#include <stdio.h>
#include<string.h>

#define SIZE 100
#define LIMIT 32

double num2dec ( char *num, unsigned int base )
{
  unsigned int point, pos, whole, boost;
  double frac;
  
  // find the point position
  for ( point=0; (num[point]!='.' && num[point] != '\0'); ++point ) ;
  // calculate the decimal equivalent of the whole part
  for ( pos=point, boost=1, whole=0; pos>0; --pos ) {
    if ( (num[pos-1] >= '0') && (num[pos-1] <= '9') )
      whole += (num[pos-1]-'0') * boost;
    if ( (num[pos-1] >= 'A') && (num[pos-1] <= 'Z') )
      whole += (num[pos-1]-'A'+10) * boost;
    boost *= base;
  }
  // calculate the decimal equivalent of the fractional part
  if ( num[point] != '\0' ) {
    for ( pos=point, boost=base, frac=0; num[pos+1] != '\0'; ++pos ) {
      if ( (num[pos+1] >= '0') && (num[pos+1] <= '9') )
        frac += (double) (num[pos+1]-'0') / boost;
      if ( (num[pos+1] >= 'A') && (num[pos+1] <= 'Z') )
        frac += (double) (num[pos+1]-'A'+10) / boost;
      boost *= base;
    }
  }
  return whole+frac;
}

char *dec2new ( double dec, unsigned int new )
{
  unsigned int whole = dec, itr = 0;
  double frac = dec - whole;
  char num[SIZE] = "", part[SIZE] = "", digit[SIZE];
  
  // calculate equivalent number in new base of the whole part
  while ( whole > 0 ) {
    sprintf(digit, "%u", whole%new);
    strcat(digit, num);
    strcpy(num, digit);
    whole /= new;
  }
  
  // calculate equivalent number in new base of the fractional part
  while ( frac > 0 ) {
    // breaking for potential non-terminating sequences
    if ( ++itr > LIMIT ) break;
    
    frac = frac * new;
    if ( frac >= 10 ) digit[0] = (int)frac + 'A' - 10;
    else digit[0] = (int)frac + '0';
    digit[1] = '\0';
    strcat(part, digit);
    frac -= (int)frac;
  }
  
  // determine whether the output is not a whole number and put point in between
  if ( part[0] != '\0' ) strcat(num, "."); 
  
  return strcat(num, part);
}

int main ()
{
  char num[SIZE];
  unsigned int base, new;
  double dec;
  
  // take a number as a string
  printf("Enter Number: "); scanf("%s", num);
  // take the base of the number
  printf("Enter Base (<= 36): "); scanf("%u", &base);
  
  // output the number in decimal (base 10)
  dec = num2dec(num,base);
  printf("Number in Base 10 (Decimal) = %.32lg\n", dec);
  
  // take a new base as input
  printf("Enter New Base (<= 36): "); scanf("%u", &new);
  
  // output the number in new base
  printf("Number in Base %u = %s\n", new, dec2new(dec,new));
  
  return 0;
}