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EEPW首頁 > 嵌入式系統(tǒng) > 設(shè)計(jì)應(yīng)用 > CRC校驗(yàn)原理與程序設(shè)計(jì)——(RS485總線系統(tǒng)應(yīng)用之1)

CRC校驗(yàn)原理與程序設(shè)計(jì)——(RS485總線系統(tǒng)應(yīng)用之1)

作者：時間：2016-12-15 來源：網(wǎng)絡(luò)

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1．CRC校驗(yàn)原理

1.1 CRC的基本概念：

本文引用地址：http://www.ex-cimer.com/article/201612/330194.htm

CRC是英文Cyclical Redundancy Check的縮寫，翻譯成中文通常稱作循環(huán)冗余校驗(yàn)或簡稱為CRC校驗(yàn)。它是數(shù)據(jù)傳輸領(lǐng)域中最常用的一種差錯校驗(yàn)方法，其特點(diǎn)是傳輸數(shù)據(jù)和CRC校驗(yàn)值的長度可以任意選定。在當(dāng)今手機(jī)、計(jì)算機(jī)和數(shù)碼產(chǎn)品普及的信息數(shù)字化時代，CRC校驗(yàn)無處不在。CRC分為多種標(biāo)準(zhǔn)，例如：CRC -12碼通常用來傳送6-bit字符串。CRC-16及CRC-CCITT碼則用是來傳送8-bit字符，其中CRC-16多為美國采用，而CRC-CCITT多為歐洲國家所采用。而CRC-32碼大都被應(yīng)用在Point-to-Point的同步傳輸中。更多的CRC校驗(yàn)標(biāo)準(zhǔn)類型參見附表：CRC校驗(yàn)標(biāo)準(zhǔn)類型。

1.2 CRC校驗(yàn)的基本原理：

在代數(shù)編碼理論中，一個數(shù)值可以表示為一個多項(xiàng)式。例如：一個十進(jìn)制數(shù)值2892，可以用多項(xiàng)式表示為2x3+ 8x2+ 9x + 2(x=10)。同理，一個二進(jìn)制數(shù)值1010101對應(yīng)的多項(xiàng)式為x6+ x4+ x2+ 1(x=2)。

生成CRC碼的基本原理是：設(shè)被校驗(yàn)的數(shù)據(jù)為K位，校驗(yàn)碼為R位，碼字長度為N(=K+R)，則對于CRC碼集中的任一碼字，存在且僅存在一個R次多項(xiàng)式g(x)，使得

　　V(x)=A(x)g(x)=xRm(x) + r(x);

　　其中: m(x)為被校驗(yàn)數(shù)據(jù)的K-1次多項(xiàng)式

r(x)為校驗(yàn)碼的R-1次多項(xiàng)式

　　g(x)稱為生成多項(xiàng)式：g(x)=g0+ g1x1+ g2x2+ ... + g(R-1)x(R-1)+ gRxR

發(fā)送方通過指定的g(x)計(jì)算出CRC校驗(yàn)碼，接收方則通過該g(x)來驗(yàn)證收到的CRC校驗(yàn)碼。綜上所述，一個完整的CRC校驗(yàn)過程是：

發(fā)送方：根據(jù)要傳送的K位原始數(shù)據(jù)(二進(jìn)制碼序列)，以標(biāo)準(zhǔn)指定的多項(xiàng)式計(jì)算出一個R位校驗(yàn)碼(CRC碼)，附在原始數(shù)據(jù)后邊，構(gòu)成一個新的二進(jìn)制碼序列共K + R位，然后發(fā)送出去。

接收方：將接收到的數(shù)據(jù)除以與發(fā)送方相同的多項(xiàng)式值，如果能夠除盡，則正確，否則證明出錯。還有另外一種處理，就是接收方用發(fā)送方相同的方法計(jì)算出接收到數(shù)據(jù)的CRC校驗(yàn)值，再與發(fā)送方發(fā)來的校驗(yàn)值比較，相同則正確，否則證明出錯。

