一、什么是CRC校验 循环校验码(Jyclic Redundancy Check,简称CRC码): 是数据通信领域中最常用的一种差错校验码,其特征是信息字段和校验字段的长度可以任意选定。
二、CRC校验计算 CRC码是由两部分组成,前部分是信息码,就是需要校验的信息,后部分是校验码,如果CRC码共长n个bit,信息码长k个bit,它的编码规则是: 1、首先将原信息码(kbit)左移r位(k+r=n),对应多项式为m(x)。 2、运用一个生成R次多项式g(x)(也可看成二进制数)用模2除上面的式子,得到的余数就是校验码,r=R。 非常简单,要说明的:模2除就是在除的过程中用模2加,模2加实际上就是我们熟悉的异或运算,就是加法不考虑进位,公式是: 0+0=1+1=0,1+0=0+1=1,即‘异’则真,‘非异’则假。 由此得到定理:a+b+b=a 也就是‘模2减’和‘模2加’直值表完全相同。 有了加减法就可以用来定义模2除法,于是就可以用生成多项式g(x)生成CRC校验码。 例如:代码1010111对应的多项式为x6+x4+x2+x+1,而多项式为x5+x3+x2+x+1对应的代码101111。 现在计算 信息码1011001(多项式为x6+x4+x3+1),生成多项式g(x)=x4+x3+1(信息码为11001)的CRC,计算过程如下 step1: 1011001左移4位得到10110010000 steo2: 采用多项式除法: 得余数为: 1010 (即校验字段为:1010) 除法没有数学上的含义,而是采用计算机的模二除法,即,除数和被除数做异或运算。进行异或运算时除数和被除数最高位对齐,按位异或。
1011001 0000
-11001
--------------------------
=01111010000
1111010000
-11001
-------------------------
=0011110000
11110000
-11001
--------------------------
=00111000
111000
- 11001
-------------------
= 001010 CRC码即为1011001,1010 (逗号前为信息码,后为校验码)
三、编程实现
 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,实际应用 发送方:发出的传输字段为: 1 0 1 1 0 0 1 1 0 10 信息字段 校验字段 接收方:使用相同的生成码进行校验:接收到的字段/生成码(二进制除法) 如果能够除尽,则正确 五CRC16-CCITT(校验码生成多项式为:G(X) =X16+X12+X5+X0 ) 1.第一种方法(若原数据长度比较长时,结果可能不对)
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;

}
调用方法
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);
}
结果: 第二种方法,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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