A computer is a programmable
machine (or more precisely, a programmable
sequential state machine).
There are two basic kinds of computers: analog and digital.
Analog computers are analog devices.
That is, they have continuous states rather than discrete numbered states. An
analog computer can represent fractional or irrational values exactly, with no
round-off. Analog computers are almost never used outside of experimental
settings.
A digital computer is a
programmable clocked sequential state machine. A digital computer uses discrete
states. A binary digital computer uses two discrete states, such as
positive/negative, high/low, on/off, used to represent the binary digits zero
and one.
The French word ordinateur,
meaning that which puts things in order, is a good description of the most
common functionality of computers.