Missing number

#include <bits/stdc++.h> 
int decimal(string a)
{
    int k = 0 ; 
    int dec = 0 ; 
    for(int i = a.size() - 1 ; i >= 0 ; i--)
    {
      int d  = a[i] - '0' ;
      dec = dec + d * pow(2 , k)  ;
      k++ ;    
    }
    return dec ; 
}
string binary(int a)
{
    string res = "" ;
    while(a != 0)
    {
        int  k = a % 2 ; 
        if(k == 0)
        {
            res = '0' + res ; 
        }
        else{
            res = '1' + res; 
        }
        a = a/ 2 ; 
    }
    if(res == "")
    {
        return "0";
    }
    return res ; 
}
string findMissingNumber(vector<string> &binaryNums, int n) 
{
    // Write your code here.
    vector <int> hash(n +1 , 0) ;
    for(int i = 0 ; i < binaryNums.size() ;i++)
    {
        int dec = decimal(binaryNums[i]);
        hash[dec]++ ;
    }
    for(int i = 0 ; i < hash.size() ;i++)
    {
        if(hash[i] == 0)
        {
            return binary(i) ;
        }
    }
    return "a" ;

}