Concatenating two strings in C++ (binary number addition)

Question

I have problem with concatenating two strings in C++. What I want to do is to convert a binary number inputted by the user and align its length so that I can further add two numbers inputted. I'm using array of string for input purpose:

char* num1, num2;

For example user types two numbers:

 100010
 1010

And I want to process them with the following structure:

100010
001010

Depending on which string is longer in loop I create another string where I add missing zeros:

    char temp2[x];
    for (int i=0; i <(x-y); i++)  //x,y is strlen(num1 or num2)
    temp2[i]=48;
    strcat(temp2, num2);

Unfortunately some strange characters appear between two strings and the second string looks like:

00d↑ą,@1010 not simply 001010

Later on I wanted to convert this string into array of int thus I could use full adder algorithm:

for(i = 0; i < lengthofString ; i++){
sum[i] = ((a[i] ^ b[i]) ^ c); // c is carry
c = ((a[i] & b[i]) | (a[i] & c)) | (b[i] & c); 
}

Advises on how to solve the problem of adding two different sizes binary numbers are also really welcome.

EDIT: OK, so I tried to follow using std::bitset library but I have no clue whether any piece of code I wrote is correct. Unfortunately I have no access to compiler now (using Android tablet). Result of my work:

#include <bitset>
#include <iostream>
#include "binary.h"

using namespace std;

void binary::add(string string1, string string2){

cin >> string1;
cin >> string2;

bitset<20> num1 (string1);
bitset<20> num2 (string2);

// not sure how to use loop operators with bitset as it's my very first piece of code and do I need to assign "c" argument first?

for(int i = 0; i < 20 ; i++){  
sum[i] = ((num1[i] ^ num2[i]) ^ c); // c is carry
c = ((num1[i] & num2[i]) | (num1[i] & c)) | (num2[i] & c); 
}

for (int j=0; i < 20; j++)
cout << sum[j];

}

Answer 1

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <sstream>

using namespace std;

main ()
{
    ostringstream os;
    istringstream is;

    float num=0;
    int a=8;
    b=6;

    cin >>a>>b;

    os << a << "."<< b;

    is(os.str());
    is >> num;

    cout << num;
    cout << num * 2;

    return 0;
}