![]() ![]() Multiple C statements (at least the decrement and compare, binary AND, test for zero, and left shift operations) must be executed for each bit in the message. Even though the unnecessary steps have been eliminated, it's extremely inefficient. It simply attempts to implement that algorithm as it was described above for this one particular generator polynomial. Listing 1 contains a naive software implementation of the CRC computation just described. So we never lose any information when the next message bit is shifted into the remainder. Also note here that the result of each XOR with the generator polynomial is a remainder that has zero in its most significant bit. So we won't actually need to track the quotient in our software implementation. What's most important to notice at this point is that we never use any of the information in the quotient, either during or after computing the CRC. The final value of the remainder is the CRC of the given message. The bit that's shifted out will always be a zero, so no information is lost. Left-shift the remainder, shifting in the next bit of the message.XOR the remainder with zero (no effect).Set the appropriate bit in the quotient to a zero, and.Otherwise (if the first bit is not a one):.XOR the remainder with the divisor and store the result back into the remainder.Set the appropriate bit in the quotient to a one, and.In the case of modulo-2 binary division, we simply: If that happens (just as in any other long division) it is necessary to indicate a successful division in the appropriate bit position in the quotient and to compute the new remainder. If the most significant bit of the remainder is a one, the divisor is said to divide into it.Beginning with the most significant bit in the original message and for each bit position that follows, look at the c+1 bit remainder:. ![]() Call the uppermost c+1 bits of the message the remainder.The modulo-2 division process is defined as follows: ![]() The divisor is a c+1-bit number known as the generator polynomial.įigure 1. The number of zero bits added to the message is the same as the width of the checksum (what I call c) in this case four bits were added. The number to be divided is the message augmented with zeros at the end. We'll use the example in Figure 1 to guide us. So even if your processor has a division instruction, you won't be able to use it.īefore writing even one line of code, let's first examine the mechanics of modulo-2 binary division. For another, modulo-2 binary division is not the same as ordinary division. For one thing, generally no registers are available to hold the very long bit sequence that is the numerator. Modulo-2 binary division doesn't map particularly well to the instruction sets of off-the-shelf processors. ![]() Knowing that all CRC algorithms are simply long division algorithms in disguise doesn't help. However, I'm going to keep the discussion at the level of the C language further steps could be taken to improve the efficiency of the final code by moving into the assembly language of your particular processor.įor most software engineers, the overwhelmingly confusing thing about CRCs is their implementation. I'll start with a naive implementation and gradually improve the efficiency of the code as I go along. I'm going to complete my 3-part discussion of checksums by showing you how to implement a CRC in C. However, sometimes you must compute a CRC in software, for example in a C or C++ program that will run in an embedded system. Generally speaking, CRCs are most efficiently calculated in dedicated hardware. If you suspect data corruption has led to a system failure, Barr Group can help by performing forensic analysis and reverse engineering services. This article shows how to implement an efficient CRC in C or C++.ĭownload Barr Group's Free CRC Code in C now.Ī CRC is a powerful type of checksum that is able to detect corruption of data that is stored in and/or transmitted between computers. Unfortunately, the modulo-2 arithmetic used to compute CRCs doesn't map easily into software. Cyclic Redundancy Codes (CRCs) are among the best checksums available to detect and/or correct errors in communications transmissions. ![]()
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