 Once "formula_12" exceeds "formula_14", the search has failed and must convey the failure of the search.In addition, the loop must be exited when the target element is found, or in the case of an implementation where this check is moved to the end, checks for whether the search was successful or failed at the end must be in place.Bentley found that most of the programmers who incorrectly implemented binary search made an error in defining the exit conditions.