//Tyler Arthur
// Program 8 Assignment 4
// CS 201



#include <iostream>
#include <cmath>
using namespace std;

bool isDigit(char c);
int digit2int(char c);
bool isValid(int d2, int d1, int d0, int base);
int base10(int d2, int d1, int d0, int base);


int main()
{
   int base;
   char a;
   char b;
   char c;
   int d2;
   int d1;
   int d0;
   cout << "Enter the first digit: " << endl;
   cin >> a;
   cout << "Enter the second digit: " << endl;
   cin >> b;
   cout << "Enter the third digit: " << endl;
   cin >> c;
   cout << "Enter the base: ";
   cin >> base;


if (isDigit(a))
{
  cout << a << " " << "is a valid digit" << endl;
 if (isDigit(b))
 {
   cout << b << " " << "is a valid digit" << endl;

     if (isDigit(c))
     {
  cout << c << " " << "is a valid digit" << endl;

       if(base <= 10 && base >=2)
       {
        cout << base << "is a valid base" << endl;

        d2 = digit2int(a);
        d1 = digit2int(b);
        d0 = digit2int(c);

          if(isValid(d2, d1, d0, base))
          {
           cout << d2 << d1 << d0 << " " << "in base" << base <<
           "is equal to" << " " << base10(d2, d1, d0, base) << " " <<
           "in base 10." << endl;

          }
          else
          {
           cout << base << " " << "is not a valid base" << endl;
          }

       }
       else
       {
       cout << d2 << d1 << d0 << " " << "in the given base is not valid"
       <<endl;
       }
       }

     else
     {
     cout << c << "is not a valid digit" << endl;
     }

     }
   else
   {
   cout << b << " " << "is not a valid base" << endl;
   }
   }

 else
 {
 cout << a << " " << "is not a valid digit" <<endl;
}


return 0;
}



bool isDigit(char c)
 {
 if (c >= '0' && c <= '9')
 {
 return true;
 }
 else
 {
 return false;
 }
 }


int digit2int(char c)
{
 return (c - '0');
}


bool isValid(int d2, int d1, int d0, int base)
{
 if(base < d2 || base < d1 || base < d0)
 {
  return true;
 }
 else
 {
 return false;
 }
}

int base10(int d2, int d1, int d0, int base)
{
return (d2 * base * base + d1 * base + d0);
}