How does comparing the Sign and Overflow Flag determine operand relationships?

Question

Jump\'s based on comparing signed integers use the Zero, Sign, and Overflow flag to determine the relationship between operands. After CMP with two signed opera

Answer 1

Performing the signed subtraction R = Destination - Source yields a signed result.

Suppose there is no overflow - the usual arithmetic laws holds: if R = Destination - Source > 0 then Destination > Source.
Having no overflow means OF = 0 and R > 0 means SF = 0.

Now suppose there is an overflow - let's call O the most significant, non-sign, bit and S the sign bit.
An overflow condition means that either a) Computing the result's O needed a borrow and result's S didn't or b) result's O didn't need a borrow and S did.

In case a) since result's S didn't need a borrow, the two S bits of the operands were either (1, 0) (1, 1) or (0, 0).
Since result's O needed a borrow, and thus flipping the first source S bit, we must exclude the second and third option.
So the operands sign bits were 1 and 0 (thus Destination < Source), the result's sign bit SF = 0 and OF = 1 by hypothesis.

In case b) since result's S did need a borrow, the two S bits of the operands were (0, 1).
Since O didn't need a borrow, the first operand S bit has been not changed and we don't need to consider any further case.
So the operands sign bits were 0 and 1 (thus Destination > Source), the result's sign bit SF = 1 and OF = 1 by hypothesis.

To recap:

• If OF = 0 then Destination > Source => SF = 0.
• If OF = 1 then Destination > Source => SF = 1.

In short OF = SF.