Two's Complement Overflow

Unlike unsigned numbers, a carry out of the most significant column does not indicate overflow.

When adding N-bit numbers, the carry out the Nth bit (i.e. the N + 1th bit) is discarded.

Example: Compute 1101₂ + 1001₂

   1101 = (-8+4+1) = -3
+  1011 = (-8+2+1) = -5
   ====
 1 1000 = -8 (no overflow)

There is no overflow when adding numbers with different sing.

If, after adding two numbers with same sign, you get a result with other sign - this is overflow.

Example: Compute 4₁₀+5₁₀ using two's complement numbers.

4-bit Overflow
  0100 = 4
+
  0101 = 5
  ----
  1001 = -7 -> Overflow

In this case sign extension will help.

Overflow can be very dangerous. Crash due to overflow.

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