Overflow: 2C

If x and y have opposite signs, then the result can't overflow:

magnitude of the result will be less than the magnitude of the larger number

| x + y | <= max (|x|, |y|)

Overflow can only occur when the numbers both have the same sign.

If the sign of the result is different, then overflow must have occurred.

For example, if x and y both have sign bit 0 (positive), and the result has

sign bit 1 (negative), then overflow must have occurred.

Add 2 k-bit numbers:

xk-1...x0

+ yk-1...y0

sk-1...s0

One way to express whether overflow occurs:

V = xk-1yk-1\sk-1 + \xk-1\yk-1sk-1

Either both sign bits of x and y are 1 and the sign bit of s is 0,

or the sign bits are both 0 and the sign bit of s is 1

Simpler formula:

V = ck-1 XOR ck-2

The overflow bit is equal to the XOR of the carry-in to the leftmost bit

with the carry-out from the leftmost bit.