很多讲的都是CRC16-CCITT标准-一直想弄明白CRC-16标

最近在搞CRC校验，用的是CRC16标准，查看了很多资料发现很多讲的都是CRC16-CCITT标准，一直想弄明白CRC-16标准中的采用查表法的方式中那两个表格中的数是如何求出来的。可惜没有一个文章仔细的讲，更没有文章给出实例来算一算。一切只能靠自己了，谁让我喜欢寻根摸底呢。研究了一下本站会员玉丫子的文章，自己琢磨了琢磨，终于知道是怎么算出来的了。CRC16算法的生成多项式x^16+x^15+x^2+1，十六进制表示为0x8005。CRC16常见的表格中的数据是按照先传输LSB，消息右移进寄存器来计算的。因此需要判断寄存器的最低位LSB，同时要将0x8005按位颠倒后(0xA001)根据LSB的情况决定是否与寄存器异或即可。CRC16的表格中对应的数依次为0~255计算出来的CRC值，因此，此处只选取其中一两个数作为实例计算CRC值。具体步骤如下所示：1)从0~255中选取需要计算的数，将其对应的十六进制数放入一个长度为16的寄存器的低八位，高八位填充0；2)如果寄存器的末位LSB为1，将寄存器的数值右移1位，再与0xA001位异或，否则仅将寄存器右移1位；3)重复第2步，直到低八位全部右移出寄存器；4)寄存器中的值则为校验码。从0~255中挑选2（对应0x02）计算其CRC值：0x02的CRC-16的表格计算（反向）0000000000000010-最低位LSB=0，高八位填充000000000000000010右移,高位填充0，并舍弃最后一位-----------------第一次计算0000000000000001-LSB=100000000000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第二次1010000000000001-LSB=101010000000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第三次1111000000000001-LSB=101111000000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第四次1101100000000001-LSB=101101100000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第五次1100110000000001-LSB=101100110000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第六次1100011000000001-LSB=101100011000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第七次1100001100000001-LSB=101100001100000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------一共右移了八次，得到的结果为CRC1100000110000001-CRC:0xC181从本文最后的附表中可以看出auchCRCHi[]的第三个值就是0x81，auchCRCLo[]的第三个值就是0xC1,可见计算无误。另一个计算实例，从0~255中挑选11（对应0x0B）计算其CRC值：0x0B的CRC-16的表格计算（反向）0000000000001011-最低位LSB=1，高八位填充000000000000001011右移,高位填充0，并舍弃最后一位^1010000000000001-与0xA001异或-----------------第一次计算1010000000000100-LSB=001010000000000100右移,舍弃最后一位-----------------第二次0101000000000010-LSB=000101000000000010右移,舍弃最后一位-----------------第三次0010100000000001-LSB=100010100000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第四次1011010000000001-LSB=101011010000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第五次1111101000000001-LSB=101111101000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第六次1101110100000001-LSB=1011011101000000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------第七次1100111010000001-LSB=101100111010000001右移,舍弃最后一位^1010000000000001-与0xA001异或-----------------一共算八次，得到的结果为CRC1100011101000001-CRC:0xC741从本文最后的附表中可以看出auchCRCHi[]的第12个值就是0x41，auchCRCLo[]的第12个值就是0xC7,可见计算无误。附：CRC-16的CRC数值表constunsignedcharauchCRCHi[]={0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40,0x01,0xC0,0x80,0x41,0x01,0xC0,0x80,0x41,0x00,0xC1,0x81,0x40};constunsignedcharauchCRCLo[]={0x00,0xC0,0xC1,0x01,0xC3,0x03,0x02,0xC2,0xC6,0x06,0x07,0xC7,0x05,0xC5,0xC4,0x04,0xCC,0x0C,0x0D,0xCD,0x0F,0xCF,0xCE,0x0E,0x0A,0xCA,0xCB,0x0B,0xC9,0x09,0x08,0xC8,0xD8,0x18,0x19,0xD9,0x1B,0xDB,0xDA,0x1A,0x1E,0xDE,0xDF,0x1F,0xDD,0x1D,0x1C,0xDC,0x14,0xD4,0xD5,0x15,0xD7,0x17,0x16,0xD6,0xD2,0x12,0x13,0xD3,0x11,0xD1,0xD0,0x10,0xF0,0x30,0x31,0xF1,0x33,0xF3,0xF2,0x32,0x36,0xF6,0xF7,0x37,0xF5,0x35,0x34,0xF4,0x3C,0xFC,0xFD,0x3D,0xFF,0x3F,0x3E,0xFE,0xFA,0x3A,0x3B,0xFB,0x39,0xF9,0xF8,0x38,0x28,0xE8,0xE9,0x29,0xEB,0x2B,0x2A,0xEA,0xEE,0x2E,0x2F,0xEF,0x2D,0xED,0xEC,0x2C,0xE4,0x24,0x25,0xE5,0x27,0xE7,0xE6,0x26,0x22,0xE2,0xE3,0x23,0xE1,0x21,0x20,0xE0,0xA0,0x60,0x61,0xA1,0x63,0xA3,0xA2,0x62,0x66,0xA6,0xA7,0x67,0xA5,0x65,0x64,0xA4,0x6C,0xAC,0xAD,0x6D,0xAF,0x6F,0x6E,0xAE,0xAA,0x6A,0x6B,0xAB,0x69,0xA9,0xA8,0x68,0x78,0xB8,0xB9,0x79,0xBB,0x7B,0x7A,0xBA,0xBE,0x7E,0x7F,0xBF,0x7D,0xBD,0xBC,0x7C,0xB4,0x74,0x75,0xB5,0x77,0xB7,0xB6,0x76,0x72,0xB2,0xB3,0x73,0xB1,0x71,0x70,0xB0,0x50,0x90,0x91,0x51,0x93,0x53,0x52,0x92,0x96,0x56,0x57,0x97,0x55,0x95,0x94,0x54,0x9C,0x5C,0x5D,0x9D,0x5F,0x9F,0x9E,0x5E,0x5A,0x9A,0x9B,0x5B,0x99,0x59,0x58,0x98,0x88,0x48,0x49,0x89,0x4B,0x8B,0x8A,0x4A,0x4E,0x8E,0x8F,0x4F,0x8D,0x4D,0x4C,0x8C,0x44,0x84,0x85,0x45,0x87,0x47,0x46,0x86,0x82,0x42,0x43,0x83,0x41,0x81,0x80,0x40};