C++ string push_back function not working - c++

Question

I am trying to generate strings with {0, 1, 2} using an integer queue to store numbers until I am ready to check if they are binary numbers. I am starting with single digits and then appending them to get longer and longer number strings. So the order I am trying to get is 0, 1, 2, 00, 01, 02, 10, 11, 12, 20, 21, 22, 000, 001, 002, 010, 011, 012 e.t.c. The problem I am having though is that when I dequeue an integer from my queue, turn it into a string and try to append it with {0, 1, 2} using s.push_back(app), nothing is appended. Below is my code and output.
int main()
{
string s; //holds strings of numbers that come from the int queue
bool isBin; //holds the boolean value returned from recognizer
int count=0; //while loop counter to not go over 20 iterations
Queue myQ; //queue created to hold all values generated
int numHolder; //holds values dequeued from int queue to be turned into string
myQ.enQueue(0);//queue 3 initial values to work with
myQ.enQueue(1);
myQ.enQueue(2);
while(count<=20)//while loop doesnt go over 20 iterations of binary numbers
{
numHolder=myQ.deQueue();//holds int values dequeued from queue
s=to_string(numHolder);//converts the int from queue to a string
/* isBin=recognizer(s);//send the string to the recognizer
if(isBin==true)
{
cout<<s<<endl;//prints string if it is binary number
count++;//increment counter because string was binary
}*/
for(int i=0; i<3; i++)//this loop adds 0 then 1 then 2 to the end of each dequeued string
{
char app = i;
s.push_back(app);//this is where string is appended with 0 1 or 2
cout<<s<<endl;
int newNum=stoi(s);//new appended string is turned into integer
myQ.enQueue(newNum);//new integer is put into queue
s.pop_back();//pops back the string so other numbers can be created with the original dequeued string
}
count++;
}
// }// end of while
}// end of main
output:
0
0
0
1
1
1
2
2
2
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I can tell by the output it has the right order for the first characters but nothing is being appended to them because the string push_back function is not working. Please help!

Answer 1

char app=i stores the characters whose binary value is 0 1 and 2, not the characters '0', '1' and '2'.
Try char app = '0'+i;
In C/C++ char is both a number type and the traditional way to store a single character. The conversion from int just treats char like a number type.