循环冗余码校验英文名称为Cyclical Redundancy Check，简称CRC。它是利用除法及余数的原理来作错误侦测（Error Detecting）的。实际应用时，发送装置计算出CRC值并随数据一同发送给接收装置，接收装置对收到的数据重新计算CRC并与收到的CRC相比较，若两个CRC值不同，则说明数据通讯出现错误。

根据应用环境与习惯的不同，CRC又可分为以下几种标准：

①CRC-12码；

②CRC-16码；

③CRC-CCITT码；

④CRC-32码。

CRC-12码通常用来传送6-bit字符串。CRC-16及CRC-CCITT码则用是来传送8-bit字符，其中CRC-16为美国采用，而CRC-CCITT为欧洲国家所采用。CRC-32码大都被采用在一种称为Point-to-Point的同步传输中。

下面着重是CRC-16检验码的生成过程。

CRC-16码由两个字节构成，在开始时CRC寄存器的每一位都预置为1，然后把CRC寄存器与8-bit的数据进行异或，之后对CRC寄存器从高到低进行移位，在最高位（MSB）的位置补零，而最低位（LSB，移位后已经被移出CRC寄存器）如果为1，则把寄存器与预定义的多项式码进行异或，否则如果 LSB为零，则无需进行异或。重复上述的由高至低的移位8次，第一个8-bit数据处理完毕，用此时CRC寄存器的值与下一个8-bit数据异或并进行如前一个数据似的8次移位。所有的字符处理完成后CRC寄存器内的值即为最终的CRC值。

下面为CRC16的计算过程，其中生成多项式为:X16+X15+X2+1：

1．设置CRC寄存器，并给其赋值FFFF(hex)。

2．将数据的第一个8-bit字符与16位CRC寄存器的低8位进行异或，并把结果存入CRC寄存器。

3．CRC寄存器向右移一位，MSB补零，移出并检查LSB。

4．如果LSB为0，重复第三步；若LSB为1，CRC寄存器与生成多项式码相异或。

5．重复第3与第4步直到8次移位全部完成。此时一个8-bit数据处理完毕。

6．重复第2至第5步直到所有数据全部处理完成。

7．最终CRC寄存器的内容即为CRC值。

校验码实现

编写CRC校验程序有两种办法：一种为计算法，一种为查表法。下面是查表法的C语言实现：

校验码算法程序实现样例（C语言）：

// Test.cpp : Defines the entry point for the console application.

#include "stdafx.h"

static unsigned char auchCRCHi[]={
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
};
static unsigned char auchCRCLo[]={
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
};

unsigned short CRC16(unsigned char* puchMsg, unsigned short usDataLen)
{
    unsigned char uchCRCHi = 0xFF ;
    unsigned char uchCRCLo = 0xFF ;
    unsigned char uIndex ;
    while (usDataLen--)
    {
    uIndex = uchCRCHi ^ *puchMsg++;
    uchCRCHi = uchCRCLo ^ auchCRCHi[uIndex];
    uchCRCLo = auchCRCLo[uIndex];
    }
    return (uchCRCHi << 8 | uchCRCLo) ;
};

void main(int argc, char* argv[])
{
    unsigned char src[21]={'1','2','3','6','3','4','2','3','4','2','9','8','7','3','6','5','2','8','9','3','5'};
    unsigned short code = CRC16(src,21);
    printf("the result is %d/n",code);
}

以下是Delphi实现的代码

unit CRC16;

interface
uses
  Windows, SysUtils;

  function CRC(a_strPuchMsg:string):LongWord;

