[danielstoner]

Hi Deo, here is your algorithm if I understood the problem

Code:

package test;

import java.util.*;

public class BinaryAdd
{
    private static boolean [] add(boolean [] a, boolean [] b)
    {
        // pad them to same length
        int l = a.length > b.length ? a.length : b.length;
        a = Arrays.copyOf(a, l);
        b = Arrays.copyOf(b, l);

        // prevent overflow, make the results bigger
        boolean [] r = new boolean[a.length + 1];
        boolean t = false;

        for (int i = 0; i < l; i++)
        {
            if (a[i] &&  b[i])
            {
                if (t)
                {
                    r[i] = true;
                    t = true;
                }
                else
                {
                    r[i] = false;
                    t = true;
                }
            }
            else if (a[i] ||  b[i])
            {
                if (t)
                {
                    r[i] = false;
                    t = true;
                }
                else
                {
                    r[i] = true;
                    t = false;
                }
            }
            else
            {
                if (t)
                {
                    r[i] = true;
                    t = false;
                }
                else
                {
                    r[i] = false;
                    t = false;
                }
            }
        }

        // check overflow
        if (t)
        {
            r[l] = true;
        }

        return r;
    }

    public static void main(String[] args)
    {
        // least significant position is at 0
        boolean a1[] = {true};
        boolean a2[] = {false};
        boolean a3[] = {true, true};
        boolean a4[] = {false, false};
        boolean a5[] = {true, false};
        boolean a6[] = {false, true};

        boolean a7[] = {true, true, true, true};
        boolean a8[] = {false, true, false, true};

        // keep in mind least significant value is at index 0
        System.out.println(Arrays.toString(a1) + " + " + Arrays.toString(a1) + " = " + Arrays.toString(add(a1, a1)));
        System.out.println(Arrays.toString(a1) + " + " + Arrays.toString(a2) + " = " + Arrays.toString(add(a1, a2)));
        System.out.println(Arrays.toString(a3) + " + " + Arrays.toString(a3) + " = " + Arrays.toString(add(a3, a3)));
        System.out.println(Arrays.toString(a7) + " + " + Arrays.toString(a8) + " = " + Arrays.toString(add(a7, a8)));
    }
}