trol

        // 0 padding for the shorter binary string
        // (this step isn't necessary, but easier for noob solution)
        if(b.length()>a.length()){
            int temp = b.length()-a.length();
            for(int i=0; i<temp; i++){
                a = "0"+a;
            }
        }else if(b.length()<a.length()){
            int temp = a.length()-b.length();
            for(int i=0; i<temp; i++){
                b = "0"+b;
            }
        }


        // Initializing
        int curSum = 0;
        int carry = 0;
        String result = "";

        // From the rightmost character to the leftmost
        for(int i=a.length()-1; i>=0; i--){
            curSum = (a.charAt(i)-48)+(b.charAt(i)-48)+carry;
            if(curSum==0){
                result = "0"+result;
                carry = 0;
            }else if(curSum==1){
                result = "1"+result;
                carry = 0;
            }else if(curSum==2){
                result = "0"+result;
                carry = 1;
            }else{
                result = "1"+result;
                carry = 1;
            }
        }

        if(carry==1){
            return "1"+result;
        }
        return result;