{"id":122,"date":"2024-06-25T12:43:16","date_gmt":"2024-06-25T12:43:16","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=122"},"modified":"2025-09-08T11:35:52","modified_gmt":"2025-09-08T06:05:52","slug":"floating-point-representation","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/cs-it\/floating-point-representation","title":{"rendered":"Floating-Point Representation"},"content":{"rendered":"\r\n<ul>\r\n<li style=\"text-align: justify;\">Very large numbers cannot be represented using fixed-point notation, nor can very small fractions.<\/li>\r\n<li style=\"text-align: justify;\">For decimal numbers, we get around this limitation by using scientific notation.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: justify;\"><strong>Example:<\/strong><br \/>976000000000 can be represented as 9.76 \u00d7 10<sup>11<\/sup>.<br \/>0.00000000000976 can be represented as 9.76 \u00d7 10<sup>\u201312<\/sup>.<\/p>\r\n<ul style=\"text-align: justify;\">\r\n<li>This same approach can be taken with binary numbers. We can represent a number in the form M \u00d7 B<sup>\u00b1E<\/sup> <br \/>where, M is mantissa, E is exponent<\/li>\r\n<\/ul>\r\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-80 aligncenter\" src=\"http:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/06\/floating-point-format.png\" alt=\"Floating Point Format\" width=\"358\" height=\"109\" \/><\/p>\r\n<ul style=\"text-align: justify;\">\r\n<li>In order to simply operations, floating point numbers are normalized. A normalized number is one in which the most significant digit of mantissa is 1. Thus, a normalized non zero number is on in the form \u00b1 1.bbb &#8230;.\u00a0b \u00d7 2<sup>\u00b1E<\/sup>.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/cs-it\/cache-memory-design\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/cs-it\/what-is-i-o-modules-and-its-types\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a> <br \/><strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-computer-organization-and-architecture\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Computer Organization and Architecture?<\/strong><\/a><\/p>\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Very large numbers cannot be represented using fixed-point notation, nor can very small fractions. For decimal numbers, we get around<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[50],"class_list":["post-122","post","type-post","status-publish","format-standard","hentry","category-cs-it","tag-floating-point-format"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=122"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/122\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}