If we assume x is base 2 then we get: x^7 + x^3 + x^2 + x^1 + x^0
To better understand it, think of this multiplication: (x^3 + x^2 + x^0)(x^3 + x^1 + x^0) This is technically called Polynomial Arithmetic.
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You can think of the CRC-32 as a series of "Binary Arithmetic with No Carries", or basically "XOR and shift operations". Also it is extremely difficult to find a polynomial that detects different bit errors effectively. Why this polynomial? Because there needs to be a standard given polynomial and the standard was set by IEEE 802.3.
The highest term (x 32) is usually not explicitly written, so it can instead be represented in hex just asįeel free to count the 1s and 0s, but you'll find they match up with the polynomial, where 1 is bit 0 (or the first bit) and x is bit 1 (or the second bit). I could use the values I found online, but I want to understand how they were created.Īny help in clearing up these incredibly confusing numbers would be very appreciated.
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I attempted to code in C how the table is formed: for (i = 0 i >= 1 īut this seems to generate values inconsistent with values I have found elsewhere on the Internet.
I've read A Painless Guide To CRC Error Detection Algorithms, and I must say it was not painless. I understand that it is the remainder from a non-carry-based arithmetic division of the message value, divided by the (generator) polynomial, but the actual implementation of it escapes me. Maybe I'm just not seeing it, but CRC32 seems either needlessly complicated, or insufficiently explained anywhere I could find on the web.