One crucial limitation in computers is that they intrinsically operate on word-size data and we have seen that it is not always possible to accurately represent the result of an addition because adding to $$n$$-bit numbers may require $$n+1$$ bits for the result. We have discussed under which circumstances the least significant $$n$$ bits of the addition result are exact, i.e. no overflow occured. For unsigned addition and subtraction the carry out of the last position gives an indication for an overflow. For signed addition and subtraction, the xor of the carries into and out of the last position detects an overflow.