public int[] numSub(int[] minuend, int[] subtrahend) {
                // flip subtrahend
                int arrayLength = minuend.length;
                int[] flipped = new int[arrayLength];
                for (int i=0; i<subtrahend.length; i++) {
                        if (subtrahend[i] == 0)
                                flipped[i] = 1;
                        else    flipped[i] = 0;
                }
                for (int i=subtrahend.length; i<arrayLength; i++) flipped[i]=1;
                // add one... = X
                int[] one = {1};
                int[] X = numAdd(one, flipped);
                // add minuend and X, but drop the MSB.
                int[] difference = numAdd(minuend, X);
                difference[difference.length-1] = 0;

                return difference;
        }