Add Binary

class Solution {
    public String addBinary(String a, String b) {
        String sum = "";
        String realSum = "";
        String min = "";
        int forward = 0;
        String max = "";
        int result = 0;
        int first;
        int second;
        if(a.length()>b.length()){

            for(int i = 0; i<a.length(); i++){
                if(a.charAt(i)!='0'){
                    max = a.substring(i);
                    break;
                }
            }
            
            for(int i = 0; i<b.length(); i++){
                if(b.charAt(i)!='0'){
                    min = b.substring(i);
                    break;
                }
            }
            
            if(min == ""){
                min = "0";
            }
            if(max == ""){
                max = "0";
            }

            
        }
        else{

            
            for(int i = 0; i<b.length(); i++){
                if(b.charAt(i)!='0'){
                    max = b.substring(i);
                    break;
                }
            }
            
            for(int i = 0; i<a.length(); i++){
                if(a.charAt(i)!='0'){
                    min = a.substring(i);
                    break;
                }
            }
            
            if(min == ""){
                min = "0";
            }
            if(max == ""){
                max = "0";
            }

        }
        
        
        for(int i = 0; i<min.length(); i++){

            first = min.charAt(min.length()-1-i) - '0';
            second = max.charAt(max.length()-1-i) - '0';
            result = first + second + forward;

            if(result < 2){
                sum += "" + result;
                forward = 0;
            }
            else{
                sum += "" + (result-2);
                forward = 1;
            }
            
        }
        
        if(a.length()==b.length()){
            if(forward == 1){
                sum += "1";
            }
            for(int i = sum.length() - 1; i >= 0; i--){
                realSum += sum.charAt(i);
            }
            
            return realSum;
        }
        
        for(int z = max.length()-min.length()-1; z>=0; z--){
            
            result = (max.charAt(z)-'0') + forward;
            
            if(result < 2){
                sum += "" + result;
                forward = 0;
            }
            else{
                sum += "" + (result - 2);
                forward = 1;
            }
        }
        
        

        if(forward == 1){
            sum += "1";
        }
        
        
        
        for(int i = sum.length() - 1; i >= 0; i--){
            realSum += sum.charAt(i);
        }
        
        return realSum;
    }
    
}