CRC32校验
CRC有不同的算法，共21种，实现CRC校验有两种方式：查表与直接计算
直接计算是根据多项式方程进行，直接计算。
查表是将上述结果保存，进行相应计算。
一、直接计算
GitHub - whik/crc-lib-c: 基于C语言的CRC校验库，包括常用的21个CRC参数模型实现
crcLib.h
#ifndef __CRCLIB_H__
#define __CRCLIB_H__
#include "stdint.h"
uint8_t crc4_itu(uint8_t *data, uint16_t length);
uint8_t crc5_epc(uint8_t *data, uint16_t length);
uint8_t crc5_itu(uint8_t *data, uint16_t length);
uint8_t crc5_usb(uint8_t *data, uint16_t length);
uint8_t crc6_itu(uint8_t *data, uint16_t length);
uint8_t crc7_mmc(uint8_t *data, uint16_t length);
uint8_t crc8(uint8_t *data, uint16_t length);
uint8_t crc8_itu(uint8_t *data, uint16_t length);
uint8_t crc8_rohc(uint8_t *data, uint16_t length);
uint8_t crc8_maxim(uint8_t *data, uint16_t length);//DS18B20
uint16_t crc16_ibm(uint8_t *data, uint16_t length);
uint16_t crc16_maxim(uint8_t *data, uint16_t length);
uint16_t crc16_usb(uint8_t *data, uint16_t length);
uint16_t crc16_modbus(uint8_t *data, uint16_t length);
uint16_t crc16_ccitt(uint8_t *data, uint16_t length);
uint16_t crc16_ccitt_false(uint8_t *data, uint16_t length);
uint16_t crc16_x25(uint8_t *data, uint16_t length);
uint16_t crc16_xmodem(uint8_t *data, uint16_t length);
uint16_t crc16_dnp(uint8_t *data, uint16_t length);
uint32_t crc32(uint8_t *data, uint16_t length);
uint32_t crc32_mpeg_2(uint8_t *data, uint16_t length);
#endif // __CRCLIB_H__crcLib.c
#include "crcLib.h"
/******************************************************************************
* Name: CRC-4/ITU x4+x+1
* Poly: 0x03
* Init: 0x00
* Refin: True
* Refout: True
* Xorout: 0x00
* Note:
*****************************************************************************/
uint8_t crc4_itu(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x0C;// 0x0C = (reverse 0x03)>>(8-4)
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-5/EPC x5+x3+1
* Poly: 0x09
* Init: 0x09
* Refin: False
* Refout: False
* Xorout: 0x00
* Note:
*****************************************************************************/
uint8_t crc5_epc(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0x48; // Initial value: 0x48 = 0x09<<(8-5)
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for ( i = 0; i < 8; i++ )
{
if ( crc & 0x80 )
crc = (crc << 1) ^ 0x48; // 0x48 = 0x09<<(8-5)
else
crc <<= 1;
}
}
return crc >> 3;
}
/******************************************************************************
* Name: CRC-5/ITU x5+x4+x2+1
* Poly: 0x15
* Init: 0x00
* Refin: True
* Refout: True
* Xorout: 0x00
* Note:
*****************************************************************************/
uint8_t crc5_itu(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x15;// 0x15 = (reverse 0x15)>>(8-5)
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-5/USB x5+x2+1
* Poly: 0x05
* Init: 0x1F
* Refin: True
* Refout: True
* Xorout: 0x1F
* Note:
*****************************************************************************/
uint8_t crc5_usb(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0x1F; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x14;// 0x14 = (reverse 0x05)>>(8-5)
else
crc = (crc >> 1);
}
}
return crc ^ 0x1F;
}
/******************************************************************************
* Name: CRC-6/ITU x6+x+1
* Poly: 0x03
* Init: 0x00
* Refin: True
* Refout: True
* Xorout: 0x00
* Note:
*****************************************************************************/
uint8_t crc6_itu(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x30;// 0x30 = (reverse 0x03)>>(8-6)
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-7/MMC x7+x3+1
* Poly: 0x09
* Init: 0x00
* Refin: False
* Refout: False
* Xorout: 0x00
* Use: MultiMediaCard,SD,ect.
