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?
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.)