CRC校验码的基本思想是利用线性编码理论， 在发送端根据要传送的k位二进制码序列，以一定的规则产生一个校验用的监督码（既CRC码）r位，并附在信息后边，构成一个新的二进制码序列数共(k+r)位，最后发送出去。在接收端，则根据信息码和CRC码之间所遵循的规则进行检验，以确定传送中是否出错。
在数据存储和数据通讯领域，CRC无处不在:著名的通讯协议X.25的FCS(帧检错序列)采用的是CRC. CCITT，ARJ、LHA等压缩工具软件采用的是CRC32，磁盘驱动器的读写采用了CRC16，通用的图像存储格式GIF、TIFF等也都用CRC作为检错手段。
CRC的本质是模-2除法的余数，采用的除数不同，CRC的类型也就不一样。通常，CRC的除数用生成多项式来表示。最常用的CRC码的生成多项式有CRC16,CRC32.
以CRC16为例,16位的CRC码产生的规则是先将要发送的二进制序列数左移16位（既乘以2^16）后，再除以一个多项式，最后所得到的余数既是CRC码，如下式所示，其中K(X)表示n位的二进制序列数，G(X)为多项式，Q(X)为整数，R(X)是余数（既CRC码）。
K(X)>>16=G(x)Q(x)+R(x)
求CRC码所采用模2加减运算法则，既是不带进位和借位的按位加减，这种加减运算实际上就是逻辑上的异或运算，加法和减法等价，乘法和除法运算与普通代数式的乘除法运算是一样，符合同样的规律。生成CRC码的多项式如下，其中CRC-16和CRC-CCITT产生16位的CRC码，而CRC-32则产生的是32位的CRC码
接收方将接收到的二进制序列数（包括信息码和CRC码）除以多项式，如果余数为0，则说明传输中无错误发生，否则说明传输有误，关于其原理这里不再多述。用软件计算CRC码时，接收方可以将接收到的信息码求CRC码，比较结果和接收到的CRC码是否相同。
CCITT推荐的高级数据链路控制规程HDLC的帧校验序列FCS中，使用CCITT-16即CRC16,其生成多项式为G(x)=x16+x12+x5+1, CRC-32的生成多项式为G(x)=x32+x26+x23+x22+x16+x11+x10+x16+x8+x7+x5+x4+x2+x+1
比如在c里面01 01 12 00 00 00 65计算CRC16得到 1b81 在java里面直接将c的代码直接改过去 有时候这样实现是不行的 有兴趣的可以试一试
比如下面的例子：
这是个c语言中的crc16
static const unsigned short crc16tab[256]= {
0x0000,0x1021,0x2042,0x3063,0x4084,0x50a5,0x60c6,0x70e7,
0x8108,0x9129,0xa14a,0xb16b,0xc18c,0xd1ad,0xe1ce,0xf1ef,
0x1231,0x0210,0x3273,0x2252,0x52b5,0x4294,0x72f7,0x62d6,
0x9339,0x8318,0xb37b,0xa35a,0xd3bd,0xc39c,0xf3ff,0xe3de,
0x2462,0x3443,0x0420,0x1401,0x64e6,0x74c7,0x44a4,0x5485,
0xa56a,0xb54b,0x8528,0x9509,0xe5ee,0xf5cf,0xc5ac,0xd58d,
0x3653,0x2672,0x1611,0x0630,0x76d7,0x66f6,0x5695,0x46b4,
0xb75b,0xa77a,0x9719,0x8738,0xf7df,0xe7fe,0xd79d,0xc7bc,
0x48c4,0x58e5,0x6886,0x78a7,0x0840,0x1861,0x2802,0x3823,
0xc9cc,0xd9ed,0xe98e,0xf9af,0x8948,0x9969,0xa90a,0xb92b,
0x5af5,0x4ad4,0x7ab7,0x6a96,0x1a71,0x0a50,0x3a33,0x2a12,
0xdbfd,0xcbdc,0xfbbf,0xeb9e,0x9b79,0x8b58,0xbb3b,0xab1a,
0x6ca6,0x7c87,0x4ce4,0x5cc5,0x2c22,0x3c03,0x0c60,0x1c41,
0xedae,0xfd8f,0xcdec,0xddcd,0xad2a,0xbd0b,0x8d68,0x9d49,
0x7e97,0x6eb6,0x5ed5,0x4ef4,0x3e13,0x2e32,0x1e51,0x0e70,
0xff9f,0xefbe,0xdfdd,0xcffc,0xbf1b,0xaf3a,0x9f59,0x8f78,
0x9188,0x81a9,0xb1ca,0xa1eb,0xd10c,0xc12d,0xf14e,0xe16f,
0x1080,0x00a1,0x30c2,0x20e3,0x5004,0x4025,0x7046,0x6067,
0x83b9,0x9398,0xa3fb,0xb3da,0xc33d,0xd31c,0xe37f,0xf35e,
0x02b1,0x1290,0x22f3,0x32d2,0x4235,0x5214,0x6277,0x7256,
0xb5ea,0xa5cb,0x95a8,0x8589,0xf56e,0xe54f,0xd52c,0xc50d,
0x34e2,0x24c3,0x14a0,0x0481,0x7466,0x6447,0x5424,0x4405,
0xa7db,0xb7fa,0x8799,0x97b8,0xe75f,0xf77e,0xc71d,0xd73c,
0x26d3,0x36f2,0x0691,0x16b0,0x6657,0x7676,0x4615,0x5634,
0xd94c,0xc96d,0xf90e,0xe92f,0x99c8,0x89e9,0xb98a,0xa9ab,
0x5844,0x4865,0x7806,0x6827,0x18c0,0x08e1,0x3882,0x28a3,
0xcb7d,0xdb5c,0xeb3f,0xfb1e,0x8bf9,0x9bd8,0xabbb,0xbb9a,
0x4a75,0x5a54,0x6a37,0x7a16,0x0af1,0x1ad0,0x2ab3,0x3a92,
0xfd2e,0xed0f,0xdd6c,0xcd4d,0xbdaa,0xad8b,0x9de8,0x8dc9,
0x7c26,0x6c07,0x5c64,0x4c45,0x3ca2,0x2c83,0x1ce0,0x0cc1,
