What is arithmetic overflow? When does it occur and how can it be detected?

Question

What will be an ideal response?

Answer 1

Arithmetic overflow takes place when one or more two’s complement numbers take part in an arithmetic operation and the sign?bit of the result is incorrect. For example, arithmetic overflow takes place when two positive integers are added and the result (when interpreted as a two’s complement value) is negative, or when two negative numbers are added and the result is positive. In 4?bit arithmetic, the signed two’s complement values 1100 and 1000 are added to give 1 0100, where the most?significant bit is a carry out. The sign of the result, 0100, is 0 indicating a positive value. Since the numbers we added were both negative, arithmetic overflow has occurred.

In two’s complement addition, arithmetic overflow can be detected by saying, “If the sign bits of the two source operands are the same, and differ from the sign bit of the result operand, then arithmetic overflow occurred.”