Arithmetic overflow occurs during a two's complement addition if the result of adding two positive numbers yields a negative result or if adding two negative numbers yields a positive result. If the sign bits of A and B are the same but the sign bit of the result is different, arithmetic overflow has occurred. If a_n-I is the sign bit of A, b_n-t is the sign bit of B, and S_n-I is the sign bit of the sum of A and B, then overflow is defined by

In practice, real systems detect overflow from C_in ≠ ft C_out to the last stage. That is, we detect overflow from  

Demonstrate that this expression is correct.

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. V = an-1 bn-1 Sn-1+ an-1 bn-1 Sn-1 '