0xef1f,0xff3e,0xcf5d,0xdf7c,0xaf9b,0xbfba,0x8fd9,0x9ff8,
0x6e17,0x7e36,0x4e55,0x5e74,0x2e93,0x3eb2,0x0ed1,0x1ef0
};
unsigned short crc16_ccitt(const void *buf, int len)
{
register int counter;
register unsigned short crc = 0;
for( counter = 0; counter < len; counter++)
crc = (crc<<8) ^ crc16tab[((crc>>8) ^ *(char *)buf++)&0x00FF];
return crc;
}
对于java的编写实现：
static final char TABLE1021[] = { /* CRC1021余式表 */
0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50a5, 0x60c6, 0x70e7, 0x8108,
0x9129, 0xa14a, 0xb16b, 0xc18c, 0xd1ad, 0xe1ce, 0xf1ef, 0x1231,
0x0210, 0x3273, 0x2252, 0x52b5, 0x4294, 0x72f7, 0x62d6, 0x9339,
0x8318, 0xb37b, 0xa35a, 0xd3bd, 0xc39c, 0xf3ff, 0xe3de, 0x2462,
0x3443, 0x0420, 0x1401, 0x64e6, 0x74c7, 0x44a4, 0x5485, 0xa56a,
0xb54b, 0x8528, 0x9509, 0xe5ee, 0xf5cf, 0xc5ac, 0xd58d, 0x3653,
0x2672, 0x1611, 0x0630, 0x76d7, 0x66f6, 0x5695, 0x46b4, 0xb75b,
0xa77a, 0x9719, 0x8738, 0xf7df, 0xe7fe, 0xd79d, 0xc7bc, 0x48c4,
0x58e5, 0x6886, 0x78a7, 0x0840, 0x1861, 0x2802, 0x3823, 0xc9cc,
0xd9ed, 0xe98e, 0xf9af, 0x8948, 0x9969, 0xa90a, 0xb92b, 0x5af5,
0x4ad4, 0x7ab7, 0x6a96, 0x1a71, 0x0a50, 0x3a33, 0x2a12, 0xdbfd,
0xcbdc, 0xfbbf, 0xeb9e, 0x9b79, 0x8b58, 0xbb3b, 0xab1a, 0x6ca6,
0x7c87, 0x4ce4, 0x5cc5, 0x2c22, 0x3c03, 0x0c60, 0x1c41, 0xedae,
0xfd8f, 0xcdec, 0xddcd, 0xad2a, 0xbd0b, 0x8d68, 0x9d49, 0x7e97,
0x6eb6, 0x5ed5, 0x4ef4, 0x3e13, 0x2e32, 0x1e51, 0x0e70, 0xff9f,
0xefbe, 0xdfdd, 0xcffc, 0xbf1b, 0xaf3a, 0x9f59, 0x8f78, 0x9188,
0x81a9, 0xb1ca, 0xa1eb, 0xd10c, 0xc12d, 0xf14e, 0xe16f, 0x1080,
0x00a1, 0x30c2, 0x20e3, 0x5004, 0x4025, 0x7046, 0x6067, 0x83b9,
0x9398, 0xa3fb, 0xb3da, 0xc33d, 0xd31c, 0xe37f, 0xf35e, 0x02b1,
0x1290, 0x22f3, 0x32d2, 0x4235, 0x5214, 0x6277, 0x7256, 0xb5ea,
0xa5cb, 0x95a8, 0x8589, 0xf56e, 0xe54f, 0xd52c, 0xc50d, 0x34e2,
0x24c3, 0x14a0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405, 0xa7db,
0xb7fa, 0x8799, 0x97b8, 0xe75f, 0xf77e, 0xc71d, 0xd73c, 0x26d3,
0x36f2, 0x0691, 0x16b0, 0x6657, 0x7676, 0x4615, 0x5634, 0xd94c,
0xc96d, 0xf90e, 0xe92f, 0x99c8, 0x89e9, 0xb98a, 0xa9ab, 0x5844,
0x4865, 0x7806, 0x6827, 0x18c0, 0x08e1, 0x3882, 0x28a3, 0xcb7d,
0xdb5c, 0xeb3f, 0xfb1e, 0x8bf9, 0x9bd8, 0xabbb, 0xbb9a, 0x4a75,
0x5a54, 0x6a37, 0x7a16, 0x0af1, 0x1ad0, 0x2ab3, 0x3a92, 0xfd2e,
0xed0f, 0xdd6c, 0xcd4d, 0xbdaa, 0xad8b, 0x9de8, 0x8dc9, 0x7c26,
0x6c07, 0x5c64, 0x4c45, 0x3ca2, 0x2c83, 0x1ce0, 0x0cc1, 0xef1f,
0xff3e, 0xcf5d, 0xdf7c, 0xaf9b, 0xbfba, 0x8fd9, 0x9ff8, 0x6e17,
0x7e36, 0x4e55, 0x5e74, 0x2e93, 0x3eb2, 0x0ed1, 0x1ef0 };
static int crc16_ccitt(byte buf[], int len) {
int counter;
int crc = 0;
for (counter = 0; counter < len; counter++) {
crc = (crc << 8) ^ TABLE1021[((crc >> 8) ^ buf[counter]) & 0x00FF];
}
return crc & 0xFFFF;
}
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