0*X9 + 1*X8 + 1*X7 + 0*X6 + 1*X5 + 0*X4 + 1*X3 + 0*X2 + 0*X1 + 1*X0 ovvero
X8 + X7 + X5 + X3 + X0 ovvero 
X8 + X7 + X5 + X3 + 1

/* bit by bit
 * The width of the CRC calculation and result.
 * Modify the typedef for a 16 or 32-bit CRC standard.
 */
typedef uint8_t crc;

#define WIDTH (8 * sizeof(crc))
#define TOPBIT (1 << (WIDTH - 1))

crc
crcSlow(uint8_t const message[], int nBytes)
{
 crc remainder = 0; 


 /*
 * Perform modulo-2 division, a byte at a time.
 */
 for (int byte = 0; byte < nBytes; ++byte)
 {
 /*
 * Bring the next byte into the remainder.
 */
 remainder ^= (message[byte] << (WIDTH - 8));

 /*
 * Perform modulo-2 division, a bit at a time.
 */
 for (uint8_t bit = 8; bit > 0; --bit)
 {
 /*
 * Try to divide the current data bit.
 */
 if (remainder & TOPBIT)
 {
 remainder = (remainder << 1) ^ POLYNOMIAL;
 }
 else
 {
 remainder = (remainder << 1);
 }
 }
 }

 /*
 * The final remainder is the CRC result.
 */
 return (remainder);

} /* crcSlow() */

crc crcTable[256];

void
crcInit(void)
{
 crc remainder;


 /*
 * Compute the remainder of each possible dividend.
 */
 for (int dividend = 0; dividend < 256; ++dividend)
 {
 /*
 * Start with the dividend followed by zeros.
 */
 remainder = dividend << (WIDTH - 8);

 /*
 * Perform modulo-2 division, a bit at a time.
 */
 for (uint8_t bit = 8; bit > 0; --bit)
 {
 /*
 * Try to divide the current data bit.
 */ 
 if (remainder & TOPBIT)
 {
 remainder = (remainder << 1) ^ POLYNOMIAL;
 }
 else
 {
 remainder = (remainder << 1);
 }
 }

 /*
 * Store the result into the table.
 */
 crcTable[dividend] = remainder;
 }



} /* crcInit() */

crc
crcFast(uint8_t const message[], int nBytes)
{
 uint8_t data;
 crc remainder = 0;


 /*
 * Divide the message by the polynomial, a byte at a time.
 */
 for (int byte = 0; byte < nBytes; ++byte)
 {
 data = message[byte] ^ (remainder >> (WIDTH - 8));
 remainder = crcTable[data] ^ (remainder << 8);
 }

 /*
 * The final remainder is the CRC.
 */
 return (remainder);

} /* crcFast() */

// Programma che calcola il CRC di una sequenza di caratteri
// immessi da tastiera, terminati con EOF

#include <stdio.h>

#define PG 0x11021 /* Polinomio generatre */

int crc(int oldcrc, unsigned char toadd); /* Aggiunge toadd al CRC calcolato */

main()
{
int resto=0; // CRC
int c; // Carattere letto
int i = 0; // Contatore dei caratteri

 printf("Inserisci una sequenza di caratteri: ");
 while((c=getchar())!=EOF)
 {
 resto=crc(resto,c); // Agginge il carattere letto al CRC dei precedenti
 i++; // Conta i caratteri letti
 }
 resto=crc(resto,0); // Agginge al CRC i primi otto zeri
 resto=crc(resto,0); // Agginge al CRC i secondi otto zeri in fondo

 printf("\nLetti %d caratteri, CRC calcolato: %x\n", i, resto); 
}

/* Aggiunge i bit del codice oldcrc al dividendo, per
 * calcolare il nuovo CRC
 */ 
int crc(int oldcrc, unsigned char toadd)
{
int i; // Indice del bit

 // I bit del carattere vanno trattati dal piu' significativo al meno
 for(i=0;i<8;i++) // Per ogni bit del byte
 {
 oldcrc= (oldcrc<<1) | (toadd>>7); // Aggiunge il bit piu' significativo
 // del codice in fondo al CRC,
 // spostando a sinistra i bit del CRC
 toadd <<= 1; // Toglie il bit gestito dal codice
 if((oldcrc & 0x10000) != 0) // Se il divisore ci sta' (alla sua maniera)
 {
 oldcrc=oldcrc^PG; // Allora lo toglie (sottrazione senza riporti,
 // quindi XOR
 }
 }
 return oldcrc; // Restituisce il CRC ricalcolato
}

Polynomial: x16 + x12 + x5 + 1
Start Value: 0xFFFF

CRC_POLYNOM = 0x8408;
CRC_PRESET = 0xFFFF;

C-Example:

unsigned internal CRC = CRC_PRESET;
for (i = 0; i < cnt; i++) /* cnt = number of protocol bytes without CRC */
{
    crc ^= DATA[i];
    for (j = 0; j < 8; j++)
    {
        if (crc & 0x0001)
            crc = (crc >> 1) ^ CRC_POLYNOM;
        else
            crc = (crc >> 1);
    }
}