Overflow

When the sum of 2 numbers is too large to contain, an overflow occurs. Here are 2 ways of detecting overflow:

• When adding 2 positive numbers, but the sum is negative, or when adding 2 negative numbers, but the sum is positive.
• When the carry bit into the sign bit is different from the carry bit out of the sign bit.

Example: Adding the $6$-bit numbers $18_{10} = 010010_2$ and $23_{10} = 010111_2$:

0 1 11   <-- carry bits
  010010 <-- Positive
+ 010111 <-- Positive
  ______
  101001 <-- Negative?!?! We got overflow!