Adding two integer arrays

I have done some searching for this, however I haven't found anything specific to what I'm working on.

I'm trying to do addition with two arrays of integers. This alone isn't difficult, however, I'm having difficulty with a specific aspect.

The array size and array elements are determined by user input. Each digit must be greater than or equal to 0 and less than or equal to 9. The problem lies in the fact that if I initialize an array in my method, I must determine the size of the array when I initialize it. But if the user enters a series of numbers, such as 8, 0, 0, 0 for the first array, and 3, 0, 0, 0 for the second array, that would result in the sum[] being one integer bigger than either of the arrays initialized by the user. I don't want to do

int[] sum = new int[x.length+1]

because in the case of it not needing an extra element, I will get an ugly 0 where I don't want to see that. I'm not necessarily asking for a direct answer with code, but perhaps a bit of wisdom that will push me in the right direction. Thanks.

public static int[] addArrays(int[] x, int[] y){
int[] sum = new int[?];
int carryOver = 0;
int singleDigit = 0;