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The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF (2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around. Any string of bits can be interpreted as the coefficients of a ...
A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. [1][2] Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated ...
Computation of cyclic redundancy checks. Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message string, with a fixed number of zeroes appended, by the "generator polynomial" string except that exclusive or operations replace ...
Usually, the second sum will be multiplied by 2 32 and added to the simple checksum, effectively stacking the sums side-by-side in a 64-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-64 checksum. The use of the modulus 2 32 − 1 = 4,294,967,295 is also generally implied. The rationale ...
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
The monkey and the coconuts is the best known representative of a class of puzzle problems requiring integer solutions structured as recursive division or fractionating of some discretely divisible quantity, with or without remainders, and a final division into some number of equal parts, possibly with a remainder.