Decimal to Binary

#include <iostream>
#include <math.h>
#include <vector>
#include <algorithm>

using namespace std;

void displayVector(vector <int> v){
    for(unsigned i=0; i<v.size(); i++){
        cout << v[i];
    }
    //cout << endl;
}

int main()
{
    // 1. Intro
    menu:
    cout << "Give me a natural number (in decimal system) to convert it into binary:\n";
    double input;
    cin >> input;

    // 2. Convert to integer in case of error
    int n = int(fabs(input));
    int numOfDigits = int(log2(n)) + 1;
    //cout << numOfDigits << endl;
    //cout << "Logs: " << log(n) << " / " << log(2) << " = " << log(n) / log(2) << " ----> " << int(log(n) / log(2)) + 1 << endl;
    cout << "Decimal: " << n << endl;

    // 3. Check the case of 0 or the overflow case
    if(n == 0){
        cout << "Binary : 0 (No specified number of digits)" << endl << endl;
        goto menu;
    }
    if(n > 1000000000){
        cout << "Cannot make calculations with numbers higher than: " << 1000000000 << endl << endl;
        return -1000;
    }

    // 4. Search the digits
    vector <int> digits = vector <int> ();
    int sum = n;
    for(int i=numOfDigits-1; i>=0; i--){
        if(sum >= pow(2, i)){
            digits.push_back(1);
            sum -= pow(2, i);
        }
        else{
            digits.push_back(0);
        }
    }

    cout << "Binary : ";
    displayVector(digits);
    cout << "  (" << numOfDigits << " digits)";
    cout << endl << endl;
    goto menu;

    return 0;
}