一、什么是CRC校驗(yàn) 循環(huán)校驗(yàn)碼（Jyclic Redundancy Check,簡(jiǎn)稱CRC碼): 是數(shù)據(jù)通信領(lǐng)域中最常用的一種差錯(cuò)校驗(yàn)碼，其特征是信息字段和校驗(yàn)字段的長(zhǎng)度可以任意選定。
二、CRC校驗(yàn)計(jì)算
CRC碼是由兩部分組成，前部分是信息碼，就是需要校驗(yàn)的信息，后部分是校驗(yàn)碼，如果CRC碼共長(zhǎng)n個(gè)bit，信息碼長(zhǎng)k個(gè)bit，它的編碼規(guī)則是：
1、首先將原信息碼(kbit)左移r位(k+r=n),對(duì)應(yīng)多項(xiàng)式為m(x)。
2、運(yùn)用一個(gè)生成R次多項(xiàng)式g(x)（也可看成二進(jìn)制數(shù)）用模2除上面的式子，得到的余數(shù)就是校驗(yàn)碼，r=R。
非常簡(jiǎn)單，要說(shuō)明的：模2除就是在除的過(guò)程中用模2加，模2加實(shí)際上就是我們熟悉的異或運(yùn)算，就是加法不考慮進(jìn)位，公式是：
0+0=1+1=0,1+0=0+1=1，即‘異’則真，‘非異’則假。
由此得到定理：a+b+b=a 也就是‘模2減’和‘模2加’直值表完全相同。
有了加減法就可以用來(lái)定義模2除法，于是就可以用生成多項(xiàng)式g(x)生成CRC校驗(yàn)碼。
例如：代碼1010111對(duì)應(yīng)的多項(xiàng)式為x6+x4+x2+x+1，而多項(xiàng)式為x5+x3+x2+x+1對(duì)應(yīng)的代碼101111。
現(xiàn)在計(jì)算 信息碼1011001（多項(xiàng)式為x6+x4+x3+1），生成多項(xiàng)式g(x)=x4+x3+1（信息碼為11001）的CRC，計(jì)算過(guò)程如下
step1: 1011001左移4位得到10110010000
steo2: 采用多項(xiàng)式除法: 得余數(shù)為: 1010 (即校驗(yàn)字段為：1010）
除法沒(méi)有數(shù)學(xué)上的含義，而是采用計(jì)算機(jī)的模二除法，即，除數(shù)和被除數(shù)做異或運(yùn)算。進(jìn)行異或運(yùn)算時(shí)除數(shù)和被除數(shù)最高位對(duì)齊，按位異或。
1011001 0000
-11001
--------------------------
=01111010000
1111010000
-11001
-------------------------
=0011110000
11110000
-11001
--------------------------
=00111000
111000
- 11001
-------------------
= 001010
CRC碼即為1011001,1010 (逗號(hào)前為信息碼，后為校驗(yàn)碼)
三、編程實(shí)現(xiàn)
  uint cal_crc(uchar *ptr, uchar len)  {
 uint crc;
uchar i;
crc=0;
  while (len--!=0) {
for (i=0x80; i!=0; i/=2) {
if ((crc&0x8000)!=0){
crc*=2; crc^=0x1021;
 } else crc*=2;
if ((*ptr&i)!=0)
crc^=0x1021;
}
ptr++;
}
return(crc);
 }
四，實(shí)際應(yīng)用
發(fā)送方：發(fā)出的傳輸字段為: 1 0 1 1 0 0 1 1 0 10
信息字段 校驗(yàn)字段
接收方：使用相同的生成碼進(jìn)行校驗(yàn):接收到的字段/生成碼（二進(jìn)制除法）
如果能夠除盡，則正確
五CRC16-CCITT(校驗(yàn)碼生成多項(xiàng)式為：G(X) =X16+X12+X5+X0 )
1.第一種方法（若原數(shù)據(jù)長(zhǎng)度比較長(zhǎng)時(shí)，結(jié)果可能不對(duì)）
 void GetSRC16CCITTCheckCode(char *cSrc, int cLen, char *cDest)
{
int Poly = 0x8408;
int len = cLen;
unsigned int Crc;
int j, i_bits, carry;
Crc = 0;
for ( j=0 ; j < len ; j++ )
{
Crc = Crc ^ cSrc[j];
for ( i_bits=0 ; i_bits < 8 ; i_bits++ )
{
carry = Crc & 1 ;
Crc = Crc / 2 ;
if ( carry )
{
Crc = Crc ^ Poly;
}
}
}
int a[] = {Crc};
cDest[0] = ((a[0] >> 8) << 32) >> 32;
cDest[1] = (a[0] << 32) >> 32;
}調(diào)用方法
void CTest22Dlg::OnButton1()
{
unsigned char tt[] = {0x00,0x01,0x01,0x03,0x00,0x02,0x13,0x09,0x00,0x01,0x00};
char aa[] = {0x00,0x00};
GetSRC16CCITTCheckCode((char*)tt,11,aa);
}
結(jié)果：  第二種方法，查表法
/**//*
13 * This mysterious table is just the CRC of each possible byte. It can be
14 * computed using the standard bit-at-a-time methods. The polynomial can
15 * be seen in entry 128, 0x8408. This corresponds to x^0 + x^5 + x^12.
16 * Add the implicit x^16, and you have the standard CRC-CCITT.
