Martin Cowen ⁽⁴⁶⁾

I've been using this interview question for the last 20 years to test embedded C engineers: Given the formula for Fahrenheit as 9 * C + 32 = F - 5 Write a function to convert unsigned char tempInC to unsigned char tempInF (ie. All values are bytes, including intermediate results). The processor has no floating point library. Recently I was intrigued to find that a very similar problem was posed by professor James M. Conrad at the University of North Carolina at Charlotte at this point in his lecture on Embedded Systems: Software Testing. The responses I used to get were similar to what the students gave in that video. Whilst some candidates would think this was a maths problem that needed rearranging to solve for tempInC, others thought that I just wanted them to write the formula in…

CRCs are used for error detection in communication systems and storage systems. They have a combination of several advantageous properties whilst only requiring a short FCS, but they do have their limitations. If you require error correction as well as detection then you have to look at a different class of algorithms and will have to add much more redundancy to the codeword. The rest of this post is about message systems, where if an error is detected, the link layer of the protocol will take various actions such as discarding the message, sending a NACK, requesting a retry, waiting for retry until a timeout occurs etc. Another use of CRCs is for protecting data in memory, where similar considerations apply but the corruption possibilities may be different so you have to consider if the single random bit-flips model is…

Most of the time engineers just have to implement communications protocols that are given to them: industry standards, decided by committees or established by the dominant players. But surprisingly often there is the opportunity to create a new protocol, either for proprietary internal use or as part of inventing a new standard for the industry, and in those cases we have to choose a CRC polynomial. Although the process sounds complicated, in many cases it can be quite simple. But first we must make sure we don't fall into one of the common pitfalls which leads to sub-optimal performance. Be wary of the many excuses for using a standard CRC Before you go ahead with a standard polynomial know that it is not the only choice and may well not be the best choice. What you are doing by choosing…

The designers of serial protocols like USB, Ethernet, CAN, or anything using "CRC-8" or "CRC-16 CCITT" did not have access to information on which CRC polynomials are the best for their bit-size and application, so were chosen on what seemed to be reasonable grounds but are now known to be sub-optimal. It is not necessarily that better polynomials were unknown in academic research but that the information had not reached an industrial design audience. In fact, it was widely believed that the performance of the polynomials was similar enough that you could just randomly pick one from a list in a book and it would be fine for your application. Koopman said CRCs have been around for a really long time. You would think that after all these years, the best CRC is a well solved problem. Unfortunately, it isn't…

In the first post of this series on CRCs, I'm just going to clarify the terminology used. I am not going to cover the maths of how CRCs work in these posts, which can get surprisingly complex for what appears to be a set of simple bitwise manipulations and instead defer to Ben Eater's excellent CRC tutorial on YouTube. Small correction to the video, as noticed by commenter David W Smith, the length shown in Prof. Koopman's tables are in bits not bytes. They are for the dataword i.e. not including the FCS. I'm going to follow Prof. Koopman in his terminology Code Word is the whole message, with the payload being the dataword. Note that in this definition, any header is included in the Data Word. The Frame Check Sequence is the addition to the payload which adds redundancy…