Final answer:
Overflow occurs when carry into the high-order bit is not equal to the carry out in an arithmetic operation, indicating that the calculation exceeded the range representable by the fixed number of bits used.
Step-by-step explanation:
Overflow in the context of computer arithmetic is indicated when the carry into the high-order bit (the leftmost bit) is not equal to the carry out of the high-order bit after an arithmetic operation. This situation arises when adding two signed numbers in binary form. Computers use a fixed number of bits to represent numbers, and the high-order bit often serves as the sign bit in signed number representations like two's complement. When adding two positive numbers results in a negative, or two negative numbers result in a positive, overflow has occurred.
For example, consider a simple 4-bit system using two's complement representation, where the highest bit is the sign bit. Adding 0101 (5 in decimal) to 0010 (2 in decimal) gives 0111 (7 in decimal), with no overflow because the carry into the high-order bit equals the carry out. However, adding 0101 (5 in decimal) to 0110 (6 in decimal) would give 1011 (-5 in decimal using two's complement), indicating an overflow since a positive plus a positive should not yield a negative result and the carries do not match.
It's important to detect overflow because it can lead to incorrect results in calculations where the actual result cannot be represented within the fixed bit-width of the computer's architecture.