原创 关于CRC校验的开发笔记

CRC-8:    c(x) = x⁸
+ x² + x + 1

CRC-10:   c(x) = x¹⁰ + x⁹ + x⁵ + x⁴
+ x + 1

CRC-12:   c(x) = x¹² + x¹¹ + x³ + x²
+ 1

CRC-16:   c(x) = x¹⁶ + x¹⁵ + x² + 1

CRC-CCITT:c(x) = x¹⁶ + x¹² + x⁵ + 1

CRC-32:   c(x) = x³² + x²⁶ + x²³ + x²²
+ x¹⁶ + x¹² + x¹¹ + x¹⁰ + x⁸
+ x⁷ + x⁵ + x⁴ + x² + x + 1

CRC can detect all single-bit errors, all
double-bit errors, any odd number of errors, any burst error where the length of
burst is less than k bits (k = degree of c(x)), and most burst error of larger
than k bits.

CRC Example:

1: M(x) = 1001,1010  //Message to be send

2: C(x) = 1,0000,0111       //Polynomial, degree =
8 (k = 8)

3: Shift left M(x) by 8 (the degree of c(x)) and add E(x) to produce message。其中E(x)
= "0000,0000"或M(x)的下一个字节。


4: Polynomial long division by c(x) to yield remainder. R(x) = 1100,1111.

5: So, the message minus R(x) would be exactly divisible by C(x).

Note: Addition, subtraction and division here means Exclusive-OR (XOR).

最后，P(x)
= M(x)*x^k + R(x) = 1001,1010,0000,0000 + 1100,1111 =
1001,1010,1100,1111

其实R(x) = E(x) xor C1(x) xor C2(x) xor
C3(x) xor C4(x).....xor Cn(x).


其中，"C1(x) xor C2(x) xor C3(x) xor C4(x).....xor Cn(x)"是由M(x)的值决定的。

所以，在单片机中，只要做一个256字节的表格，根据M(x)查出"C1(x)
xor C2(x) xor C3(x) xor C4(x).....Cn(x)"的值，再与E(x)异或就可以得到R(x)了。

当然，也可以做两个16字节的表格，分别查出"C1(x) xor
C2(x)" 和 "C3(x) xor C4(x)"的值，再将他们异或，然后将结果与E(x)异或，得到R(x)。

然后，再把R(x)作为下一轮的M(x),继续查表，与下一字节异或，产生新的Rx(x)。如此循环，直到最后一个字节,然后，将结果作为M(x)再查一次表（是为最后添加的那个0x00查的）。

CRC-8的51单片机实现：


51的表格（汇编）：


db 000h,007h,00eh,009h,01ch,01bh,012h,015h,038h,03fh,036h,031h,024h,023h,02ah,02dh;

db 070h,077h,07eh,079h,06ch,06bh,062h,065h,048h,04fh,046h,041h,054h,053h,05ah,05dh;

db 0e0h,0e7h,0eeh,0e9h,0fch,0fbh,0f2h,0f5h,0d8h,0dfh,0d6h,0d1h,0c4h,0c3h,0cah,0cdh;

db 090h,097h,09eh,099h,08ch,08bh,082h,085h,0a8h,0afh,0a6h,0a1h,0b4h,0b3h,0bah,0bdh;

db 0c7h,0c0h,0c9h,0ceh,0dbh,0dch,0d5h,0d2h,0ffh,0f8h,0f1h,0f6h,0e3h,0e4h,0edh,0eah;

db 0b7h,0b0h,0b9h,0beh,0abh,0ach,0a5h,0a2h,08fh,088h,081h,086h,093h,094h,09dh,09ah;

db 027h,020h,029h,02eh,03bh,03ch,035h,032h,01fh,018h,011h,016h,003h,004h,00dh,00ah;

db 057h,050h,059h,05eh,04bh,04ch,045h,042h,06fh,068h,061h,066h,073h,074h,07dh,07ah;

db 089h,08eh,087h,080h,095h,092h,09bh,09ch,0b1h,0b6h,0bfh,0b8h,0adh,0aah,0a3h,0a4h;

db 0f9h,0feh,0f7h,0f0h,0e5h,0e2h,0ebh,0ech,0c1h,0c6h,0cfh,0c8h,0ddh,0dah,0d3h,0d4h;

