Carry and signed overflow answer different questions. Carry reports a result exceeding the unsigned word width. Twos-complement overflow reports a result outside the signed range. Adding two values with the same sign overflows if the stored result has the opposite sign.
Worked example
Using four-bit twos complement, 0111 + 0001 = 1000. This appears as −8 even though 7 + 1 should be 8: signed overflow occurred without a final carry. Conversely, 1111 + 0001 produces carry 1 and result 0000; −1 + 1 = 0 is valid.
What to watch for
Do not use the carry bit alone as a signed-overflow flag. Interpret both operands and the result using the same width and encoding.
Try it yourself
Does four-bit 1100 + 1110 overflow?
Answer: These values are −4 and −2. Their sum is −6, stored as 1010. There is an unsigned carry, but no signed overflow.
How to study this topic
Write the base and bit width beside every value. Expand place weights before using a shortcut, then convert your answer back to decimal as an independent check. Representation and value are different ideas.
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