implementation

const
  ct_ArrayCRCHi: array[0..255] of LongWord=
  (
    $00, $C1, $81, $40, $01, $C0, $80, $41, $01, $C0,
    $80, $41, $00, $C1, $81, $40, $01, $C0, $80, $41,
    $00, $C1, $81, $40, $00, $C1, $81, $40, $01, $C0,
    $80, $41, $01, $C0, $80, $41, $00, $C1, $81, $40,
    $00, $C1, $81, $40, $01, $C0, $80, $41, $00, $C1,
    $81, $40, $01, $C0, $80, $41, $01, $C0, $80, $41,
    $00, $C1, $81, $40, $01, $C0, $80, $41, $00, $C1,
    $81, $40, $00, $C1, $81, $40, $01, $C0, $80, $41,
    $00, $C1, $81, $40, $01, $C0, $80, $41, $01, $C0,
    $80, $41, $00, $C1, $81, $40, $00, $C1, $81, $40,
    $01, $C0, $80, $41, $01, $C0, $80, $41, $00, $C1,
    $81, $40, $01, $C0, $80, $41, $00, $C1, $81, $40,
    $00, $C1, $81, $40, $01, $C0, $80, $41, $01, $C0,
    $80, $41, $00, $C1, $81, $40, $00, $C1, $81, $40,
    $01, $C0, $80, $41, $00, $C1, $81, $40, $01, $C0,
    $80, $41, $01, $C0, $80, $41, $00, $C1, $81, $40,
    $00, $C1, $81, $40, $01, $C0, $80, $41, $01, $C0,
    $80, $41, $00, $C1, $81, $40, $01, $C0, $80, $41,
    $00, $C1, $81, $40, $00, $C1, $81, $40, $01, $C0,
    $80, $41, $00, $C1, $81, $40, $01, $C0, $80, $41,
    $01, $C0, $80, $41, $00, $C1, $81, $40, $01, $C0,
    $80, $41, $00, $C1, $81, $40, $00, $C1, $81, $40,
    $01, $C0, $80, $41, $01, $C0, $80, $41, $00, $C1,
    $81, $40, $00, $C1, $81, $40, $01, $C0, $80, $41,
    $00, $C1, $81, $40, $01, $C0, $80, $41, $01, $C0,
    $80, $41, $00, $C1, $81, $40
  );
  ct_ArrayCRCLo:array[0..255] of LongWord=
  (
    $00, $C0, $C1, $01, $C3, $03, $02, $C2, $C6, $06,
    $07, $C7, $05, $C5, $C4, $04, $CC, $0C, $0D, $CD,
    $0F, $CF, $CE, $0E, $0A, $CA, $CB, $0B, $C9, $09,
    $08, $C8, $D8, $18, $19, $D9, $1B, $DB, $DA, $1A,
    $1E, $DE, $DF, $1F, $DD, $1D, $1C, $DC, $14, $D4,
    $D5, $15, $D7, $17, $16, $D6, $D2, $12, $13, $D3,
    $11, $D1, $D0, $10, $F0, $30, $31, $F1, $33, $F3,
    $F2, $32, $36, $F6, $F7, $37, $F5, $35, $34, $F4,
    $3C, $FC, $FD, $3D, $FF, $3F, $3E, $FE, $FA, $3A,
    $3B, $FB, $39, $F9, $F8, $38, $28, $E8, $E9, $29,
    $EB, $2B, $2A, $EA, $EE, $2E, $2F, $EF, $2D, $ED,
    $EC, $2C, $E4, $24, $25, $E5, $27, $E7, $E6, $26,
    $22, $E2, $E3, $23, $E1, $21, $20, $E0, $A0, $60,
    $61, $A1, $63, $A3, $A2, $62, $66, $A6, $A7, $67,
    $A5, $65, $64, $A4, $6C, $AC, $AD, $6D, $AF, $6F,
    $6E, $AE, $AA, $6A, $6B, $AB, $69, $A9, $A8, $68,
    $78, $B8, $B9, $79, $BB, $7B, $7A, $BA, $BE, $7E,
    $7F, $BF, $7D, $BD, $BC, $7C, $B4, $74, $75, $B5,
    $77, $B7, $B6, $76, $72, $B2, $B3, $73, $B1, $71,
    $70, $B0, $50, $90, $91, $51, $93, $53, $52, $92,
    $96, $56, $57, $97, $55, $95, $94, $54, $9C, $5C,
    $5D, $9D, $5F, $9F, $9E, $5E, $5A, $9A, $9B, $5B,
    $99, $59, $58, $98, $88, $48, $49, $89, $4B, $8B,
    $8A, $4A, $4E, $8E, $8F, $4F, $8D, $4D, $4C, $8C,
    $44, $84, $85, $45, $87, $47, $46, $86, $82, $42,
    $43, $83, $41, $81, $80, $40
  );

function CRC(a_strPuchMsg:string):LongWord;
var
  l_CRCHi, l_CRCLo, l_Index, l_DataLen, i:LongWord;
begin
  l_DataLen:= Length(a_strPuchMsg);
  l_CRCHi := $FF ;
  l_CRCLo := $FF ;
  l_Index :=0;
  i:=1;
  while (i<=l_DataLen) do
  begin
    l_Index := l_CRCHi xor Integer(a_strPuchMsg[i]);
    l_CRCHi := l_CRCLo xor ct_ArrayCRCHi[l_Index];
    l_CRCLo := ct_ArrayCRCLo[l_Index];
    Inc(i);
  end;
  Result:= (l_CRCHi shl 8) or l_CRCLo;
end;

end.