17 */
unsigned int const crc_ccitt_table[256] = {
0x0000, 0x1189, 0x2312, 0x329b, 0x4624, 0x57ad, 0x6536, 0x74bf,
0x8c48, 0x9dc1, 0xaf5a, 0xbed3, 0xca6c, 0xdbe5, 0xe97e, 0xf8f7,
0x1081, 0x0108, 0x3393, 0x221a, 0x56a5, 0x472c, 0x75b7, 0x643e,
0x9cc9, 0x8d40, 0xbfdb, 0xae52, 0xdaed, 0xcb64, 0xf9ff, 0xe876,
0x2102, 0x308b, 0x0210, 0x1399, 0x6726, 0x76af, 0x4434, 0x55bd,
0xad4a, 0xbcc3, 0x8e58, 0x9fd1, 0xeb6e, 0xfae7, 0xc87c, 0xd9f5,
0x3183, 0x200a, 0x1291, 0x0318, 0x77a7, 0x662e, 0x54b5, 0x453c,
0xbdcb, 0xac42, 0x9ed9, 0x8f50, 0xfbef, 0xea66, 0xd8fd, 0xc974,
0x4204, 0x538d, 0x6116, 0x709f, 0x0420, 0x15a9, 0x2732, 0x36bb,
0xce4c, 0xdfc5, 0xed5e, 0xfcd7, 0x8868, 0x99e1, 0xab7a, 0xbaf3,
0x5285, 0x430c, 0x7197, 0x601e, 0x14a1, 0x0528, 0x37b3, 0x263a,
0xdecd, 0xcf44, 0xfddf, 0xec56, 0x98e9, 0x8960, 0xbbfb, 0xaa72,
0x6306, 0x728f, 0x4014, 0x519d, 0x2522, 0x34ab, 0x0630, 0x17b9,
0xef4e, 0xfec7, 0xcc5c, 0xddd5, 0xa96a, 0xb8e3, 0x8a78, 0x9bf1,
0x7387, 0x620e, 0x5095, 0x411c, 0x35a3, 0x242a, 0x16b1, 0x0738,
0xffcf, 0xee46, 0xdcdd, 0xcd54, 0xb9eb, 0xa862, 0x9af9, 0x8b70,
0x8408, 0x9581, 0xa71a, 0xb693, 0xc22c, 0xd3a5, 0xe13e, 0xf0b7,
0x0840, 0x19c9, 0x2b52, 0x3adb, 0x4e64, 0x5fed, 0x6d76, 0x7cff,
0x9489, 0x8500, 0xb79b, 0xa612, 0xd2ad, 0xc324, 0xf1bf, 0xe036,
0x18c1, 0x0948, 0x3bd3, 0x2a5a, 0x5ee5, 0x4f6c, 0x7df7, 0x6c7e,
0xa50a, 0xb483, 0x8618, 0x9791, 0xe32e, 0xf2a7, 0xc03c, 0xd1b5,
0x2942, 0x38cb, 0x0a50, 0x1bd9, 0x6f66, 0x7eef, 0x4c74, 0x5dfd,
0xb58b, 0xa402, 0x9699, 0x8710, 0xf3af, 0xe226, 0xd0bd, 0xc134,
0x39c3, 0x284a, 0x1ad1, 0x0b58, 0x7fe7, 0x6e6e, 0x5cf5, 0x4d7c,
0xc60c, 0xd785, 0xe51e, 0xf497, 0x8028, 0x91a1, 0xa33a, 0xb2b3,
0x4a44, 0x5bcd, 0x6956, 0x78df, 0x0c60, 0x1de9, 0x2f72, 0x3efb,
0xd68d, 0xc704, 0xf59f, 0xe416, 0x90a9, 0x8120, 0xb3bb, 0xa232,
0x5ac5, 0x4b4c, 0x79d7, 0x685e, 0x1ce1, 0x0d68, 0x3ff3, 0x2e7a,
0xe70e, 0xf687, 0xc41c, 0xd595, 0xa12a, 0xb0a3, 0x8238, 0x93b1,
0x6b46, 0x7acf, 0x4854, 0x59dd, 0x2d62, 0x3ceb, 0x0e70, 0x1ff9,
0xf78f, 0xe606, 0xd49d, 0xc514, 0xb1ab, 0xa022, 0x92b9, 0x8330,
0x7bc7, 0x6a4e, 0x58d5, 0x495c, 0x3de3, 0x2c6a, 0x1ef1, 0x0f78
};
static inline unsigned int crc_ccitt_byte(unsigned int crc, const char c)
{
return (crc >> 8) ^ crc_ccitt_table[(crc ^ c) & 0xff];
}
unsigned int crc_ccitt(char const *buffer, size_t iBeginIndex, size_t len)
{
unsigned int crc = 0;
int j, i_bits, carry;
for( j=iBeginIndex ; j < len ; j++ )
{
crc = crc_ccitt_byte(crc, buffer[j]);
}
return crc;
}
void CUtility::GetSRC16CCITTCheckCode(char *cSrc, int cBegIndex, int cLen, char *cDest)
{
unsigned int Crc = crc_ccitt(cSrc,cBegIndex,cLen);
int a[] = {Crc};
cDest[0] = ((a[0] >> 8) << 32) >> 32;
cDest[1] = (a[0] << 32) >> 32;
// char cStr[cLen-cBegIndex] = {0};
// for(int i=cBegIndex; i<cLen; i++)
// {
// TRACE(L"%02X ",cSrc[i]);
// }
// int Poly = 0x8408;
// int len = cLen;
// unsigned int Crc;
// int j, i_bits, carry;
// Crc = 0;
// for ( j=cBegIndex ; j < len ; j++ )
// {
// Crc = Crc ^ cSrc[j];
// for ( i_bits=0 ; i_bits < 8 ; i_bits++ )
// {
// carry = Crc & 1 ;
// Crc = Crc / 2 ;
// if ( carry )
// {
// Crc = Crc ^ Poly;
// }
// }
// }
//
// int a[] = {Crc};
//
// cDest[0] = ((a[0] >> 8) << 32) >> 32;
// cDest[1] = (a[0] << 32) >> 32;
}
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