How CRC algorithms work for CCITT16 and how to get them for CCITT8
I'm looking for a CRC-8 checksum implementation - and while reading on CRC in general I came across this algorithm for CCITT-16 (polynomial X ^ 16 + X ^ 12 + X ^ 5 + 1):
unsigned char ser_data;
static unsigned int crc;
crc = (unsigned char)(crc >> 8) | (crc << 8);
crc ^= ser_data;
crc ^= (unsigned char)(crc & 0xff) >> 4;
crc ^= (crc << 8) << 4;
crc ^= ((crc & 0xff) << 4) << 1;
Alternatively as a macro:
#define crc16(chk, byte) \
{ \
chk = (unsigned char) (chk >> 8) | (chk << 8); \
chk ^= byte; \
chk ^= (unsigned char)(chk & 0xFF) >> 4; \
chk ^= (chk << 8) << 4; \
chk ^= ((chk & 0xFF) << 4) << 1; \
}
I have two questions:
- How is this algorithm derived from a polynomial?
- Is there a similar simple algorithm for CCITT8 (polynomial X ^ 8 + X ^ 2 + X + 1)?
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3 answers
Here is a C CRC8-CCITT implementation based on the code from this answer ( fooobar.com/questions/327864 / ... ):
uint8_t crc8_ccitt(uint8_t crc, const uint8_t *data, size_t dataLength){
static const uint8_t POLY = 0x07;
const uint8_t *end = data + dataLength;
while(data < end){
crc ^= *data++;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
crc = crc & 0x80 ? (crc << 1) ^ POLY : crc << 1;
}
return crc;
}
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this webpage: https://decibel.ni.com/content/docs/DOC-11072 contains a link to a .zip file for each of the common (including the ones you are asking for) crc calculation algorithms.
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