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Parallel CRC Generator

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Every modern communication protocol uses one or more error detection algorithms. Cyclic Redundancy Check, or CRC, is by far the most popular one. CRC properties are defined by the generator polynomial length and coefficients. The protocol specification usually defines CRC in hex or polynomial notation. For example, CRC5 used in USB 2.0 protocol is represented as 0x5 in hex notation or as G(x)=x5+x2+1 in the polynomial. This CRC is implemented in hardware as a shift register as shown in the following picture.crc5

The problem is that in many cases shift register implementation is suboptimal. It only allows the calculation of one bit every clock. If a design has 32-bit wide datapath, meaning that every clock CRC module has to calculate CRC on 32-bit of data, this scheme will not work. Somehow this serial shift register implementation has to be converted into a parallel N-bit wide circuit, where N is the design datapath width, so that every clock N bits are processed.

I started researching the available literature on parallel CRC calculation methods and found only a handful of papers ([2], [3]) that deal with this issue. Most sources are academic and focus on the theoretical aspect of the problem. They are too impractical to implement in software or hardware for a quick code generation.

I came up with the following scheme that I’ve used to build an online Parallel CRC Generator tool. Here is a description of the steps in which I make use USB CRC5 mentioned above.    crc5-parallel

(1) Let’s denote N=data width, M=CRC width. For example, if we want to generate parallel USB CRC5 for 4-bit datapath, N=4, M=5.

(2) Implement serial CRC generator routine using given polynomial or hex notation. It’s easy to do in any programming language or script: C, Java, Perl, Verilog, etc.

(3) Parallel CRC implementation is a function of N-bit data input as well as M-bit current state CRC, as shown in the above figure. We’re going to build two matrices: Mout (next state CRC) as a function of Min(current state CRC) when N=0 and Mout as a function of Nin when M=0.

(4) Using the routine from (2) calculate CRC for the N values when Min=0. Each value is one-hot encoded, that is there is only one bit set. For N=4 the values are 0x1, 0x2, 0x4, 0x8.  Mout = F(Nin,Min=0)

(5) Build NxM matrix, Each row contains the results from (3) in increasing order. For example, 1’st row contains the result of input=0x1, 2’nd row is input=0x2, etc. The output is M-bit wide, which the desired CRC width. Here is the matrix for USB CRC5 with N=4.


(6) Each column in this matrix, and that’s the interesting part, represents an output bit Mout[i] as a function of Nin.

(7) Using the routine from (3) calculate CRC for the M values when Nin=0. Each value is one-hot encoded, that is there is only one bit set. For M=5 the values are 0x1, 0x2, 0x4, 0x8, 0x10.  Mout = F(Nin=0,Min)

(8) Build MxM matrix, Each row contains the results from (7) in increasing order. Here is the matrix for USB CRC5 with N=4

matrix2(9) Now, build an equation for each Mout[i] bit: all Nin[j] and Min[k] bits in column [i] participate in the equation. The participating inputs are XORed together.

Mout[0] = Min[1]^Min[4]^Nin[0]^Nin[3]

Mout[1] = Min[2]^Nin[1]

Mout[2] = Min[1]^Min[3]^Min[4]^Nin[0]^Nin[2]^Nin[3]

Mout[3] = Min[2]^Min[4]^Nin[1]^Nin[3]

Mout[4] = Min[0]^Min[3]^Nin[2]

That is our parallel CRC.

I presume since the invention of the CRC algorithm more than 40 years ago, somebody has already came up with this approach. I just coulnd’t find it and “reinvented the wheel”.

Keep me posted if the CRC Generation tool works for you, or you need more clarifications on the algorithm.

[September 29th, 2010] Users frequently ask why their implementation of serial CRC doesn’t match the generated parallel CRC with the same polynomial. There are few reasons for that:
– bit order into serial CRC isn’t the same as how the data is fed into the parallel CRC
– input data bits are inverted
– LFSR is not initialized the same way. A lot of protocols initialize it with F-s, and that’s what is done in the parallel CRC.

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Error Control Coding


  1. CRC on Wikipedia
  2. G. Campobello, G Patane, M Russo, “Parallel CRC Realization”
  3. W Lu, S. Wong, “A Fast CRC Update Implementation”

  1. Tennirva
    March 7th, 2012 at 04:01 | #1

    Hello Evgeni, I’m posting this message to check if it will be shown immediately. Because I already posted a message before.


