private static String gradeSchoolMult(int[] multX, int[] multY){
		// the size of the result is at most going to be the size of X and Y
		
		int[] result = new int[multX.length + multY.length];
		
		// this is where the algorithm really starts; the previous lines were "pre-computation"
		// fix y (the second multiplier) on a single digit, multiply it through for each digit in x
		startTime = System.currentTimeMillis();
		for (int i = 0; i < multY.length; i++) {
			for (int j = 0; j < multX.length; j++){
				result[i + j] += multY[i]*multX[j];
			}
		}

private static int[] carryCorrect(int[] toCorrect) {
		// we're starting at 1 because the first digit will never need correction
		for (int i = 1; i < toCorrect.length; i++){		
			// affecting i+1 is normally dangerous as it can lead to an index out of bounds exception
			// except here we know that most significant digit won't ever trigger these if-statements
			if (toCorrect[i] > 1) {
				// if the entry is an even number, we know that this should be a binary 0
				if (toCorrect[i]%2 == 0) {	
					toCorrect[i+1] += toCorrect[i]/2; // carry the total complete bits to the next column
					toCorrect[i] = 0;
				// otherwise the entry is an odd number, so 
				} else {
					toCorrect[i+1] += (toCorrect[i] - 1)/2; // carry the total complete bits to the next column
					toCorrect[i] = 1;
				}
			}
		}
		
		return toCorrect;
	}