Lowest exponent of a CRC polynomial












0














I have never seen a CRC polynomial without the lowest term x⁰ = 1.



Are there any exceptions I haven't seen yet?
Why do all CRC polynomials have the lowest term x⁰?






crc polynomials







share|improve this question



























    0














    I have never seen a CRC polynomial without the lowest term x⁰ = 1.



    Are there any exceptions I haven't seen yet?
    Why do all CRC polynomials have the lowest term x⁰?






    crc polynomials







    share|improve this question

























      0












      0








      0







      I have never seen a CRC polynomial without the lowest term x⁰ = 1.



      Are there any exceptions I haven't seen yet?
      Why do all CRC polynomials have the lowest term x⁰?






      crc polynomials







      share|improve this question













      I have never seen a CRC polynomial without the lowest term x⁰ = 1.



      Are there any exceptions I haven't seen yet?
      Why do all CRC polynomials have the lowest term x⁰?






      crc polynomials




      crc polynomials






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Nov 11 at 20:16









      Silicomancer

      4,05933475




      4,05933475
























          1 Answer
          1






          active

          oldest

          votes


















          2














          A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.



          However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.






          share|improve this answer























            Your Answer






            StackExchange.ifUsing("editor", function () {
            StackExchange.using("externalEditor", function () {
            StackExchange.using("snippets", function () {
            StackExchange.snippets.init();
            });
            });
            }, "code-snippets");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "1"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f53252820%2flowest-exponent-of-a-crc-polynomial%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            2














            A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.



            However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.






            share|improve this answer




























              2














              A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.



              However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.






              share|improve this answer


























                2












                2








                2






                A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.



                However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.






                share|improve this answer














                A CRC polynomial of the form xn + ... + x0 is used for a n bit CRC (it is used with a borrowless divide of the data bits by the CRC polynomial that produces an n bit remainder, the CRC). If the CRC polynomial is of the form xn + ... + x1 (no x0 term), then it is effectively a n-1 bit CRC.



                However, there are cases where common code may use different tables for fast computations of 32 bit or 16 bit CRC's, where the only difference in the main part of the code is the constants. The code is written as if the CRC is of the form x32 + ... + x0, but to allow most of the same code to generate a 16 bit CRC, the polynomial is of the form x32 + ... + x16. There's a final step correction done to shift the final CRC right by 16 bits to place the 16 bit CRC in the proper bits. An example of this is in this 500+ line fast crc32/16 assembly example using pclmulqdq insruction (carryless multiply), which in this case is setup to produce a 16 bit CRC.







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited Nov 11 at 22:17

























                answered Nov 11 at 22:07









                rcgldr

                15.1k31333




                15.1k31333






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Stack Overflow!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    To learn more, see our tips on writing great answers.





                    Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                    Please pay close attention to the following guidance:


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f53252820%2flowest-exponent-of-a-crc-polynomial%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    這個網誌中的熱門文章

                    Tangent Lines Diagram Along Smooth Curve

                    圖片
                    7 1 I am trying to replicate a diagram and have a minimal example. I don't know how to add additional tangents between the specified points and preserve smoothness. documentclass{article} usepackage{tikz} usetikzlibrary{calc,intersections} begin{document} begin{tikzpicture} % Axes draw [->, name path=x] (-1,0) -- (11,0) node [right] {$x$}; draw [->] (0,-1) -- (0,6) node [above] {$y$}; % Origin node at (0,0) [below left] {$0$}; % Points coordinate (start) at (1,-0.8); coordinate (c1) at (3,3); coordinate (c2) at (5.5,1.5); coordinate (c3) at (8,4); coordinate (end) at (10.5,-0.8); % show the points foreach n in {start,c1,c2,c3,end} fill [black] (n) circle (2pt) node [below] {}; % join the coordinates draw [thick,name path=curve] (start) to[out=70,in=180] (c1) to[out=0,in=180]
                    閱讀完整內容

                    Yusuf al-Mu'taman ibn Hud

                    圖片
                    Main article: Taifa of Zaragoza Al-Mu'taman Ruler of Zaragoza Reign 1081–1085 Predecessor Ahmad al-Muqtadir Successor Al-Mustain II Born Zaragoza Died 1085 Full name Yusuf ibn Ahmad al-Mu'taman ibn Hūd House Banu Hud Yusuf ibn Ahmad al-Mu'taman ibn Hūd (Arabic: المؤتمن بالله يوسف إبن أحمد إبن هود ‎, al-Mutaman bi l-Lah , died c. 1085) was the third king of the Banu Hud dynasty who ruled over the Taifa of Zaragoza from 1081 to 1085. Yusuf al-Mutaman reigned during the height of power of Muslim Zaragoza , following the thriving period of his father Ahmad al-Muqtadir. He continued his father's efforts and created around him a court of intellectuals, living in the beautiful palace of Aljafería, nicknamed as "the palace of joy". Al-Mu'taman was also a scholarly king and a patron of science, philosophy and arts. As an example of a wise king, he knew astrology, philosophy, and especially mathematics, a discipline in which
                    閱讀完整內容

                    Zucchini

                    圖片
                    This article is about the vegetable. For other uses, see Zucchini (disambiguation). Zucchini (courgette) A striped and a uniform color zucchini Genus Cucurbita Species Cucurbita pepo Origin 19th century northern Italy The zucchini ( / z uː ˈ k iː n i / , American English) or courgette ( / k ʊər ˈ ʒ ɛ t / , British English) is a summer squash which can reach nearly 1 metre (100 cm; 39 in) in length, but is usually harvested when still immature at about 15 to 25 cm (6 to 10 in). [1] A zucchini is a thin-skinned cultivar of what in Britain and Ireland is referred to as a marrow. [2] [3] In South Africa, a zucchini is known as a baby marrow. Along with certain other squashes and pumpkins, the zucchini belongs to the species Cucurbita pepo . It can be dark or light green. A related hybrid, the golden zucchini, is a deep yellow or orange color. [4] In a culinary context, the zucchini is treated as a vegetable; it is usually cooked and presented as a savory dish o
                    閱讀完整內容