The word *computer* can be defined in many ways and can also take many different meanings; a somewhat common definition may be this: computer is a machine that automatically performs mathematical computations. We can also see it as a machine for processing information or, very generally, as any tool that helps computation, in which case one's fingers or even a mathematical formula itself can be considered a computer. Here we are of course mostly concerned with electronic digital computers.

We can divide computers based on many attributes, e.g.:

- by continuous or discrete
**representation of data**: digital vs analog - by
**hardware technology**: electronic ("lightning in sand"), mechanical, quantum, biological etc. - by
**purpose**: special purpose vs general purpose, personal, server, embedded, supercomputers, gaming computer etc. - by
**programmability**: non-programmable, partially or fully programmable - by the theoretical
**model of computation**it is based on: Turing machine, lambda calculus etc. - by
**computational power**: how difficult problems the computer is able to solve, i.e. where in the Chomsky hierarchy it stands (typically we want Turing complete computers) - by
**other criteria**: price, reliability, durability etc.

Computers are theoretically studied by computer science. The kind of computer we normally talk about consists of two main parts:

**hardware**: physical parts**software**: programs executed by the hardware, made by programmers

**The power of computers is limited**, Alan Turing mathematically proved that there exist problems that can never be completely solved by any algorithm, i.e. there are problems a computer (including our brain) will never be able to solve (even if solution exists). This is related to the fact that the power of mathematics itself is limited in a similar way (see Godel's theorems). Turing also invented the theoretical model of a computer called the Turing machine. Besides the mentioned theoretical limitation, many solvable problems may take too long to compute, at least with computers we currently know (see computational complexity and P vs NP).

Computers we normally talk about in daily conversations are electronic digital mostly personal computers such as desktops and laptops, possibly also cell phones, tablets etc.

Such a computer consists of some kind of case (chassis), internal hardware plus peripheral devices that serve for input and output -- these are for example a keyboard and mouse (input devices), a monitor (output device) or harddisk (input/output device). The internals of the computer normally include:

**motherboard**: The main electronic circuit of the computer into which other components are plugged and which creates the network and interfaces that interconnect them (a chipset). It contains slots for expansion cards as well as connectors for external devices, e.g. USB. In a small memory on the board there is the most basic software (firmaware), such as BIOS, to e.g. enable installation of other software. The board also carries the clock generator for synchronization of all hardware, heat sensors etc.**CPU**(central processing unit): Core of the computer, the chip plugged into motherboard that performs general calculations and which runs programs, i.e. software.**RAM/working memory**: Lower capacity volatile (temporary, erased when powered off) working memory of the computer, plugged into motherboard. It is used as a "pen and paper" by the CPU when performing calculations.**disk**: Non-volatile (persisting when powered off) large capacity memory for storing files and other data, connected to the motherboard via some kind of bus. Different types of disks exist, most commonly hard disks and SSDs.**expansion cards (GPU, sound card, network card, ...)**: Additional hardware cards plugged into motherboard for either enabling or accelerating specific functionality (e.g. GPU for graphics etc.).**PSU**(power supply unit): Converts the input electrical power from the plug to the electrical power needed by the computer.- other things like fans for cooling, batteries in laptops etc.

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