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  2. Arithmetic logic unit - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_logic_unit

    In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. [1] [2] This is in contrast to a floating-point unit (FPU), which operates on floating point numbers.

  3. Bitwise operation - Wikipedia

    en.wikipedia.org/wiki/Bitwise_operation

    Bitwise AND of 4-bit integers. A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × ...

  4. Bitwise operations in C - Wikipedia

    en.wikipedia.org/wiki/Bitwise_operations_in_C

    The bitwise XOR (exclusive or) performs an exclusive disjunction, which is equivalent to adding two bits and discarding the carry. The result is zero only when we have two zeroes or two ones. [3] XOR can be used to toggle the bits between 1 and 0. Thus i = i ^ 1 when used in a loop toggles its values between 1 and 0. [4]

  5. Bit array - Wikipedia

    en.wikipedia.org/wiki/Bit_array

    Haskell likewise currently lacks standard support for bitwise operations, but both GHC and Hugs provide a Data.Bits module with assorted bitwise functions and operators, including shift and rotate operations and an "unboxed" array over Boolean values may be used to model a Bit array, although this lacks support from the former module.

  6. Commutative property - Wikipedia

    en.wikipedia.org/wiki/Commutative_property

    Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction , that do not have it (for example, "3 − 5 ≠ 5 − 3" ); such operations are not commutative, and so are ...

  7. Schur polynomial - Wikipedia

    en.wikipedia.org/wiki/Schur_polynomial

    where the sum is taken over all partitions λ, and (), () denote the complete symmetric functions and elementary symmetric functions, respectively. If the sum is taken over products of Schur polynomials in n {\displaystyle n} variables ( x 1 , … , x n ) {\displaystyle (x_{1},\dots ,x_{n})} , the sum includes only partitions of length ℓ ( λ ...

  8. China's economy expands 5% in 2024, hitting target helped by ...

    www.aol.com/chinas-economy-expands-5-2024...

    HONG KONG (AP) — China's economy expanded at a 5% annual pace in 2024, slower than the year before but in line with Beijing’s target of “around 5%” growth, thanks to strong exports and ...

  9. Circular shift - Wikipedia

    en.wikipedia.org/wiki/Circular_shift

    Circular shifts are used often in cryptography in order to permute bit sequences. Unfortunately, many programming languages, including C, do not have operators or standard functions for circular shifting, even though virtually all processors have bitwise operation instructions for it (e.g. Intel x86 has ROL and ROR).

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