Is the following a valid alternative definition of overflow in twos complement arithmetic?
If the exclusiveOR of the carry bits into and out of the leftmost column is 1, then
there is an overflow condition. Otherwise, there is not.

The overflow rule was stated as follows: If two numbers are added, and they are
both positive or both negative, then overflow occurs if and only if the result has
the opposite sign.
There are four cases:
•Both numbers positive (sign bit = 0) and no carry into the leftmost bit position:
There is no carry out of the leftmost bit position, so the XOR is 0. The result has a
sign bit = 0, so there is no overflow.
•Both numbers positive and a carry into the leftmost bit position: There is no carry
out of the leftmost position, so the XOR is 1. The result has a sign bit = 1, so there
is overflow.
•Both numbers negative and no carry into the leftmost position: There is a carry
out of the leftmost position, so the XOR is 1. The result has a sign bit of 0, so there
is overflow.
•Both numbers negative and a carry into the leftmost position. There is a carry out
of the leftmost position, so the XOR is 0. The result has a sign bit of 1, so there is
no overflow.
Therefore, the XOR result always agrees with the presence or absence of overflow.
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