2. CRC校驗(yàn)碼的計(jì)算步驟：

例如：有一個要發(fā)送的7位二進(jìn)制數(shù)1011001；對應(yīng)的m(x)=x6+ x4+ x3+ 1。設(shè)CRC校驗(yàn)碼取4位并設(shè)g(x)=x4+ x + 1，則該多項(xiàng)式對應(yīng)的值是10011。根據(jù)CRC規(guī)則，為保證被除數(shù)夠除，首先需將要發(fā)送的數(shù)擴(kuò)大2R即24倍(左移4位)，得到10110010000，對應(yīng)的xRm(x)=x10+ x8+ x7+ x4。

CRC校驗(yàn)碼的生成本質(zhì)其實(shí)就是采用模2除法取余數(shù)，該除法的簡捷計(jì)算就是將除數(shù)和被除數(shù)按位做異或(相同為0，不同為1。0^0=0; 0^1=1; 1^0=1; 1^1=0)運(yùn)算。需要注意的是，進(jìn)行異或運(yùn)算時除數(shù)必須和被除數(shù)最高有效位對齊。下面是將10110010000除以11001手工計(jì)算的演示，得到余數(shù)為1010，該值即是數(shù)據(jù)1011001的CRC校驗(yàn)值。

　　10110010000將1011001左移4位

　　10011多項(xiàng)式值與被除數(shù)最高有效位對齊

　　=00101010000第1次異或結(jié)果

　　10011多項(xiàng)式值與被除數(shù)最高有效位對齊

　　=00001100000第2次異或結(jié)果

　　10011多項(xiàng)式值與被除數(shù)最高有效位對齊

　　=00000101100第3次異或結(jié)果

　　10011多項(xiàng)式值與被除數(shù)最高有效位對齊

　　=00000001010第4次異或結(jié)果

為了簡便計(jì)算機(jī)程序求解CRC，在實(shí)際應(yīng)用中通常把多項(xiàng)式值的最高位舍掉，并且將參加計(jì)算的數(shù)據(jù)高低位顛倒后再計(jì)算。前面的演算數(shù)據(jù)顛倒后的運(yùn)算情況如下：

00001001101

11001

00001010100

11001

00000110000

11001

00110100000

11001

01010000000

提請注意：只有真正讀懂以上手工演算的步驟和規(guī)律，才能理解下節(jié)內(nèi)容。

3. CRC校驗(yàn)的程序設(shè)計(jì)

下面以最常用的CRC-16-IBM校驗(yàn)標(biāo)準(zhǔn)為例來說明CRC校驗(yàn)碼的生成過程。因?yàn)镃RC-16碼由兩個字節(jié)構(gòu)成，所以首先要準(zhǔn)備一個16位的CRC寄存器，并將每一位都置1。具體的計(jì)算步驟為：

① 設(shè)置CRC寄存器，并給其賦值FFFFH。

② 將被校驗(yàn)數(shù)據(jù)的第一個字節(jié)(8Bit)與CRC寄存器的低8位進(jìn)行異或，結(jié)果存CRC寄存器。

③CRC寄存器的值向右移一位，最高位(MSB)補(bǔ)零，檢查移出的最低位(LSB)是否為1。

④ 如果LSB為0，重復(fù)第三步；若LSB為1，CRC寄存器與CRC16多項(xiàng)式值A(chǔ)001H相異或。

⑤ 重復(fù)第③與第④步，直到該字節(jié)的8次移位全部完成。

⑥ 如果被校驗(yàn)數(shù)據(jù)有多個字節(jié)，則重復(fù)第②至第⑤步直到所有數(shù)據(jù)全部處理完。

⑦ 最終CRC寄存器的內(nèi)容即為CRC值。

3.1用查表法求CRC函數(shù)的程序

查表法省去了將被校驗(yàn)數(shù)據(jù)移位并與多項(xiàng)式異或計(jì)算的步驟，因此比計(jì)算法更快捷，但程序編碼量偏大。

3.1.1用VC編寫的程序

unsigned short CRC16(puchMsg, usDataLen)

unsigned char * puchMsg ;

unsigned short usDataLen ;

{

unsigned char uchCRCHi = 0xFF ;

unsigned char uchCRCLo = 0xFF ;

unsigned uIndex ;

while (usDataLen--)

{

uIndex = uchCRCLo ^ * puchMsg++ ;

uchCRCLo = uchCRCHi ^ auchCRCLo [uIndex] ;

uchCRCHi = auchCRCHi [uIndex] ;

