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](information.md) or, very generally, as any tool that helps computation, in which case one's fingers or even a [mathematical](math.md) formula itself can be considered a computer. Here we are of course mostly concerned with electronic [digital](digital.md) computers.
- by **[hardware](hw.md) technology**: [electronic](electronics.md) ("lightning in sand"), [mechanical](mechanical.md), [quantum](quantum.md), biological etc.
- by **purpose**: special purpose vs general purpose, [personal](pc.md), [server](server.md), [embedded](embedded.md), [supercomputers](supercomputer.md), gaming computer etc.
- by the theoretical **[model of computation](model_of_computation.md)** it is based on: [Turing machine](turing_machine.md), [lambda calculus](lambda_calculus.md) etc.
- by **computational power**: how difficult problems the computer is able to solve, i.e. where in the [Chomsky hierarchy](chomsky_hierarchy.md) it stands (typically we want [Turing complete](turing_completeness.md) computers)
- by **other criteria**: price, reliability, durability etc.
**The power of computers is limited**, [Alan Turing](turing.md) mathematically proved that there exist problems that can never be completely solved by any [algorithm](algorithm.md), i.e. there are problems a computer (including our [brain](brain.md)) 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](incompleteness_theorems.md)). Turing also invented the theoretical model of a computer called the [Turing machine](turing_machine.md). Besides the mentioned theoretical limitation, many solvable problems may take too long to compute, at least with computers we currently know (see [computational complexity](computational_complexity.md) and [P vs NP](p_vs_np.md)).
Computers we normally talk about in daily conversations are [electronic](electronics.md) [digital](digital.md) mostly personal computers such as [desktops](desktop.md) and [laptops](laptop.md), possibly also [cell phones](phone.md), [tablets](tablet.md) etc.
Such a computer consists of some kind of [case](case.md) (chassis), internal [hardware](hardware.md) plus [peripheral devices](peripheral.md) that serve for [input and output](io.md) -- these are for example a [keyboard](keyboard.md) and [mouse](mouse.md) (input devices), a [monitor](monitor.md) (output device) or [harddisk](hdd.md) (input/output device). The internals of the computer normally include:
- **[motherboard](motherboard.md)**: 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](chipset.md)). It contains slots for expansion cards as well as connectors for external devices, e.g. [USB](usb.md). In a small memory on the board there is the most basic software ([firmaware](firmware.md)), such as [BIOS](bios.md), to e.g. enable installation of other software. The board also carries the [clock](clock.md) generator for synchronization of all hardware, heat sensors etc.
- **[CPU](cpu.md)** (central processing unit): Core of the computer, the chip plugged into motherboard that performs general calculations and which runs [programs](program.md), i.e. [software](sw.md).
- **[RAM](ram.md)/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](disk.md)**: [Non-volatile](volatile.md) (persisting when powered off) large capacity memory for storing [files](file.md) and other [data](data.md), connected to the motherboard via some kind of [bus](bus.md). Different types of disks exist, most commonly [hard disks](hdd.md) and [SSDs](ssd.md).
- **expansion cards ([GPU](gpu.md), sound card, network card, ...)**: Additional hardware cards plugged into motherboard for either enabling or accelerating specific functionality (e.g. GPU for graphics etc.).
- **[PSU](psu.md)** (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](cooling.md), batteries in laptops etc.
