13.2 Polynomial Implementation

The CRC polynomial equation is user configurable, allowing any polynomial equation to be used for the CRC checksum calculation. The polynomial and accumulator sizes are determined by the PLEN bits. For an n-bit accumulator, PLEN = n-1 and the corresponding polynomial is n+1 bits. This allows the accumulator to be any size up to 32 bits with a corresponding polynomial up to 33 bits. The MSb and LSb of the polynomial are always ‘1’ which is forced by hardware. Therefore, the LSb of the CRCXOR Low Byte register is hardwired high and always reads as ‘1’.

All polynomial bits between the MSb and LSb are specified by the CRCXOR registers. For example, when using the standard CRC32, the polynomial is defined as 0x4C11DB7 $(x^{32}+x^{26}+x^{23}+x^{22}+x^{16}+x^{12}+x^{11}+x^{10}+x^8+x^7+x^5+x^4+x^2+x+1)$. In this polynomial, the X³² and X⁰ terms are the MSb and LSb controlled by hardware. The X³¹ and X¹ terms are specified by setting the CRCXOR[31:0] bits with the corresponding polynomial value, which in this example is 0x04C11DB6. Reading the CRCXOR registers will return 0x04C11DB7 because the LSb is always ‘1’. Refer to the following example for more details.