}

return (uchCRCLo << 8 | uchCRCHi) ;

}

static char auchCRCHi[] = {

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 } ;

static unsigned char auchCRCLo[] = {

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 } ;

3.1.2用VB編寫的程序

Private Function CRC16(data() As Byte) As String

　Dim CRC16Hi As Byte

　Dim CRC16Lo As Byte

　CRC16Hi = &HFF

　CRC16Lo = &HFF

　Dim i As Integer

　Dim iIndex As Long

　For i = 0 To UBound(data)

　　iIndex = CRC16Lo Xor data(i)

　　CRC16Lo = CRC16Hi Xor GetCRCLo(iIndex)’低位處理

CRC16Hi = GetCRCHi(iIndex)’高位處理

　Next i

　Dim ReturnData(1) As Byte

　ReturnData(0) = CRC16Hi’CRC高位

　ReturnData(1) = CRC16Lo’CRC低位

　CRC16 = ReturnData

End Function

Function GetCRCHi(Ind As Long) As Byte’CRC高位字節(jié)值表

GetCRCHi = Choose(Ind + 1,_

&H00, &HC0, &HC1, &H01, &HC3, &H03, &H02, &HC2, &HC6, &H06,_

&H07, &HC7, &H05, &HC5, &HC4, &H04, &HCC, &H0C, &H0D, &HCD,_

&H0F, &HCF, &HCE, &H0E, &H0A, &HCA, &HCB, &H0B, &HC9, &H09,_

&H08, &HC8, &HD8, &H18, &H19, &HD9, &H1B, &HDB, &HDA, &H1A,_

&H1E, &HDE, &HDF, &H1F, &HDD, &H1D, &H1C, &HDC, &H14, &HD4,_

&HD5, &H15, &HD7, &H17, &H16, &HD6, &HD2, &H12, &H13, &HD3,_

&H11, &HD1, &HD0, &H10, &HF0, &H30, &H31, &HF1, &H33, &HF3,_

&HF2, &H32, &H36, &HF6, &HF7, &H37, &HF5, &H35, &H34, &HF4,_

&H3C, &HFC, &HFD, &H3D, &HFF, &H3F, &H3E, &HFE, &HFA, &H3A,_

&H3B, &HFB, &H39, &HF9, &HF8, &H38, &H28, &HE8, &HE9, &H29,_

&HEB, &H2B, &H2A, &HEA, &HEE, &H2E, &H2F, &HEF, &H2D, &HED,_

&HEC, &H2C, &HE4, &H24, &H25, &HE5, &H27, &HE7, &HE6, &H26,_

&H22, &HE2, &HE3, &H23, &HE1, &H21, &H20, &HE0, &HA0, &H60,_

&H61, &HA1, &H63, &HA3, &HA2, &H62, &H66, &HA6, &HA7, &H67,_

&HA5, &H65, &H64, &HA4, &H6C, &HAC, &HAD, &H6D, &HAF, &H6F,_

&H6E, &HAE, &HAA, &H6A, &H6B, &HAB, &H69, &HA9, &HA8, &H68,_

&H78, &HB8, &HB9, &H79, &HBB, &H7B, &H7A, &HBA, &HBE, &H7E,_

&H7F, &HBF, &H7D, &HBD, &HBC, &H7C, &HB4, &H74, &H75, &HB5,_

&H77, &HB7, &HB6, &H76, &H72, &HB2, &HB3, &H73, &HB1, &H71,_

&H70, &HB0, &H50, &H90, &H91, &H51, &H93, &H53, &H52, &H92,_

&H96, &H56, &H57, &H97, &H55, &H95, &H94, &H54, &H9C, &H5C,_

&H5D, &H9D, &H5F, &H9F, &H9E, &H5E, &H5A, &H9A, &H9B, &H5B,_

&H99, &H59, &H58, &H98, &H88, &H48, &H49, &H89, &H4B, &H8B,_

&H8A, &H4A, &H4E, &H8E, &H8F, &H4F, &H8D, &H4D, &H4C, &H8C,_

&H44, &H84, &H85, &H45, &H87, &H47, &H46, &H86, &H82, &H42,_

&H43, &H83, &H41, &H81, &H80, &H40)

