23-bit mantissa and 9-bit exponent range and precision












0












$begingroup$


I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.




Some computers (such as IBM mainframes) used to implement real data
using a 23-bit mantissa and a 9-bit exponent. What precision and range
can we expect from real data on these machines?




My understanding:



This floating point system has the following representation:



S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM



with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?



As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.



Is this correct?










share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.




    Some computers (such as IBM mainframes) used to implement real data
    using a 23-bit mantissa and a 9-bit exponent. What precision and range
    can we expect from real data on these machines?




    My understanding:



    This floating point system has the following representation:



    S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM



    with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?



    As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.



    Is this correct?










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.




      Some computers (such as IBM mainframes) used to implement real data
      using a 23-bit mantissa and a 9-bit exponent. What precision and range
      can we expect from real data on these machines?




      My understanding:



      This floating point system has the following representation:



      S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM



      with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?



      As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.



      Is this correct?










      share|cite|improve this question









      $endgroup$




      I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.




      Some computers (such as IBM mainframes) used to implement real data
      using a 23-bit mantissa and a 9-bit exponent. What precision and range
      can we expect from real data on these machines?




      My understanding:



      This floating point system has the following representation:



      S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM



      with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?



      As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.



      Is this correct?







      computer-science binary computational-mathematics floating-point






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 11 at 23:00









      sequencesequence

      4,26331437




      4,26331437






















          0






          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          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
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3070420%2f23-bit-mantissa-and-9-bit-exponent-range-and-precision%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes
















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • 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.


          Use MathJax to format equations. MathJax reference.


          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%2fmath.stackexchange.com%2fquestions%2f3070420%2f23-bit-mantissa-and-9-bit-exponent-range-and-precision%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







          Popular posts from this blog

          Human spaceflight

          Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

          張江高科駅