{"id":77,"date":"2022-05-10T15:56:57","date_gmt":"2022-05-10T14:56:57","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/?page_id=77"},"modified":"2022-05-10T16:10:50","modified_gmt":"2022-05-10T15:10:50","slug":"floating-point-representation","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/floating-point-representation\/","title":{"rendered":"Floating Point Representation"},"content":{"rendered":"

What is a Real Number<\/span><\/b><\/h2>\n
    \n
  • Integer = whole number\u00a0<\/span><\/li>\n<\/ul>\n

    \u00a0 \u00a0 \u00a0 \u00a01, 4, 67, 1234, 134567, -12<\/p>\n

      \n
    • Real Number = Decimal numbers<\/span><\/li>\n<\/ul>\n

      \u00a0 \u00a0 \u00a0\u00a01.25, 158.54, 7895.36, -45.56<\/p>\n

      Representing Real Numbers\u00a0<\/span><\/b><\/h3>\n
        \n
      • Real numbers always contain a decimal point (.)<\/span><\/li>\n
      • But \u2013 the decimal point (.) cannot be stored in binary!<\/span><\/li>\n
      • However, if we can represent a real number with<\/span>\u00a0<\/span>the decimal point always in the same place<\/span>\u00a0<\/span>then we don\u2019t need to store the decimal point!<\/span><\/li>\n<\/ul>\n

        Fortunately such a system exists!<\/span><\/p>\n

        SCIENTIFIC NOTATION<\/span><\/b><\/p>\n

        Examples:<\/span><\/p>\n

        123456.7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0 0.1234567 x 10<\/span>6<\/span><\/p>\n

        0.001234\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0 0.1234 x 10<\/span>-2<\/span><\/p>\n

        1234.567\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0 0.1234567 x 10<\/span>4<\/span><\/p>\n

        All<\/span>\u00a0real numbers can be written in this common and consistent format<\/span><\/p>\n

        \"\"<\/p>\n

        Real numbers are always stored in two parts:<\/span><\/p>\n

          \n
        • The first part holds the mantissa converted into binary<\/span><\/li>\n
        • The second part holds the exponent also converted into binary<\/span><\/li>\n<\/ul>\n

          The\u00a0<\/span>mantissa<\/strong>\u00a0<\/strong>is the actual digits of the numbers, <\/span>this is the size of the number\u00a0<\/span><\/p>\n

          The\u00a0<\/span>exponent<\/strong>\u00a0<\/strong>is the power to which the base is raised, this s<\/span>tores the number of places to move the decimal point<\/span><\/p>\n

          \"\"<\/p>\n

          Changing the number of bits used to hold the mantissa or the exponent affects the number.<\/p>\n

            \n
          • Increasing\u00a0<\/strong>the number of bits used for the\u00a0mantissa\u00a0<\/strong>increases the\u00a0accuracy\u00a0<\/strong>to which the number is stored<\/li>\n
          • Increasing\u00a0<\/strong>the number of bits used for the\u00a0exponent\u00a0<\/strong>increases\u00a0the\u00a0range\u00a0<\/strong>of numbers that can be stored<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

            What is a Real Number Integer = whole number\u00a0 \u00a0 \u00a0 \u00a0 \u00a01, 4, 67, 1234, 134567, -12 Real Number = Decimal numbers \u00a0 \u00a0 \u00a0\u00a01.25, 158.54, 7895.36, -45.56 Representing Real Numbers\u00a0 Real numbers always contain a decimal point (.) But \u2013 the decimal point (.) cannot be stored in binary! However, if we can […]<\/p>\n","protected":false},"author":79984,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-77","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/pages\/77","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/users\/79984"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/comments?post=77"}],"version-history":[{"count":8,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/pages\/77\/revisions"}],"predecessor-version":[{"id":89,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/pages\/77\/revisions\/89"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phsn5computingscience\/wp-json\/wp\/v2\/media?parent=77"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}