End Function

Function GetCRCLo(Ind As Long) As Byte’CRC低位字節(jié)值表

GetCRCLo = Choose(Ind + 1,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41,_

&H00, &HC1, &H81, &H40, &H00, &HC1, &H81, &H40, &H01, &HC0,_

&H80, &H41, &H01, &HC0, &H80, &H41, &H00, &HC1, &H81, &H40,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H00, &HC1,_

&H81, &H40, &H01, &HC0, &H80, &H41, &H01, &HC0, &H80, &H41,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H00, &HC1,_

&H81, &H40, &H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40, &H00, &HC1, &H81, &H40,_

&H01, &HC0, &H80, &H41, &H01, &HC0, &H80, &H41, &H00, &HC1,_

&H81, &H40, &H01, &HC0, &H80, &H41, &H00, &HC1, &H81, &H40,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40, &H00, &HC1, &H81, &H40,_

&H01, &HC0, &H80, &H41, &H00, &HC1, &H81, &H40, &H01, &HC0,_

&H80, &H41, &H01, &HC0, &H80, &H41, &H00, &HC1, &H81, &H40,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41,_

&H00, &HC1, &H81, &H40, &H00, &HC1, &H81, &H40, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41,_

&H01, &HC0, &H80, &H41, &H00, &HC1, &H81, &H40, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40, &H00, &HC1, &H81, &H40,_

&H01, &HC0, &H80, &H41, &H01, &HC0, &H80, &H41, &H00, &HC1,_

&H81, &H40, &H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41,_

&H00, &HC1, &H81, &H40, &H01, &HC0, &H80, &H41, &H01, &HC0,_

&H80, &H41, &H00, &HC1, &H81, &H40)
End Function

3.2用計(jì)算法求CRC函數(shù)的程序

計(jì)算法的優(yōu)點(diǎn)是程序編碼量小，雖然比查表法速度偏慢，但當(dāng)被校驗(yàn)的數(shù)據(jù)量不大時并不明顯。

3.2.1用VC編寫的程序

unsigned short CRC16(unsigned char buf[], int n)

{

unsigned short crc = 0xffff ;

for(i = 0; i < n; i++)

{

crc ^ = buf[i] ;

for(b = 0; b < 8; b++)

{

bool f = crc & 1 ;

crc >> = 1 ;

if(f)

crc ^ = 0xa001 ;

}

}

return(crc) ;

}

3.2.2用VB編寫的程序

Function CRC16(Data() As Byte, No As Integer, CRC16Lo As Byte, CRC16Hi As Byte) As String