  2. Fabien_782
    March 12th, 2012 at 07:43 | #2

    Hi everyone,

    i’m currently working on an hardware implementation of crc32 algorithm using the 2-step method, but it seems that the functions given in this paper by A. Simionescu: “CRC Tool: Computing CRC in Parallel for Ethernet,” Nobug Consulting,
    are not doing fine.

    If i’m not missunderstanding, here is he thing:

    Using a polynomial’s degree of 123, each intermediate values of CRC calculated on each clock cycles with incoming words are on 123 bits. the initial value of CRC must be (others=>’0′) using this methode. The huge advantage of this way to compute CRC is that on last word, you don’t have to pay attention on empty bytes, because either you have 0 or 1 or 2 … empty bytes, if your word is filled with ‘0’ where it’s empty, your final CRC value will be the same.
    => Much less logical elements used.

    But, what is weird with functions given on this article, is that the final value of CRC isn’t generated properly.

    Does anyone implemented these functions and did it worked fine on first try ?

    Thanks in advance,

  3. Serjik
    April 10th, 2012 at 09:55 | #3

    Hi, if any body needs “CRC32 for 802.3″ with equal results whith this sites crc32 generator,


    can use crc_chk.v and crc_gen.v files at this opensource project:

    Regards Serjik.

  4. DG
    April 22nd, 2012 at 09:54 | #4

    hi ,site is really great especially for beginner like me.can any one tell how the reg value lfsr_q linked with crc_out and also what abt its initial value.

  5. April 22nd, 2012 at 19:57 | #5


    LFSR value is the same as CRC. Its initial value depends on the protocol.


  6. Rean
    October 8th, 2012 at 19:40 | #6


    The article is really useful. Thanks alot.

    A little question. Why do we use ONE HOT values for the two matrices input ?


  7. October 9th, 2012 at 08:47 | #7

    Because it enables any combination of the input values.


  8. Rean
    October 22nd, 2012 at 23:16 | #8

    Thanks for reply — (I am nearly half way to the correct understanding)

    Does it means that — it mimics the behaviour of LFSR in a sense that : There is only one input to a CRC and it matters only when it is SET (=1) — & since it is a shift register it shifts towards the output.


  9. Ludwig
    July 11th, 2013 at 07:47 | #9

    Hello Evgeni,

    Thanks for the awesome Tool! I generated VHDL Code for a CRC5 for 20 Bits.

    Where is my Mistake:
    I feed a dataword into the data_in and do not change it.
    crc_en is 0.
    I feed a Clock into clk.
    I set the rst to 1 for a few clock cycles and then to 0
    after a few clocks I set crc_en to 1 and get the CRC at crc_out?
    This CRC is fed back by the crc routine as new start-word?
    When I get the next positive clk edge The Routine does the CRC-“check” and I should get the start-word as a result?
    This is not the case 🙁

    can you please help me?


  10. July 11th, 2013 at 14:09 | #10

    Hi Ludwig,

    When you feed back the current CRC value, the logic calculates the next CRC based on the current one and the data_in.
    So it’s not the CRC for start word anymore.
    If you want to calculate CRC for start word, you need to reset the CRC first.


  11. Ludwig
    July 12th, 2013 at 02:15 | #11

    Hi Evgeni,

    Thank you for the quick response!
    Okay I understand, that I have to reset before each crc computation.

    So I put my data into data_in, reset, enable, and get my CRC. That works.
    I transmit both to the receiver.

    How do I check for correct Transmission on the receiving end?
    In other words: how do I feed Data and CRC into the Routine to get the “00000”, which says, that there was no transmission error?

    Thank you

  12. July 23rd, 2013 at 10:14 | #12

    Hi Ludwig,

    You check CRC in a similar way you generate it. Pass the received data thru the CRC module and then compare with the expected CRC.


  13. Majeed Nader
    August 7th, 2013 at 06:44 | #13

    Hello Evgeni,

    I really need help to Implement CRC for a system which the data width is 1120 bit ( 140 bit) and the polynomial is order is 28 which is (x^28 + x^26 + x^24 + x^23 + x^18 + x^17 +x^16 + x^15 + x^14 + x^11 + x^8 + x^4 + x^3 + 1) or (1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1 ).
    The online system does not work for that long data width.
    Could you please, give the Verilog for the above CRC.
    I appreciate your cooperation, and thanks in advance.

    * Correction: 1120 bit (140 byte)

  14. August 7th, 2013 at 07:11 | #14

    Hi Majeed,

    You can download a standalone application and source code for CRC generator from OpenCores

    You can increase DATA_MAX_WIDTH from 1024 in the code to the size you need, then recompile.