*****************************************************************************/
uint8_t crc7_mmc(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for ( i = 0; i < 8; i++ )
{
if ( crc & 0x80 )
crc = (crc << 1) ^ 0x12; // 0x12 = 0x09<<(8-7)
else
crc <<= 1;
}
}
return crc >> 1;
}
/******************************************************************************
* Name: CRC-8 x8+x2+x+1
* Poly: 0x07
* Init: 0x00
* Refin: False
* Refout: False
* Xorout: 0x00
* Note:
*****************************************************************************/
uint8_t crc8(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for ( i = 0; i < 8; i++ )
{
if ( crc & 0x80 )
crc = (crc << 1) ^ 0x07;
else
crc <<= 1;
}
}
return crc;
}
/******************************************************************************
* Name: CRC-8/ITU x8+x2+x+1
* Poly: 0x07
* Init: 0x00
* Refin: False
* Refout: False
* Xorout: 0x55
* Alias: CRC-8/ATM
*****************************************************************************/
uint8_t crc8_itu(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for ( i = 0; i < 8; i++ )
{
if ( crc & 0x80 )
crc = (crc << 1) ^ 0x07;
else
crc <<= 1;
}
}
return crc ^ 0x55;
}
/******************************************************************************
* Name: CRC-8/ROHC x8+x2+x+1
* Poly: 0x07
* Init: 0xFF
* Refin: True
* Refout: True
* Xorout: 0x00
* Note:
*****************************************************************************/
uint8_t crc8_rohc(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0xFF; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xE0; // 0xE0 = reverse 0x07
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-8/MAXIM x8+x5+x4+1
* Poly: 0x31
* Init: 0x00
* Refin: True
* Refout: True
* Xorout: 0x00
* Alias: DOW-CRC,CRC-8/IBUTTON
* Use: Maxim(Dallas)'s some devices,e.g. DS18B20
*****************************************************************************/
uint8_t crc8_maxim(uint8_t *data, uint16_t length)
{
uint8_t i;
uint8_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; i++)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x8C; // 0x8C = reverse 0x31
else
crc >>= 1;
}
}
return crc;
}
/******************************************************************************
* Name: CRC-16/IBM x16+x15+x2+1
* Poly: 0x8005
* Init: 0x0000
* Refin: True
* Refout: True
* Xorout: 0x0000
* Alias: CRC-16,CRC-16/ARC,CRC-16/LHA
*****************************************************************************/
uint16_t crc16_ibm(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xA001; // 0xA001 = reverse 0x8005
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-16/MAXIM x16+x15+x2+1
* Poly: 0x8005
* Init: 0x0000
* Refin: True
* Refout: True
* Xorout: 0xFFFF
* Note:
*****************************************************************************/
uint16_t crc16_maxim(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xA001; // 0xA001 = reverse 0x8005
else
crc = (crc >> 1);
}
}
return ~crc; // crc^0xffff
}
/******************************************************************************
