Binary String to Integer Stack

Struggling to separate a string into a stack containing 1's and 0's. Currently I am trying to iterate through the string and parse them into integers to add to a stack. I am entering 1010, in which the result is 1010 , 010, 10, 0 instead of the desired stack being 1, 0, 1, 0

I have used atoi and stoi along with indexing and the .at method to where I still have the same issue.

#include <iostream>
#include <string>
#include <stack>

using namespace std;

bool isParsableInt(string input) {
    string nums = "1234567890";
    string test = input;
    int attempt;
    try {
        if (test == "") { return false; }
        if (test[0] == '-') {
            test = test.substr(1, test.length() - 1);
        }
        for (int i = 0; i < test.length(); i++) {
            if (nums.find(test[i]) == string::npos) { return false; }
            attempt = atoi(&test[i]); // String to integer
        }
        return true;
    }
    catch (...) { // Catches any error thrown
        return false;
    }
}



stack<int> createBinaryStack() {
    string input;
    stack<int> result = stack<int>();
    while (true){
        cout << "Enter a binary number : ";
        cin >> input;
        if (!isParsableInt(input)) {
            cout << "Invalid Input found - Must be 1's & 0's" << endl;
            continue;
        }
        if (count(input, '0') + count(input, '1') != input.length()) {
            cout << "Invalid Number found - Must be 1's & 0's" << endl;
            continue;
        }
        for (int i = 0; i < input.length(); i++) {
            cout << stoi(&input.at(i)) << "\t"; // Issue on atoi and stoi functions do not seem to work
            result.push(stoi(&input.at(i)));
        }
        cout << endl;
        return result;
    }
}


int binaryStackToDecimal(stack<int> stk){
    int count = stk.size();
    int total = 0;
    for (int i = 0; i < count; i++) {
        if (stk.top() != 1 && stk.top() != 0) {
            return -1; 
        }
        total += stk.top() * pow(2, i);
        stk.pop();
    }
    return total;
}



int main(){
    stack<int> stk = createBinaryStack();
    while (!stk.empty()) {
        cout << stk.top();
        stk.pop();
    }
    cout << endl;
    cout << binaryStackToDecimal(stk);
}