A computer is a machine for manipulating data according to a list of instructions known as a program. Computers are extremely versatile. In fact, they are universal information-processing machines.
Due to technological advancement, modern electronic computers are exponentially more capable than those of preceding generations.
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A computer system is the combination of hardware and software. A typical computer system employs a computer that uses programmable devices to store, retrieve, and process data.
The personal computer or PC exemplifies one example of a computer system. An Automatic Teller Machine (ATM) is another example of a computer system. The Internet does NOT exemplify a computer system per se, but rather a network of computer networks.
Even the simplest computer classifies as a computer system, because at least two components (hardware and software) have to work together.

Source: wikipedia.org