* Name: CRC-16/USB x16+x15+x2+1
* Poly: 0x8005
* Init: 0xFFFF
* Refin: True
* Refout: True
* Xorout: 0xFFFF
* Note:
*****************************************************************************/
uint16_t crc16_usb(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0xffff; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xA001; // 0xA001 = reverse 0x8005
else
crc = (crc >> 1);
}
}
return ~crc; // crc^0xffff
}
/******************************************************************************
* Name: CRC-16/MODBUS x16+x15+x2+1
* Poly: 0x8005
* Init: 0xFFFF
* Refin: True
* Refout: True
* Xorout: 0x0000
* Note:
*****************************************************************************/
uint16_t crc16_modbus(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0xffff; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xA001; // 0xA001 = reverse 0x8005
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-16/CCITT x16+x12+x5+1
* Poly: 0x1021
* Init: 0x0000
* Refin: True
* Refout: True
* Xorout: 0x0000
* Alias: CRC-CCITT,CRC-16/CCITT-TRUE,CRC-16/KERMIT
*****************************************************************************/
uint16_t crc16_ccitt(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x8408; // 0x8408 = reverse 0x1021
else
crc = (crc >> 1);
}
}
return crc;
}
/******************************************************************************
* Name: CRC-16/CCITT-FALSE x16+x12+x5+1
* Poly: 0x1021
* Init: 0xFFFF
* Refin: False
* Refout: False
* Xorout: 0x0000
* Note:
*****************************************************************************/
uint16_t crc16_ccitt_false(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0xffff; //Initial value
while(length--)
{
crc ^= (uint16_t)(*data++) << 8; // crc ^= (uint6_t)(*data)<<8; data++;
for (i = 0; i < 8; ++i)
{
if ( crc & 0x8000 )
crc = (crc << 1) ^ 0x1021;
else
crc <<= 1;
}
}
return crc;
}
/******************************************************************************
* Name: CRC-16/X25 x16+x12+x5+1
* Poly: 0x1021
* Init: 0xFFFF
* Refin: True
* Refout: True
* Xorout: 0XFFFF
* Note:
*****************************************************************************/
uint16_t crc16_x25(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0xffff; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0x8408; // 0x8408 = reverse 0x1021
else
crc = (crc >> 1);
}
}
return ~crc; // crc^Xorout
}
/******************************************************************************
* Name: CRC-16/XMODEM x16+x12+x5+1
* Poly: 0x1021
* Init: 0x0000
* Refin: False
* Refout: False
* Xorout: 0x0000
* Alias: CRC-16/ZMODEM,CRC-16/ACORN
*****************************************************************************/
uint16_t crc16_xmodem(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0; // Initial value
while(length--)
{
crc ^= (uint16_t)(*data++) << 8; // crc ^= (uint16_t)(*data)<<8; data++;
for (i = 0; i < 8; ++i)
{
if ( crc & 0x8000 )
crc = (crc << 1) ^ 0x1021;
else
crc <<= 1;
}
}
return crc;
}