Dim CL As Byte, CH As Byte, SaveLo As Byte, SaveHi As Byte

CRC16Hi = &HFF為16位CRC校驗(yàn)寄存器賦初始值FFFF

CRC16Lo = &HFF

CH = &HA0為16位CRC校驗(yàn)多項(xiàng)式賦初始值A(chǔ)001

CL = &H1

For i = 1 To No

CRC16Lo = CRC16Lo Xor Data(i - 1)每一個數(shù)據(jù)與CRC寄存器進(jìn)行異或

For j = 1 To 8

SaveHi = CRC16Hi

SaveLo = CRC16Lo

CRC16Hi = CRC16Hi 2高位右移一位

CRC16Lo = CRC16Lo 2低位右移一位

If ((SaveHi And &H1) = &H1) Then如果高位字節(jié)最右一位為1

CRC16Lo = CRC16Lo Or &H80則低位字節(jié)最左一位補(bǔ)1，否則自動補(bǔ)0

End If

If ((SaveLo And &H1) = &H1) Then如低位字節(jié)最右一位為1，則與多項(xiàng)式值異或

CRC16Hi = CRC16Hi Xor CH

CRC16Lo = CRC16Lo Xor CL

End If

Next j

Next i

End Function

參考文獻(xiàn)：

①GB/T 19582.1-2008《基于Modbus協(xié)議的工業(yè)自動化網(wǎng)絡(luò)規(guī)范》

②《Modbus協(xié)議中文版》可在互聯(lián)網(wǎng)上下載

附表：CRC校驗(yàn)標(biāo)準(zhǔn)類型

CRC校驗(yàn)名	多項(xiàng)式(標(biāo)準(zhǔn)引用名)	對應(yīng)的16進(jìn)制值或反值注：已去掉最高位的1
CRC-1	x + 1 (most hardware; also known as parity bit)	01或01 (01)
CRC-4-ITU	x4+x+ 1 (ITU G.704, p. 12)	03或0C (09)
CRC-5-ITU	x5+x4+x2+ 1 (ITU G.704, p. 9)	15或15 (1A)
CRC-5-USB	x5+x2+ 1 (USB token packets)	05或14 (12)
CRC-6-ITU	x6+x+ 1 (ITU G.704, p. 3)	03或30 (21)
CRC-7	x7+x3+ 1 (telecom systems, MMC,SD)	09或48 (44)
CRC-8-ATM	x8+x2+x+ 1 (ATM HEC)	07或E0 (83)
CRC-8-CCITT	x8+x7+x3+x2+ 1 (1-Wire bus)	8D或B1 (C6)
CRC-8-Dallas/Maxim	x8+x5+x4+ 1 (1-Wire bus)	31或8C (98)
CRC-8	x8+x7+x6+x4+x2+ 1	D5或AB (EA)
CRC-8-SAE J1850	x8+x4+x3+x2+ 1	1D或B8 (8E)
CRC-10	x10+x9+x5+x4+x+ 1	233或331 (319)
CRC-11	x11+x9+x8+x7+x+ 1 (FlexRay)	385或50E (5C2)
CRC-12	x12+x11+x3+x2+x+ 1 (telecom systems )	80F或F01 (C07)
CRC-15-CAN	x15+x14+x10+x8+x7+x4+x3+ 1	4599或4CD1 (62CC)
CRC-16-Fletcher	Not a CRC; see Fletchers checksum	Used in Adler-32 A & B CRCs
CRC-16-CCITT	x16+x12+x5+ 1 (CRC-CCITT, G.hn PHY headers, 802.15.4, X.25, V.41, CDMA, Bluetooth, XMODEM, HDLC,PPP, IrDA, BACnet, MMC,SD)	1021或8408 (8810)
CRC-16-DNP	x16+x13+x12+x11+x10+x8+x6+x5+x2+ 1 (DNP, IEC 870, M-Bus)	3D65或A6BC (9EB2)
CRC-16-IBM	x16+x15+x2+ 1 (CRC-16, SDLC, USB, many others)	8005或A001 (C002)
CRC-24-Radix-64	x24+x23+x18+x17+x14+x11+x10+x7+x6+x5+x4+x3+x+ 1 (FlexRay)	864CFB或DF3261 (C3267D)
CRC-30	x30+x29+x21+x20+x15+x13+x12+x11+x8+x7+x6+x2+x+ 1 (CDMA)	2030B9C7或38E74301 (30185CE3)
CRC-32-Adler	Not a CRC; see Adler-32	See Adler-32
CRC-32-IEEE 802.3	x32+x26+x23+x22+x16+x12+x11+x10+x8+x7+x5+x4+x2+x+ 1 (V.42, MPEG-2, PNG [10], POSIX cksum)	04C11DB7或EDB88320 (82608EDB)
CRC-32C (Castagnoli)	x32+ x28+ x27+ x26+ x25+ x23+ x22+ x20+ x19+ x18+ x14+ x13+ x11+ x10+ x9+ x8+ x6+ 1 (G.hn payload)	1EDC6F41或82F63B78 (8F6E37A0)
CRC-32K (Koopman)	x32+x30+x29+x28+x26+x20+x19+x17+x16+x15+x11+x10+x7+x6+x4+x2+x+ 1	741B8CD7或EB31D82E (BA0DC66B)
CRC-64-ISO	x64+x4+x3+ x + 1 (HDLC-ISO 3309)	000000000000001B或D800000000000000 (800000000000000D)
CRC-64-ECMA-182	x64+ x62+ x57+ x55+ x54+ x53+ x52+ x47+ x46+ x45+ x40+ x39+ x38+ x37+ x35+ x33+ x32+ x31+ x29+ x27+ x24+ x23+ x22+ x21+ x19+ x17+ x13+ x12+ x10+ x9+ x7+ x4+ x + 1 (As described in ECMA-182 p.51)	42F0E1EBA9EA3693或C96C5795D7870F42 (A17870F5D4F51B49)

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關(guān)鍵詞： CRC校驗(yàn)RS485總

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