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A computer is a physical system that represents information and carries out defined operations on it. In a stored-program design, instructions and data are held in computer memory, and a processor interprets instructions to update state. A simple program can read two represented numbers, add them and store the result; the represented bit patterns acquire meaning through the chosen encoding. Digital computers use discrete states, while analogue computers represent quantities through continuously varying physical variables. A mathematical model of computation abstracts these mechanisms to study capability and resource use.

Computer architecture studies the organization and behaviour of computers, connecting the operations visible to software with the hardware that executes them. An instruction set architecture specifies the machine-level contract, including instructions, accessible processor registers and addressing behaviour. A microarchitecture is a particular implementation of that contract, including execution units, instruction pipelining and memory caches.^[ref]

Two CPUs can implement the same instruction set architecture while taking different times to run the same computer program. One might overlap independent instructions or use a larger memory cache; neither choice changes what an addition instruction is required to compute. A useful performance model writes execution time as instruction count times average cycles per instruction divided by clock frequency. The factors interact: a design that raises clock frequency can also change cycles per instruction. This separates a program's required behaviour from the engineering choices that determine its cost.

Computer memory stores information that a computer can retrieve while executing computer programs. A memory location holds a value, and a memory address selects a location under the machine's addressing rules. In a byte-addressed example, consecutive bytes have consecutive memory addresses; a four-byte value can occupy four locations. The interpretation of those stored bits as a number, an instruction or another representation belongs to the computer program and architecture.

Computer memory has different physical and logical roles. Non-volatile memory retains stored information without power, while other technologies require power to retain it. A memory cache holds selected information for faster reuse; virtual memory presents an operating-system process with its own address space. These describe different properties, so a cached value and its virtual address should not be confused with the physical storage holding it.

In the paging examples, resident memory pages occupy main computer memory, and address translation maps a virtual address to a physical address. The operating system can change a mapping while keeping an operating-system process's numerical virtual address unchanged. This separation makes controlled sharing and isolation possible.^[ref]

Physicist whose work includes the stabilizer formalism for quantum error correction. His The Heisenberg Representation of Quantum Computers by Daniel Gottesman develops the Pauli group description of Clifford circuits. Verified institutional profile.

Developed the Bell-LaPadula model with Leonard J. LaPadula.

The IBM 1401 is a transistorized data-processing computer introduced in 1959, used for business workloads involving punched cards, printing and magnetic tape. Its stored programs transformed records and coordinated input/output devices, making it a historically important example of computing organized around data processing.^[ref]

It also provides a concrete scientific-computing benchmark. Bresenham reported a 333-core-location IBM 1401 program controlling an IBM 1627 Plotter, with approximately1.5 milliseconds of computation between successive plotted increments.^[ref] The report connects an algorithm's arithmetic choices to actual program storage and timing. These are measurements for that implementation and task, rather than universal instruction timings for every 1401 program.

Developed the Bell-LaPadula model with David Elliott Bell.

The Macintosh is a family of computers made by Apple. Its early machines provide a concrete example of integrating a processor, computer memory, a display and pointing-device input into an interactive system. The original 128K model and its 512K successor combined a built-in screen with keyboard and mouse connections; the service manual distinguishes their memory capacities.^[ref]

The early display contained $512\times 342$ pixels. To model a monochrome framebuffer with one bit per pixel, the minimum packed image storage isThat is $21.375\times 1024$ bytes, before any additional image buffers or program data. This is an original storage calculation using the documented display dimensions, rather than a claim about a particular program's memory allocation.^[ref]

The example connects a visible pixel to an addressable representation in computer memory. Drawing a black line requires changing selected bits; a graphical user interface uses such drawing operations to represent controls and documents. Raising either display dimension increases storage even if the processor and the number of values represented per pixel remain unchanged.

Multics is a time-sharing operating system developed from a research project begun in 1965. It provided an interactive computing service to multiple users through terminals, sharing the underlying computer while protecting users' work. Its surviving documentation and source make it a concrete historical case for studying operating system design and protection. The participants' archive records its transition into a commercial system and operational use until 2000.^[ref]

// Target: computer-science.bigb

A plotter is a computer-controlled drawing device that produces physical marks by moving a pen or another marking tool relative to a surface. Geometric commands become motions and pen-up or pen-down actions. In a digital stepping plotter, available moves impose a coordinate mesh, so a mathematical line must be approximated by legal steps.

Jack Elton Bresenham's 1965 paper describes a plotter with eight possible neighbor moves, typically on a mesh spaced one hundredth of an inch apart.^[ref] For a segment from $(0,0)$ to $(5,2)$, the controller must distribute two upward increments among five rightward increments. Bresenham's line algorithm updates an integer decision value to choose successive moves. This connects computational geometry to an apparatus whose resolution and permitted motions determine the drawing.

Software consists of instructions and associated data used by a computer. A spreadsheet is software that stores spreadsheet cells and evaluates their spreadsheet formulas.

A virtual machine presents a specified machine interface implemented using another system. A system virtual machine supplies virtual processors, memory and devices to a guest operating system. A hypervisor mediates access to the underlying resources; execution can combine hardware assistance and software emulation.^[ref]

For example, a guest can maintain its own kernel and filesystem view while a host schedules several guests on one physical machine. A Java virtual machine instead exposes a bytecode execution model to programs, illustrating a different level of abstraction. A container usually shares the host kernel rather than supplying a separate full guest kernel. The interface being virtualized determines which compatibility and isolation properties a particular virtual machine provides.