/******************************************************************************
* Name: CRC-16/DNP x16+x13+x12+x11+x10+x8+x6+x5+x2+1
* Poly: 0x3D65
* Init: 0x0000
* Refin: True
* Refout: True
* Xorout: 0xFFFF
* Use: M-Bus,ect.
*****************************************************************************/
uint16_t crc16_dnp(uint8_t *data, uint16_t length)
{
uint8_t i;
uint16_t crc = 0; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xA6BC; // 0xA6BC = reverse 0x3D65
else
crc = (crc >> 1);
}
}
return ~crc; // crc^Xorout
}
/******************************************************************************
* Name: CRC-32 x32+x26+x23+x22+x16+x12+x11+x10+x8+x7+x5+x4+x2+x+1
* Poly: 0x4C11DB7
* Init: 0xFFFFFFF
* Refin: True
* Refout: True
* Xorout: 0xFFFFFFF
* Alias: CRC_32/ADCCP
* Use: WinRAR,ect.
*****************************************************************************/
uint32_t crc32(uint8_t *data, uint16_t length)
{
uint8_t i;
uint32_t crc = 0xffffffff; // Initial value
while(length--)
{
crc ^= *data++; // crc ^= *data; data++;
for (i = 0; i < 8; ++i)
{
if (crc & 1)
crc = (crc >> 1) ^ 0xEDB88320;// 0xEDB88320= reverse 0x04C11DB7
else
crc = (crc >> 1);
}
}
return ~crc;
}
/******************************************************************************
* Name: CRC-32/MPEG-2 x32+x26+x23+x22+x16+x12+x11+x10+x8+x7+x5+x4+x2+x+1
* Poly: 0x4C11DB7
* Init: 0xFFFFFFF
* Refin: False
* Refout: False
* Xorout: 0x0000000
* Note:
*****************************************************************************/
uint32_t crc32_mpeg_2(uint8_t *data, uint16_t length)
{
uint8_t i;
uint32_t crc = 0xffffffff; // Initial value
while(length--)
{
crc ^= (uint32_t)(*data++) << 24;// crc ^=(uint32_t)(*data)<<24; data++;
for (i = 0; i < 8; ++i)
{
if ( crc & 0x80000000 )
crc = (crc << 1) ^ 0x04C11DB7;
else
crc <<= 1;
}
}
return crc;
}main.c
#include
#include
#include "crcLib.h"
int main()
{
uint8_t data;
uint8_t crc;
data = 0x34;
crc = crc8_maxim(&data, 1);
printf("data:%02x, crc:%02x\n", data, crc);
return 0;
} 二、查表方式
#ifndef __CRC__H
#define __CRC__H
static const unsigned long crc_table[256] =
{
0x00000000UL, 0x77073096UL, 0xee0e612cUL, 0x990951baUL, 0x076dc419UL,
0x706af48fUL, 0xe963a535UL, 0x9e6495a3UL, 0x0edb8832UL, 0x79dcb8a4UL,
0xe0d5e91eUL, 0x97d2d988UL, 0x09b64c2bUL, 0x7eb17cbdUL, 0xe7b82d07UL,
0x90bf1d91UL, 0x1db71064UL, 0x6ab020f2UL, 0xf3b97148UL, 0x84be41deUL,
0x1adad47dUL, 0x6ddde4ebUL, 0xf4d4b551UL, 0x83d385c7UL, 0x136c9856UL,
0x646ba8c0UL, 0xfd62f97aUL, 0x8a65c9ecUL, 0x14015c4fUL, 0x63066cd9UL,
0xfa0f3d63UL, 0x8d080df5UL, 0x3b6e20c8UL, 0x4c69105eUL, 0xd56041e4UL,
0xa2677172UL, 0x3c03e4d1UL, 0x4b04d447UL, 0xd20d85fdUL, 0xa50ab56bUL,
0x35b5a8faUL, 0x42b2986cUL, 0xdbbbc9d6UL, 0xacbcf940UL, 0x32d86ce3UL,
0x45df5c75UL, 0xdcd60dcfUL, 0xabd13d59UL, 0x26d930acUL, 0x51de003aUL,
0xc8d75180UL, 0xbfd06116UL, 0x21b4f4b5UL, 0x56b3c423UL, 0xcfba9599UL,
0xb8bda50fUL, 0x2802b89eUL, 0x5f058808UL, 0xc60cd9b2UL, 0xb10be924UL,
0x2f6f7c87UL, 0x58684c11UL, 0xc1611dabUL, 0xb6662d3dUL, 0x76dc4190UL,