db 069h,06eh,067h,060h,075h,072h,07bh,07ch,051h,056h,05fh,058h,04dh,04ah,043h,044h;

db 019h,01eh,017h,010h,005h,002h,00bh,00ch,021h,026h,02fh,028h,03dh,03ah,033h,034h;

db 04eh,049h,040h,047h,052h,055h,05ch,05bh,076h,071h,078h,07fh,06ah,06dh,064h,063h;

db 03eh,039h,030h,037h,022h,025h,02ch,02bh,006h,001h,008h,00fh,01ah,01dh,014h,013h;

db 0aeh,0a9h,0a0h,0a7h,0b2h,0b5h,0bch,0bbh,096h,091h,098h,09fh,08ah,08dh,084h,083h;

db 0deh,0d9h,0d0h,0d7h,0c2h,0c5h,0cch,0cbh,0e6h,0e1h,0e8h,0efh,0fah,0fdh,0f4h,0f3h;



51的表格（C语言）：

const unsigned char code CRC8[256] = {

0x00,0x07,0x0e,0x09,0x1c,0x1b,0x12,0x15,0x38,0x3f,0x36,0x31,0x24,0x23,0x2a,0x2d,

0x70,0x77,0x7e,0x79,0x6c,0x6b,0x62,0x65,0x48,0x4f,0x46,0x41,0x54,0x53,0x5a,0x5d,

0xe0,0xe7,0xee,0xe9,0xfc,0xfb,0xf2,0xf5,0xd8,0xdf,0xd6,0xd1,0xc4,0xc3,0xca,0xcd,

0x90,0x97,0x9e,0x99,0x8c,0x8b,0x82,0x85,0xa8,0xaf,0xa6,0xa1,0xb4,0xb3,0xba,0xbd,

0xc7,0xc0,0xc9,0xce,0xdb,0xdc,0xd5,0xd2,0xff,0xf8,0xf1,0xf6,0xe3,0xe4,0xed,0xea,

0xb7,0xb0,0xb9,0xbe,0xab,0xac,0xa5,0xa2,0x8f,0x88,0x81,0x86,0x93,0x94,0x9d,0x9a,

0x27,0x20,0x29,0x2e,0x3b,0x3c,0x35,0x32,0x1f,0x18,0x11,0x16,0x03,0x04,0x0d,0x0a,

0x57,0x50,0x59,0x5e,0x4b,0x4c,0x45,0x42,0x6f,0x68,0x61,0x66,0x73,0x74,0x7d,0x7a,

0x89,0x8e,0x87,0x80,0x95,0x92,0x9b,0x9c,0xb1,0xb6,0xbf,0xb8,0xad,0xaa,0xa3,0xa4,

0xf9,0xfe,0xf7,0xf0,0xe5,0xe2,0xeb,0xec,0xc1,0xc6,0xcf,0xc8,0xdd,0xda,0xd3,0xd4,

0x69,0x6e,0x67,0x60,0x75,0x72,0x7b,0x7c,0x51,0x56,0x5f,0x58,0x4d,0x4a,0x43,0x44,

0x19,0x1e,0x17,0x10,0x05,0x02,0x0b,0x0c,0x21,0x26,0x2f,0x28,0x3d,0x3a,0x33,0x34,

0x4e,0x49,0x40,0x47,0x52,0x55,0x5c,0x5b,0x76,0x71,0x78,0x7f,0x6a,0x6d,0x64,0x63,

0x3e,0x39,0x30,0x37,0x22,0x25,0x2c,0x2b,0x06,0x01,0x08,0x0f,0x1a,0x1d,0x14,0x13,

0xae,0xa9,0xa0,0xa7,0xb2,0xb5,0xbc,0xbb,0x96,0x91,0x98,0x9f,0x8a,0x8d,0x84,0x83,

0xde,0xd9,0xd0,0xd7,0xc2,0xc5,0xcc,0xcb,0xe6,0xe1,0xe8,0xef,0xfa,0xfd,0xf4,0xf3,

};



i = 1 , m = UARTIn[0] ;

while(i <= UARTPtr){

  m = CRC8[m] ^ UARTIn;

  i++;

}

m = CRC8[m];