YES , The overflow flag be set if you add a negative integer to a negative integer and produce a positive result.
In computer processors, the overflow flag is usually a single bit in a system status register used to indicate when an arithmetic overflow has occurred in an operation, indicating that the signed two's-complement result would not fit in the number of bits used for the operation.
Some architectures may be configured to automatically generate an exception on an operation resulting in overflow. Although not very precise, the overflow flag could be considered a two's complement form of a carry flag, but the typical usage is quite different.
The overflow flag would then be set so the program can be aware of the problem and mitigate this or signal an error. The overflow flag is thus set when the most significant bit is changed by adding two numbers with the same sign. Overflow never occurs when the sign of two addition operands are different.
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