0x01db7106UL, 0x98d220bcUL, 0xefd5102aUL, 0x71b18589UL, 0x06b6b51fUL,
0x9fbfe4a5UL, 0xe8b8d433UL, 0x7807c9a2UL, 0x0f00f934UL, 0x9609a88eUL,
0xe10e9818UL, 0x7f6a0dbbUL, 0x086d3d2dUL, 0x91646c97UL, 0xe6635c01UL,
0x6b6b51f4UL, 0x1c6c6162UL, 0x856530d8UL, 0xf262004eUL, 0x6c0695edUL,
0x1b01a57bUL, 0x8208f4c1UL, 0xf50fc457UL, 0x65b0d9c6UL, 0x12b7e950UL,
0x8bbeb8eaUL, 0xfcb9887cUL, 0x62dd1ddfUL, 0x15da2d49UL, 0x8cd37cf3UL,
0xfbd44c65UL, 0x4db26158UL, 0x3ab551ceUL, 0xa3bc0074UL, 0xd4bb30e2UL,
0x4adfa541UL, 0x3dd895d7UL, 0xa4d1c46dUL, 0xd3d6f4fbUL, 0x4369e96aUL,
0x346ed9fcUL, 0xad678846UL, 0xda60b8d0UL, 0x44042d73UL, 0x33031de5UL,
0xaa0a4c5fUL, 0xdd0d7cc9UL, 0x5005713cUL, 0x270241aaUL, 0xbe0b1010UL,
0xc90c2086UL, 0x5768b525UL, 0x206f85b3UL, 0xb966d409UL, 0xce61e49fUL,
0x5edef90eUL, 0x29d9c998UL, 0xb0d09822UL, 0xc7d7a8b4UL, 0x59b33d17UL,
0x2eb40d81UL, 0xb7bd5c3bUL, 0xc0ba6cadUL, 0xedb88320UL, 0x9abfb3b6UL,
0x03b6e20cUL, 0x74b1d29aUL, 0xead54739UL, 0x9dd277afUL, 0x04db2615UL,
0x73dc1683UL, 0xe3630b12UL, 0x94643b84UL, 0x0d6d6a3eUL, 0x7a6a5aa8UL,
0xe40ecf0bUL, 0x9309ff9dUL, 0x0a00ae27UL, 0x7d079eb1UL, 0xf00f9344UL,
0x8708a3d2UL, 0x1e01f268UL, 0x6906c2feUL, 0xf762575dUL, 0x806567cbUL,
0x196c3671UL, 0x6e6b06e7UL, 0xfed41b76UL, 0x89d32be0UL, 0x10da7a5aUL,
0x67dd4accUL, 0xf9b9df6fUL, 0x8ebeeff9UL, 0x17b7be43UL, 0x60b08ed5UL,
0xd6d6a3e8UL, 0xa1d1937eUL, 0x38d8c2c4UL, 0x4fdff252UL, 0xd1bb67f1UL,
0xa6bc5767UL, 0x3fb506ddUL, 0x48b2364bUL, 0xd80d2bdaUL, 0xaf0a1b4cUL,
0x36034af6UL, 0x41047a60UL, 0xdf60efc3UL, 0xa867df55UL, 0x316e8eefUL,
0x4669be79UL, 0xcb61b38cUL, 0xbc66831aUL, 0x256fd2a0UL, 0x5268e236UL,
0xcc0c7795UL, 0xbb0b4703UL, 0x220216b9UL, 0x5505262fUL, 0xc5ba3bbeUL,
0xb2bd0b28UL, 0x2bb45a92UL, 0x5cb36a04UL, 0xc2d7ffa7UL, 0xb5d0cf31UL,
0x2cd99e8bUL, 0x5bdeae1dUL, 0x9b64c2b0UL, 0xec63f226UL, 0x756aa39cUL,
0x026d930aUL, 0x9c0906a9UL, 0xeb0e363fUL, 0x72076785UL, 0x05005713UL,
0x95bf4a82UL, 0xe2b87a14UL, 0x7bb12baeUL, 0x0cb61b38UL, 0x92d28e9bUL,
0xe5d5be0dUL, 0x7cdcefb7UL, 0x0bdbdf21UL, 0x86d3d2d4UL, 0xf1d4e242UL,
0x68ddb3f8UL, 0x1fda836eUL, 0x81be16cdUL, 0xf6b9265bUL, 0x6fb077e1UL,
0x18b74777UL, 0x88085ae6UL, 0xff0f6a70UL, 0x66063bcaUL, 0x11010b5cUL,
0x8f659effUL, 0xf862ae69UL, 0x616bffd3UL, 0x166ccf45UL, 0xa00ae278UL,
0xd70dd2eeUL, 0x4e048354UL, 0x3903b3c2UL, 0xa7672661UL, 0xd06016f7UL,
0x4969474dUL, 0x3e6e77dbUL, 0xaed16a4aUL, 0xd9d65adcUL, 0x40df0b66UL,
0x37d83bf0UL, 0xa9bcae53UL, 0xdebb9ec5UL, 0x47b2cf7fUL, 0x30b5ffe9UL,
0xbdbdf21cUL, 0xcabac28aUL, 0x53b39330UL, 0x24b4a3a6UL, 0xbad03605UL,
0xcdd70693UL, 0x54de5729UL, 0x23d967bfUL, 0xb3667a2eUL, 0xc4614ab8UL,
0x5d681b02UL, 0x2a6f2b94UL, 0xb40bbe37UL, 0xc30c8ea1UL, 0x5a05df1bUL,
0x2d02ef8dUL
};
unsigned long crc32_check(uint8_t *buf, int len)
{
unsigned long rslt = 0xffffffff;
for (int n = 0; n < len; n++)
{
rslt = crc_table[(rslt ^ buf[n]) & 0xff] ^ (rslt >> 8);
}
return rslt ^ 0xffffffff;
}
#endifuint32_t check_crc=0,check_CRC;
uint8_t update_buff_[4]={0x01,0x01,0x01,0x01};
check_crc=crc32_check(&update_buff_[0], 4);
三、在线验证
CRC（循环冗余校验）在线计算_ip33.com