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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
overflow
The condition that occurs when the result of a
calculation is too big to store in the intended format. For
example, the result of adding one to 255 cannot be represented
as an unsigned, eight-bit integer. In a signed integer
representation, overflow can occur when an integer becomes
either too positive or too negative.
Overflow can also occur in the exponent of a floating point
number representation. The term "underflow" is sometimes
used for negative overflow of the exponent.
Ignoring overflow will result in nonsensicle results such as
255 + 1 = 0. At the hardware level, the ALU typically
indicates overflow by setting an overflow flag bit which the
program can test. Programming languages will typically
respond to overflow by raising some kind of signal or other
error condition to halt normal execution.
Some languages attempt to avoid overflow by providing
(optional) variable length number representation
(multiprecission arithmetic) so that the maximum number
representable is limited only by the amount of storage
available.
(2008-05-30)