{"id":40,"date":"2022-05-16T19:07:15","date_gmt":"2022-05-16T18:07:15","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/?page_id=40"},"modified":"2022-05-16T19:07:15","modified_gmt":"2022-05-16T18:07:15","slug":"two-complement-to-denary","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/two-complement-to-denary\/","title":{"rendered":"Two Complement to Denary"},"content":{"rendered":"

Before doing anything, we need to decide if the two\u2019s complement is a positive or negative number.<\/span><\/p>\n

Firstly you need to look at the most significant bit (the leftmost bit); if it is a 0 then it is positive and simply convert the number to decimal. For example:<\/span><\/p>\n\n\n\n\n
128<\/span><\/td>\n64<\/span><\/td>\n32<\/span><\/td>\n16<\/span><\/td>\n8<\/span><\/td>\n4<\/span><\/td>\n2<\/span><\/td>\n1<\/span><\/td>\n<\/tr>\n
0<\/span><\/td>\n0<\/span><\/td>\n1<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n1<\/span><\/td>\n0<\/span><\/td>\n1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Because the leftmost bit is a 0<\/span>\u00a0then we know the number is positive so we simply add <\/span><\/p>\n

32 + 4 + 1 = +37.<\/span><\/p>\n

Negative two\u2019s complement number<\/span><\/b><\/h2>\n

If the most significant bit<\/span>\u00a0(the leftmost bit); is a 1<\/span>\u00a0then we have to convert the number to a positive number then work out the denary equivalent.\u00a0<\/span><\/p>\n

You do this in exactly the same way you converted a positive number to negative i.e.<\/span><\/p>\n

    \n
  1. invert all the bits (so a 1 becomes a 0 and a 0 becomes a 1)<\/span><\/li>\n
  2. then add 1<\/span><\/li>\n
  3. convert to denary.<\/span><\/li>\n<\/ol>\n

    Example<\/h2>\n

    Convert the two\u2019s complement binary number 11111011 to denary.<\/span><\/p>\n\n\n\n\n
    \n

    1<\/span>28<\/span><\/p>\n<\/td>\n

    		64<\/span><\/td>\n32<\/span><\/td>\n16<\/span><\/td>\n8<\/span><\/td>\n4<\/span><\/td>\n2<\/span><\/td>\n1<\/span><\/td>\n<\/tr>\n
    1<\/span><\/td>\n1<\/span><\/td>\n1<\/span><\/td>\n1<\/span><\/td>\n1<\/span><\/td>\n0<\/span><\/td>\n1<\/span><\/td>\n\n

    1<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Because the most significant bit is a 1, we know it is a negative number therefore we need to convert it to a positive number first.<\/span><\/p>\n

    Change all the\u00a0<\/span>1<\/span><\/b>\u2019s to\u00a0<\/span>0<\/span><\/b>\u00a0and\u00a0<\/span>0<\/span><\/b>\u2019s to\u00a0<\/span>1<\/span><\/b>.<\/span><\/p>\n

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

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

    0 0 0 0 0 1 0 0<\/span>
    \n0 0 0 0 0 0 0<\/span>\u00a01 +<\/span><\/b>
    \n0 0 0 0 0 1 0 1<\/span><\/b><\/p>\n

    So\u00a0<\/span>00000101\u00a0<\/span><\/b>as Two\u2019s Complement =\u00a0<\/span>-5<\/span><\/b><\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    Before doing anything, we need to decide if the two\u2019s complement is a positive or negative number. Firstly you need to look at the most significant bit (the leftmost bit); if it is a 0 then it is positive and simply convert the number to decimal. For example: 128 64 32 16 8 4 2 […]<\/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-40","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages\/40","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=40"}],"version-history":[{"count":1,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages\/40\/revisions"}],"predecessor-version":[{"id":41,"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/pages\/40\/revisions\/41"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/glowblogs\/phshighercomputingscience\/wp-json\/wp\/v2\/media?parent=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}