1
$\begingroup$

I know that in the case of a 16 bit word, if we have x - 115 in decimal, the smallest x that would cause overflow would be (32767 + 115 + 1)= 32883 because it would represent a number that is larger than the largest positive integer we could represent in a 16 bit word. However, I was wondering what would the largest value of x be? would it be (2^16)? which would cause 2 carries after the addition. Or would the largest x be a number that would only result in 1 carry alone?

$\endgroup$
1
$\begingroup$

You get overflow if the result is larger than the maximal integer, in this case 32767. You get underflow if it is smaller than the minimal one, in this case -32768. (In the context of floating-point operations, underflow happens when a non-zero number is rounded to zero.)

$\endgroup$
  • $\begingroup$ If you look at my question, that's exactly what I have explained. My question is not really that though. I would like to know what would the largest value of x be(not the largest integer value as the result) that will cause overflow? is it going to be (2^16 - 1), since this is the largest number the a 16 bit word could represent? $\endgroup$ – O.A. Sep 28 '14 at 22:23
  • $\begingroup$ The largest value of $x$ that will cause overflow cannot be 65535, since a 16 bit signed integer cannot hold that number. $\endgroup$ – Yuval Filmus Sep 28 '14 at 23:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.