Question

Why Overflow is indicated when the carry in to the high-order bit is not equal to the carry out. Explain.

Answer 1

If the carry in and carry out is not the same then overflow occurs because even on adding the same sign numbers the sign has changed. Negative +Negative becomes positive or Positive+Positive becomes negative because the bits are not enough to accommodate the extra bit change that has occurred due to difference in carry in and carry out.

Let's understand it by taking an example

11

+11

=10

In this the sign has not changed and the carryin=carry out

11

10

01

Here the sign changed and overflow has occured because even on adding two negatives we got a positive and here the carry in not equal to carry out

Also in case of positive

01

01

10

Here also carry in is not same as carry out hence the sign changed and number became negative

Or

01

00

01

Here the sign doesnot change and overflow has not occured and the number is still positive