A/D Converter

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

using namespace std;
// Auxiliary Function
vector <int> binary(int n){
    int numOfDigits = int(log(n) / log(2)) + 1;
    // 3. Check the case of 0 or the overflow case
    if(n > INT_MAX){
        cout << "Cannot make calculations with numbers higher than: " << INT_MAX << endl << endl;
    }
    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);
        }
    }
    return digits;
}



int main()
{
    // 1. Intro
    cout << "Welcome to the A/D Converter!\n\n";
    cout << "1. Give me the Reference Voltage (V_ref): ";
    double V_ref;
    cin >> V_ref;
    while(V_ref <= 0){
        cout << "Non-positive V_ref is not acceptable.\n";
        cout << "Give me the Reference Voltage (V_ref): ";
        cin >> V_ref;
    }
    cout << "\n2. Now give me how many digits the transformed binary word must have (up to 2).\n";
    cout << "Number of digits: ";
    int numOfDigits;
    cin >> numOfDigits;
    while(numOfDigits < 2){
        cout << "Number of digits: ";
        cin >> numOfDigits;
    }

    cout << "\n3. Last step is to give me the voltage you count with your polymeter to convert it into binary word (V_count).\n";
    double V_count;
    cin >> V_count;
    while(V_count < 0 || V_count > V_ref){
        cout << "Give me the voltage you count with your polymeter to convert it into binary word (V_count).\n";
        cin >> V_count;
    }

    // 2. Convert
    double step = V_ref / (pow(2, numOfDigits) - 1);
    vector <double> voltages = vector <double> ();
    for(double voltage=0; voltage<=V_ref; voltage+=step){
        voltages.push_back(voltage);
    }

    int indexNumber = -1;
    for(unsigned int i=0; i<voltages.size(); i++){
        if(voltages[i]-step/2 <= V_count && V_count < voltages[i]+step/2){
            indexNumber = i;
        }
    }
    cout << V_count << " ---> ";
    vector <int> digits = binary(indexNumber);
    unsigned int digitsSize = digits.size();
    // Complete with zeros when necessary
    for(unsigned int i=0; i<numOfDigits-digitsSize; i++){
        cout << "0";
    }
    // Display the vector "digits"
    for(unsigned int i=0; i<digitsSize; i++){
        cout << digits[i];
    }

    return 0;
}