To understand what's going on here, you'll need some basic knowledge about number systems conversion, which you can find here.

Decimal to binary

int x, y;
int a[100];

cout << "Enter a decimal number: ";
cin >> x;

int i = 0;
do {
    i++;
    a[i] = x % 2;
    x = x / 2;
    y = 2 * x + a[i];
}while (y >= 2);

cout << "Your number in the binary system is: ";
for (; i > 0; i--) {
    cout << a[i];
}
                                    

Binary to decimal

string x;
int result = 0;

cout << "Enter a binary number: ";
cin >> x;

for (short int i = 0; i < x.length(); i++) {
    if (x[i] == '1')
        result = result * 2 + 1;
    else
        result = result * 2;
}

cout << "Your number in the decimal system is: " << result << endl;
                                    

Any number system to decimal

We can use the Horner's method to convert any number system to decimal.

#include <iostream>
#include <vector>

using namespace std;

int horner(int factors[], int polynomialDegree, int x) {
    int result = factors[0];
    for (int i = 1; i <= polynomialDegree; i++)
            result = result * x + factors[i];
    return result;
}

int main() {
    string number = "1010";
    int number_system = 2;

    vector<int> results;
    int *a = new int[number.length()];
    for (int i = 0; i < number.length(); i++)
        a[i] = (int(number[i])) - 48;
    results.push_back(horner(a, number.length() - 1, number_system));

    for (int i = 0; i < results.size(); i++)
        cout << results[i] << "\n";

    return 0;
}