must be closed by definition. No other properties are imposed
Magma_(algebra)
Arithmetic operation
calculated with an abacus. Logarithm tables can be used to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm
Division_(mathematics)
BINARY LOGARITHM
BINARY LOGARITHM
Girl/Female
English
Originally a diminutive used for names ending in -bina, like Albina, Columbina, and Robina, now...
Female
Hebrew
(×‘Ö¼Ö´×™× Ö¸×”) Hebrew name BINA means "intelligence, wisdom."Â
Male
Hindi/Indian
(विनय) Hindi name VINAY means "leading asunder."
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Girl/Female
Indian
(the wife of Sage Kashyap)
Female
Turkish
Turkish name PINAR means "spring."
Male
English
English unisex form of Latin Hilarius and Hilaria, HILARY means "joyful; happy."Â Originally, this was strictly a masculine name.
Female
English
English pet form of German Belinda, possibly BINDY means "bright serpent" or "bright linden tree."
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Boy/Male
Irish
An ancient Irish name whos meaning is lost in antiquety.
Surname or Lastname
English
English : variant spelling of Vickery.
Boy/Male
Latin
Happy; Cheerful.
Girl/Female
Indian
Modesty
Female
Hebrew
Variant spelling of Hebrew Bina, BINAH means "intelligence, wisdom."Â
Surname or Lastname
English (chiefly South Yorkshire)
English (chiefly South Yorkshire) : topographic name for someone who lived on land enclosed by a bend in a river, from Old English binnan ēa ‘within the river’, or a habitational name from places in Kent called Binney and Binny, which have this origin.Scottish : habitational name from Binney or Binniehill near Falkirk, named in Gaelic as Beinnach, from beinn ‘hill’ + the locative suffix -ach.
Boy/Male
American, Australian, French, German, Greek, Latin, Polish, Swedish
Cheerful; Happy; Joyful; Similar to Hilary
Boy/Male
Indian, Punjabi, Sikh
Blessing
Boy/Male
Indian
An intimate particle of the God of heaven
Male
Hindi/Indian
Variant spelling of Hindi Vijay, BIJAY means "victory."
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
BINARY LOGARITHM
BINARY LOGARITHM
Surname or Lastname
English
English : habitational name from a place in Berkshire named with the Old English personal name Benna + Old English hamm ‘river meadow’.John Benham was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Girl/Female
Muslim
Hardworking
Girl/Female
Indian
Auspicious, Blessed
Girl/Female
Indian
Beautiful
Surname or Lastname
English
English : probably a variant spelling of Ralph.
Boy/Male
Greek
A tribe of giants.
Boy/Male
Sikh
A wish, Desire (1)
Boy/Male
Gujarati, Hindu, Indian, Kannada
Perfect
Female
Greek
(ΜαÏγαÏίτες) Greek name derived from the word margaron, MARGARITES means "pearl."
Girl/Female
Tamil
BINARY LOGARITHM
BINARY LOGARITHM
BINARY LOGARITHM
BINARY LOGARITHM
BINARY LOGARITHM
a.
Compounded or consisting of two things or parts; characterized by two (things).
n.
A binary compound of silicon, or one regarded as binary.
n.
A binary compound of phosphorus.
n.
A binary compound of zinc.
n.
A register of daily events or transactions; a daily record; a journal; a blank book dated for the record of daily memoranda; as, a diary of the weather; a physician's diary.
n.
A pale yellow color, like that of a canary bird.
a.
lasting for one day; as, a diary fever.
n.
A binary compound of hydrogen; a hydride.
v. i.
To perform the canary dance; to move nimbly; to caper.
n.
A binary compound of iodine, or one which may be regarded as binary; as, potassium iodide.
a.
Of or pertaining to the Canary Islands; as, canary wine; canary birds.
n.
That which is constituted of two figures, things, or parts; two; duality.
a.
Containing ten; tenfold; proceeding by tens; as, the denary, or decimal, scale.
n.
See Finery.
a.
Of or pertaining to the urine; as, the urinary bladder; urinary excretions.
n.
A canary bird.
a.
Of a pale yellowish color; as, Canary stone.
n.
A binary compound of selenium, or a compound regarded as binary; as, ethyl selenide.
a.
Relating or belonging to bile; conveying bile; as, biliary acids; biliary ducts.
n.
Wine made in the Canary Islands; sack.