Bitwise operation in the context of General-purpose register

A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary processor in a given computer. Its electronic circuitry executes instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts with that of external components, such as main memory and I/O circuitry, and specialized coprocessors such as graphics processing units (GPUs).

The form, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged. Principal components of a CPU include the arithmetic–logic unit (ALU) that performs arithmetic and logic operations, processor registers that supply operands to the ALU and store the results of ALU operations, and a control unit that orchestrates the fetching (from memory), decoding and execution (of instructions) by directing the coordinated operations of the ALU, registers, and other components. Modern CPUs devote a lot of semiconductor area to caches and instruction-level parallelism to increase performance and to CPU modes to support operating systems and virtualization.

Computer data storage or digital data storage is the retention of digital data via technology consisting of computer components and recording media. Digital data storage is a core function and fundamental component of computers.

Generally, the faster and volatile storage components are referred to as "memory", while slower persistent components are referred to as "storage". This distinction was extended in the Von Neumann architecture, where the central processing unit (CPU) consists of two main parts: The control unit and the arithmetic logic unit (ALU). The former controls the flow of data between the CPU and memory, while the latter performs arithmetic and logical operations on data. In practice, almost all computers use a memory hierarchy, which puts memory close to the CPU and storage further away.

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs).

The inputs to an ALU are the data to be operated on, called operands, and a code indicating the operation to be performed (opcode); the ALU's output is the result of the performed operation. In many designs, the ALU also has status inputs or outputs, or both, which convey information about a previous operation or the current operation, respectively, between the ALU and external status registers.

A processor register is a quickly accessible location available to a computer's processor. Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.

Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic random-access memory (RAM) as main memory, with the latter usually accessed via one or more cache levels.

In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, word, etc. can be set either on or off, or inverted from on to off (or vice versa) in a single bitwise operation. An additional use of masking involves predication in vector processing, where the bitmask is used to select which element operations in the vector are to be executed (mask bit is enabled) and which are not (mask bit is clear).

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces the identity) and in which composing any two of the three non-identity elements produces the third one. It can be described as the symmetry group of a non-square rectangle (with the three non-identity elements being horizontal reflection, vertical reflection and 180-degree rotation), as the group of bitwise exclusive-or operations on two-bit binary values, or more abstractly as ${\displaystyle \mathbb {Z} _{2}\times \mathbb {Z} _{2}}$, the direct product of two copies of the cyclic group of order 2 by the Fundamental Theorem of Finitely Generated Abelian Groups. It was named Vierergruppe (German: [ˈfiːʁɐˌɡʁʊpə] , meaning four-group) by Felix Klein in 1884. It is also called the Klein group, and is often symbolized by the letter ${\displaystyle V}$ or as ${\displaystyle K_{4}}$.

The Klein four-group, with four elements, is the smallest group that is not cyclic. Up to isomorphism, there is only one other group of order four: the cyclic group of order 4. Both groups are abelian.