Detect Signed Overflow

What to look for

Signed overflow happens when the result of an arithmetic operation cannot be represented in the fixed signed integer range being used. This is about the stored result, not whether the operation is mathematically valid.

Quick method

1. Identify the signed format being used, if it is given.
2. Compute the exact mathematical result of the operation.
3. Compare it with the allowed signed range for that format.
   • If the result is outside the range, signed overflow occurred.
   • If it is inside the range, there is no signed overflow.
4. For addition and subtraction, also watch for the sign pattern:
   • Adding two positive numbers should not give a negative result.
   • Adding two negative numbers should not give a positive result.
   • A sign flip that contradicts the inputs is a strong overflow signal.

How to verify

Check your final answer by asking: “Could this value actually be stored in the given signed representation?” If not, the operation overflowed.

Common mistake

Do not confuse signed overflow with an ordinary carry out of the top bit. A carry may happen without signed overflow, and signed overflow may happen even when the bit pattern seems reasonable.

Final check

Your answer should be a simplified statement such as overflow or no overflow, based on the representable signed range.