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An n-bit LUT can encode any n-input Boolean function by storing the truth table of the function in the LUT. This is an efficient way of encoding Boolean logic functions, and LUTs with 4-6 bits of input are in fact the key component of modern field-programmable gate arrays (FPGAs) which provide reconfigurable hardware logic capabilities.
Reverse lookup is a procedure of using a value to retrieve a unique key in an associative array. [1]Applications of reverse lookup include reverse DNS lookup, which provides the domain name associated with a particular IP address, [2]
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive integers. Möbius μ function: Sum of the nth primitive roots of unity, it depends on the prime factorization of n. Prime omega functions; Chebyshev functions
Formally, a function of n variables is a function whose domain is a set of n-tuples. [note 3] For example, multiplication of integers is a function of two variables, or bivariate function, whose domain is the set of all ordered pairs (2-tuples) of integers, and whose codomain is the set of integers. The same is true for every binary operation.
In general, functions or operators with a given arity follow the naming conventions of n-based numeral systems, such as binary and hexadecimal. A Latin prefix is combined with the -ary suffix. For example: A nullary function takes no arguments. Example: () = A unary function takes one argument. Example: () =
A classical example of this phenomenon [9] is given by the divisor summatory function, the summation function of d(n), the number of divisors of n: = = + + + + + + = An average order of an arithmetic function is some simpler or better-understood function which has the same summation function asymptotically, and ...
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.