  15. Majeed Nader
    August 7th, 2013 at 07:16 | #15

    Detail of my previous post:

    Also the encoding is performed in a systematic form, which means that in GF(2), the polynomial:
    (M1 X^k+27 + M2 X^k+26 + M1 X^k+25 +…..+ M^k X28 + p1 X^27 + p2 X^26 +…..+ p27 X^1 + p28)
    where:Denote the bits in the input message by M1, M2 …Mk (K=1120 bit) and the parity bits by p1, p2,…,p28.

  16. Majeed Nader
    August 7th, 2013 at 07:20 | #16

    Thanks so much.
    Can I also Implement the above systematic form in the standalone application?

  17. August 7th, 2013 at 20:02 | #17

    Hi Majeed,

    I’m not familiar with the systematic form.


  18. Majeed Nader
    August 8th, 2013 at 11:42 | #18

    Thanks so much. I appreciate your cooperation

  19. Smitha
    November 11th, 2013 at 00:25 | #19


    I have downloaded the code from your website for 802.3 for 8 bit of data, 32 bit polynomial.

    here i have few doubts.
    1.CRC EN should be held high for complete data( means am sending 1478 bytes of data)
    2.when i compare the CRC out with thw online CRC generators, the output is not matching?
    3.The same check will be done at s/w application also, so they are asking give me polynomial number like that .. when i simulate your code by default the number will be “4E08BFB4” is it the one?
    its very urgent required

    Please reply me as early as possible

  20. November 11th, 2013 at 11:11 | #20


    1. CRC En should be held for the valid data
    2. There are several possible reasons for the mismatch: byte and bit ordering, incorrect polynomial. I’d recommend reading earlier discussions on this thread.


  21. Thomas
    November 14th, 2013 at 13:27 | #21

    Evgeni many thanks for this wonderfull tool!!!!
    implemented 8 bit crc on 40 bit input with HD of 4.
    CRC computation is instant (rising edge) and fully synthesizable!!!

  22. November 14th, 2013 at 14:44 | #22

    Hi Thomas,

    Great to hear that you found the tool useful.


  23. Ajinkya
    January 11th, 2014 at 21:23 | #23

    Hi Evgeni,
    I want to implement CRC for modbus which uses CRC-16 ANSI or 0x8005 (normal form) & 0xA001 (reverse form). I used your tool but it isn’t giving correct output.
    I initializeed CRC register to all 1’s (modbus specification).
    Are there some additional operations needed to get the correct output?
    for e.g. data = 0xFF CRC =0x00FF & data = 0x00 CRC =0x40BF (using modbus calculator)

    Please reply me as early as possible


  24. January 11th, 2014 at 23:40 | #24

    Hi Ajinkya,

    I most cases it’s a bit or byte ordering problem. Try to simplify the code; for example start with serial data (1 bit), instead of parallel.


  25. Ajinkya
    January 12th, 2014 at 05:48 | #25

    Thanx Evgeni !!
    It worked by reversing both data and crc registers.

    It is a great tool for crc!! genius

  26. echo
    February 18th, 2014 at 14:06 | #26

    In the pdf file, there seems a typo in the equation for CRC5:
    It should be: Mout[0] = Min[1]^Min[4]^Nin[0]^Nin[3]

    Instead, the doc says Mout[0] = Min[1]^Min[4]^Min[0]^Min[3]

  27. February 18th, 2014 at 15:08 | #27

    Yes, there is a typo.
    Correction is buried in the comments here:

  28. Musthaq Mohammed
    April 1st, 2014 at 01:32 | #28

    Hello sir,
    I am currently working on a ethernet code where i need to implement a CRC32 module for 32 bit datain. Can you please guide me through it?


  29. Musthaq Mohammed
    April 1st, 2014 at 21:26 | #29

    Hello Evgeni,
    Well, i generated the verilog code for 802.3 protocol for 32 bit datain. Since I want to validate the crc output, I am not able to do it. Can you please guide me through it?
    Hopes to listen from you soon.


  30. April 1st, 2014 at 21:35 | #30

    Hi Musthaq,

    To validate the generated CRC, you’d need some other CRC checker.


  31. Musthaq Mohammed
    April 1st, 2014 at 21:48 | #31

    Hi Evgeni,
    Thanks for your reply. Do you have any idea on where I can get a crc checker.


  32. Musthaq Mohammed
    April 2nd, 2014 at 21:51 | #32

    Hello again,

    Well, some of the online calculators i tried doesn’t match with the value that your generated module provides. So, is there any thing else i need to be taken account of, like reverse datain or something like that?

