Add Binary

Given two binary strings, return their sum (also a binary string).

For example,
a = "11"
b = "1"
Return "100".

class Solution {
public:
    string addBinary(string a, string b) {
        int flag=0;
        int aIndex=a.size()-1;
        int bIndex=b.size()-1;
        string c;
        while(aIndex>=0 && bIndex>=0){
            int num=(a[aIndex]-'0')+(b[bIndex]-'0')+flag;
            flag=num/2;
            num=num%2;
            c=char(num+'0')+c;
            aIndex--;
            bIndex--;
        }
        while(aIndex>=0){
            int num=a[aIndex]-'0'+flag;
            flag=num/2;
            num=num%2;
            c=char(num+'0')+c;
            aIndex--;
        }
        while(bIndex>=0){
            int num=b[bIndex]-'0'+flag;
            flag=num/2;
            num=num%2;
            c=char(num+'0')+c;
            bIndex--;
        }
        if(flag==1){
            c='1'+c;
        }
        return c;

    
        
    }
};