{"id":35,"date":"2022-05-16T18:57:53","date_gmt":"2022-05-16T17:57:53","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/?page_id=35"},"modified":"2022-05-16T19:00:45","modified_gmt":"2022-05-16T18:00:45","slug":"two-complement-to-binary","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/two-complement-to-binary\/","title":{"rendered":"Two Complement to Binary"},"content":{"rendered":"

Representing Negative Integers<\/span><\/span>\u00a0<\/span><\/h2>\n

All numbers belong to the set or group called real numbers<\/span><\/span>\u00a0<\/span><\/p>\n

\"\"<\/p>\n

Inside the set of real numbers is a set of all positive and negative whole numbers.\u00a0 A better way of representing negative numbers is by using\u00a0<\/span>Two’s Complement<\/span><\/b>.\u00a0<\/span><\/p>\n

Two’s\u00a0 Complement is deigned so that the set of integers show symmetry about zero.<\/span><\/p>\n

To find the Two’s Complement\u00a0 of a number :<\/h2>\n
    \n
  • Change all the<\/span>\u00a01’s<\/span><\/b>\u00a0to\u00a0<\/span>0<\/span><\/b>\u00a0and<\/span>\u00a00’s<\/span><\/b>\u00a0to<\/span>\u00a01<\/span><\/b><\/li>\n
  • Add 1<\/span><\/li>\n<\/ul>\n

    Example 1<\/h2>\n

    How would\u00a0<\/span>– 5<\/span><\/b>\u00a0be represented using two complement?<\/span><\/p>\n

    5 =\u00a0<\/span>0 0 0 0 0 1 0 1<\/span><\/b><\/p>\n

    Change all the 1’s to 0 and 0’s to 1<\/span><\/p>\n

    0 0 0 0 0\u00a0 1 0 1<\/span>
    \n1 1 1 1 1 0 1 0<\/span><\/b><\/p>\n

    Add 1\u00a0<\/span><\/p>\n

    1 1 1 1 1 0 1 0<\/span>
    \n0 0 0 0 0 0 0\u00a0<\/span>1<\/span><\/b>\u00a0+<\/span>
    \n1 1 1 1 1 0 1 1<\/span><\/b><\/p>\n

    So -5 as Two Complement =\u00a0<\/span>1 1 1 1 1 0 1 1<\/span><\/b>\u00a0<\/span><\/p>\n

    Example 2<\/span><\/h2>\n

    How would<\/span>\u00a0– 88<\/span><\/b>\u00a0be represented using two complement?<\/span><\/p>\n

    88 =\u00a0<\/span>0 1 0 1 1 0 0 0<\/span><\/b><\/p>\n

    Change all the 1’s to 0 and 0’s to 1<\/span><\/p>\n

    0 1 0 1 1 0 0 0<\/span>
    \n1 0 1 0 0 1 1 1<\/span><\/b><\/p>\n

    Add 1\u00a0<\/span><\/p>\n

    1 0 1 0 0 1 1 1<\/span><\/b>
    \n0 0 0 0 0 0 0\u00a0<\/span>1<\/span><\/b>\u00a0+<\/span>
    \n1 0 1 0 1 0 0 0<\/span><\/b><\/p>\n

    So -88 as Two Complement =\u00a0<\/span>1 0 1 0 1 0 0 0<\/span><\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

    Representing Negative Integers\u00a0 All numbers belong to the set or group called real numbers\u00a0 Inside the set of real numbers is a set of all positive and negative whole numbers.\u00a0 A better way of representing negative numbers is by using\u00a0Two’s Complement.\u00a0 Two’s\u00a0 Complement is deigned so that the set of integers show symmetry about zero. […]<\/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-35","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/users\/79984"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":3,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":39,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages\/35\/revisions\/39"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}