    Hopes you replies soon.


  33. April 2nd, 2014 at 22:27 | #33

    Yes, most likely the mismatch is due to byte or bit order, or incorrect initialization.

  34. Musthaq Mohammed
    April 3rd, 2014 at 00:48 | #34

    So, Can you please tell me the procedure to drive the datain and any link for the crc32 calculator, which will help me to validate the result?

  35. April 3rd, 2014 at 07:24 | #35

    @Musthaq Mohammed
    The procedure is simple: feed the output of CRC generator into CRC checker, and verify that the results are the same. Do this for multiple values of the data.

  36. zwabbit
    April 9th, 2014 at 13:39 | #36

    I’ve been trying to work through your steps to make sure I understand the logic enough so that I can explain it to others if I end up using a module generated with your tool, but I’m having issues validating the serial LFSR implementation for CRC32. I’m using the diagram at the top where you show a hardware CRC5 implementation as a reference so I have the input data bit xor’ed with the highest bit of the current CRC32 value. That’s then fed back in and xor’ed as appropriate with the other bits that correspond to the polynomial. The 32bit word that’s being fed in is also being fed in LSB first. Does that sound more or less correct?

  37. April 9th, 2014 at 18:19 | #37


    Data widths of CRC generator and checker is unknown in general. CRC generator might be serial (1 bit), whereas checker is parallel (2,4,8,32, etc). So it has to work for any combination.
    Let’s consider the following example with 8 first data bits numbered as 1,2,3,4,5,6,7,8.
    If CRC generator is serial, it generates CRC 8 times for bits 1..8.
    If CRC checker is 4-bit parallel, it checks data in 2 chunks: bits 1..4 and 5..8.
    But at the end of 8’th bit both CRCs have to match.

    This imposes LSB-first bit order.


  38. Greg
    July 1st, 2014 at 11:00 | #38

    Hi Evgeni,
    I have utilized your parallel CRC generator for the generation of a 16bit CRC with polynomial: 0xBAAD (koopman notation). Everything works perfectly when I initialize the state registers within the RTL to 0. That is, I have a model which I use to verify the RTL and both the model and the RTL match during simulation.
    However when I initialize the state registers to all 1’s prior to a CRC computation the model and the RTL no longer match. Please note that I also initialize the model with all 1’s as well. I actually have two models (generated differently) which seem to both agree when the state registers are initialized to all 1’s or all 0’s. I have read the previous comments on this thread and in particular your comment about some potential causes for mismatch could be the bit ordering or state initialization. So really the part that has me scratching my head is that when I change only the initialization state of the RTL and the model, they are no longer in agreement. Do you have any suggestions as to how I might isolate this problem?


  39. July 1st, 2014 at 12:07 | #39

    Hi Greg,

    You can start with generating serial CRC, where data width is 1bit, and compare the output with your 1-bit CRC model. That’s the simplest way to weed out all bit/byte ordering issues.


  40. Greg
    July 1st, 2014 at 15:53 | #40

    Hi Evgeni,
    I have finally spotted the problem. I tried changing my model for a different implementation. I have used this document as a reference for two possible serial CRC implementations: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1234528 (Parallel CRC Realization
    Giuseppe Campobello, Giuseppe Patane`, and Marco Russo)

    I tried the second variant: LFSR2 as mentioned in the text and this version matches the DUT when the state is initialized to 1’s prior to CRC computation. I don’t yet know why there is a difference as both work correctly when the state is initialized to 0’s. The nice thing about the second variant is that trailing zeros of dimension matching the CRC do not need to be driven through the CRC engine to arrive at the CRC checksum.

    Thanks for your help.

  41. Met
    July 6th, 2014 at 11:06 | #41

    Hi Evgeni, please explain to me how to build the matrix. I do not understand where are the 0x1, etc. and what they mean

  42. Dev
    July 17th, 2014 at 23:21 | #42

    Hello @ Evgeni

    I found your tool and article are very useful. Thanks for that.
    I want to generate crc16 for 0x1021 poly. I generated simple 8bit data, 16 bit crc core using outputlogic.com and using it in my module. But am getting results which are not matching with the results of s/w (same specs) coded in serial which is tested rigorously. I tried even bit reversal and poly reverse…etc. Can u help me on this..Actually I want to generate crc16 for higher data width, so I thought if I can get for 8bit, I can proceed further.

    Thanks alot in advance.

