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  2. Bitwise operation - Wikipedia

    en.wikipedia.org/wiki/Bitwise_operation

    In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand ...

  3. Prefix sum - Wikipedia

    en.wikipedia.org/wiki/Prefix_sum

    The reverse operation, decoding a Gray-coded value x into a binary number, is more complicated, but can be expressed as the prefix sum of the bits of x, where each summation operation within the prefix sum is performed modulo two. A prefix sum of this type may be performed efficiently using the bitwise Boolean operations available on modern ...

  4. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    In computer science, modular arithmetic is often applied in bitwise operations and other operations involving fixed-width, cyclic data structures. The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context. The logical operator XOR sums 2 bits ...

  5. Nim - Wikipedia

    en.wikipedia.org/wiki/Nim

    This operation is also known as "bitwise xor" or "vector addition over GF" (bitwise addition modulo 2). Within combinatorial game theory it is usually called the nim-sum, as it will be called here. The nim-sum of x and y is written x ⊕ y to distinguish it from the ordinary sum, x + y. An example of the calculation with heaps of size 3, 4, and ...

  6. GF (2) - Wikipedia

    en.wikipedia.org/wiki/GF(2)

    GF(2) can be identified with the field of the integers modulo 2, that is, the quotient ring of the ring of integers Z by the ideal 2Z of all even numbers: GF(2) = Z/2Z. Notations Z 2 and Z 2 {\displaystyle \mathbb {Z} _{2}} may be encountered although they can be confused with the notation of 2 -adic integers .

  7. Mathematics of cyclic redundancy checks - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_cyclic...

    Note that is equivalent to zero in the above equation because addition of coefficients is performed modulo 2: = + = (+) = (). Polynomial addition modulo 2 is the same as bitwise XOR. Since XOR is the inverse of itself, polynominal subtraction modulo 2 is the same as bitwise XOR too.

  8. Fletcher's checksum - Wikipedia

    en.wikipedia.org/wiki/Fletcher's_checksum

    Here, this is done after each addition, so that at the end of the for loop the sums are always reduced to 8 bits. At the end of the input data, the two sums are combined into the 16-bit Fletcher checksum value and returned by the function on line 13. Each sum is computed modulo 255 and thus remains less than 0xFF at all times.

  9. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    Modulo operations might be implemented such that a division with a remainder is calculated each time. For special cases, on some hardware, faster alternatives exist. For example, the modulo of powers of 2 can alternatively be expressed as a bitwise AND operation (assuming x is a positive integer, or using a non-truncating definition):