# Two's complement overflow

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?

• The largest value of $x$ that will cause overflow cannot be 65535, since a 16 bit signed integer cannot hold that number. – Yuval Filmus Sep 28 '14 at 23:00