  43. Hetal
    December 9th, 2014 at 12:18 | #43

    Hi Evgeni,

    I am trying to use your CRC-32 generator with 32-bit of data as input. I do the following:

    Step1: Reset
    Step2: Wait for some cycles.
    Step3: Drive input data as 0x31323334 (ascii 1234) and set crc_en=1
    Step4: Wait for one cycle
    Step5: Drive crc_en=0

    I am getting 0xA695c4aa as output while on website
    Output should not have been that but one of these:
    Normal 0x04C11DB7
    Big Endian(ABCD) 7C 87 D0 FA
    Little Endian(DCBA) FA D0 87 7C

    Though, I have a basic question – from the theory that you explained if the data is 0x31323334 in serial case you start taking the data from bit[31]-> bit[0] to build your parallel CRC generator – is that correct and if so, do I need to change the input data to be something like this
    and so on
    i.e. the data would become 0x2ccc4c8c – though with even tat I don’t get one of the above answers but some completely different answer.

    Please help.

  44. lavanya
    February 20th, 2015 at 02:11 | #44

    lavanya :
    Hi Evgeni,
    I found your tool very useful.But I have a doubt in the logic implemented in the H1 & H2 matrices.can u pls explain me the logic implemented in USB CRC5 using Xor gates.

    can u pls give me the theoritical calculations for USB crc5
    Thanking u

  45. February 20th, 2015 at 07:49 | #45


    If you understand the theory behind serial CRC with 1-bit data, then it’s straightforward to migrate to parallel CRC with N-bit of data. Basically, it’s N serial CRC operations squeezed into a single operations. That single operation is encoded as two matrices H1 and H2.


  46. OscarO
    February 27th, 2015 at 06:41 | #46


    I tried your tool to generate code for CCITT CRC-16 with 1021 poly. I tried to put in the message 123456789 (0x31323334353637389). I got a result of 0x29b1, however this article (http://srecord.sourceforge.net/crc16-ccitt.html#long-hand) says that is a bad CRC. It goes on to explain that the data should be augmented by 16 zeroes (the width of the poly). I did that by increasing the bit width of the generated Verilog and putting in 88’h3132333435363738390000 as the data. It still did not give the “correct” CRC of 0xE5CC, I got 0x0B84. Any thoughts on this?


  47. February 27th, 2015 at 08:31 | #47

    Hi Oscar,

    Data augmentation is already built into the CRC generator.

    Typical problems with CRCs are byte ordering, bit swizzling, and CRC negation. Make sure that most significant byte comes in first. The same goes with bits.
    Many CRC standards require negating (flipping) CRC bits.

    A couple of things to try: all-zero data, and serial data (1-bit wide, that will eliminate possible data ordering issues)


  48. Dhana
    March 25th, 2015 at 14:34 | #48

    Dhana :
    Hi Evgeni and every one reading this,
    Thanks for the detailed steps given the article, Evgeni. My polynomial is x^6+x+1 and I choose 8-bit data width. Followed steps 1 through 6 of the article and generated the equations and implemented the logic in vhdl (hand written code). When I ran simulation for 8-bit data, for all 256 combinations, serial implementation and parallel implementation produced same crc6.
    But when I made the input data to 16-bits long, fed first byte to parallel crc calculator and in next clock cycle, fed the second byte.
    The output of the parallel and serial implementations do not match anymore for any data size not equal to 8. Since hardware responds correctly when serial implementation generated crc6 is appended to a frame, the parallel implementation is producing incorrect result.
    I have read through every comment and your reply but could not figure out a solution and hence asking for your help
    My questions,
    1. When more than one byte of data needs crc calculation, what is the order or procedure to feed the data to parallel crc calculation equation or vhdl code or function?
    For example, for 16 bit data,
    a. initialized crc6 with init value (all 1’s)
    b. first fed least 8-bits of data to crc calculation
    c. used the crc result from the above step-b and next 8-bits of data (most significant 8 bit of data) to calculate new crc using same equations.
    d. output result and go back to step-a.
    But my above procedure produces incorrect CRC6.
    2. When the total number of bits that needs CRC calculation is not multiples of ‘8′, should I append appropriate number of ‘0′ or ‘1′ at the beginning or end of the original data?
    I tried both, but I did not get correct CRC. But I should NOT be doing anything for my question-2, since I learn how to solve my question-1 in the first place.
    If you could share logic on how to solve my problem, I would be thankful to you.
    Thanks for your time.

  49. April 9th, 2015 at 01:27 | #49

    hi, everyone if any could help me in coding crc in verilog with its test bench
    thanks in advance

  50. Ashok
    June 13th, 2015 at 02:52 | #50


    may i know that how you are realizing matrix H1 and matrix H2.


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