Binary addition is straight forward \u2013 all we need to do is follow these simple rules:<\/p>\n\n\n\n
0 + 0 = 0<\/strong><\/p>\n\n\n\n 1 + 0 = 1<\/strong><\/p>\n\n\n\n 0 + 1 = 1<\/strong><\/p>\n\n\n\n 1 + 1 = 10<\/strong><\/p>\n\n\n\n 1 + 1 + 1 = 11<\/strong><\/p>\n\n\n\n Binary addition is often done in multiple columns and we always start with the column on the right and move to the next column on the left<\/strong>. <\/p>\n\n\n\n EG<\/strong> – add binary numbers 10 + 01<\/p>\n\n\n\n 10 + 01 = 11<\/strong><\/p>\n\n\n\n If we get a 1 + 1 our rules state we get 10<\/strong>.\u00a0 We should carry the 1 over to the column on the left and include this when adding up the next column.\u00a0 The 0 will stay in the current column.\u00a0<\/p>\n\n\n\n EG<\/strong> – add binary numbers 01 + 01<\/p>\n\n\n\n 01 + 01 = 10<\/strong><\/p>\n\n\n\n If we get a 1 + 1 in our furthest left column we simply add another digit on.<\/p>\n\n\n\n EG<\/strong> – add binary numbers 11 + 01<\/p>\n\n\n\n 11 + 01 = 100<\/strong><\/p>\n\n\n\n If we get a 1 + 1 + 1 (because of a carry) our rules state we get 11. We should carry the 1 over to the column on the left and include this when adding up the next column. The 1 will stay in the current column. <\/p>\n\n\n\n EG<\/strong> – add binary numbers 11 + 11<\/p>\n\n\n\n 11 + 11 = 110<\/strong><\/p>\n\n\n\n The OCR Computer Science GCSE specification expects you to be able to add 8 bits of binary together EG<\/strong><\/p>\n\n\n\n If a binary addition creates an extra digit like in some of the examples above it can cause an overflow error in the processor. An 8-bit processor cannot handle 9 bits and will only receive the first 8 bits leading to unexpected results.<\/p>\n\n\n\n A famous example of an overflow error is the Ariane 5 space rocket launch which went wrong due to an overflow error (luckily it was an unmanned space rocket and no one was hurt!). \u00a0\u00a0\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":" Binary addition is straight forward \u2013 all we need to do is follow these simple rules: 0 + 0 =…<\/p>\n","protected":false},"author":1,"featured_media":2581,"parent":1039,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"disable_featured_image":true,"footnotes":""},"class_list":["post-1565","page","type-page","status-publish","has-post-thumbnail","hentry"],"blog_post_layout_featured_media_urls":{"thumbnail":["https:\/\/computerscienced.co.uk\/site\/wp-content\/uploads\/2021\/09\/undraw_building_blocks_n0nc.svg",150,150,true],"full":["https:\/\/computerscienced.co.uk\/site\/wp-content\/uploads\/2021\/09\/undraw_building_blocks_n0nc.svg",1040,649,false]},"categories_names":null,"comments_number":"0","_links":{"self":[{"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1565","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/comments?post=1565"}],"version-history":[{"count":7,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1565\/revisions"}],"predecessor-version":[{"id":6138,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1565\/revisions\/6138"}],"up":[{"embeddable":true,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1039"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/media\/2581"}],"wp:attachment":[{"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/media?parent=1565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}} <\/td> 1<\/td> 0<\/td><\/tr> +<\/strong><\/td> 0<\/td> 1<\/td><\/tr> =<\/strong><\/td> 1<\/strong><\/td> 1<\/strong><\/td><\/tr> Explanation<\/strong><\/td> (1 + 0 = 1)<\/td> (0 + 1 = 1)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nBinary 1 + 1<\/h2>\n\n\n\n
<\/td> 0<\/td> 1<\/td><\/tr> +<\/strong><\/td> 0<\/td> 1<\/td><\/tr> =<\/strong><\/td> 1<\/strong><\/td> 0<\/strong><\/td><\/tr> Carry<\/strong><\/td> 1<\/td> <\/td><\/tr> Explanation<\/strong><\/td> (0 + 0 + 1 = 1 the 1 is our carry from the column on the right)<\/td> (1 + 1 = 10 the 1 is carried to the next column and the 0 is placed in the current column)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nBinary 1 + 1 (in the left column)<\/h2>\n\n\n\n
<\/td> <\/td> 1<\/td> 1<\/td><\/tr> +<\/strong><\/td> <\/td> 0<\/td> 1<\/td><\/tr> =<\/strong><\/td> 1<\/strong><\/td> 0<\/strong><\/td> 0<\/strong><\/td><\/tr> Carry<\/strong><\/td> 1<\/td> 1<\/td> <\/td><\/tr> Explanation<\/strong><\/td> <\/td> (1 + 0 + 1 = 10 the 1 is carried to the next column and the 0 is placed in the current column)<\/td> (1 + 1 = 10 the 1 is carried to the next column and the 0 is placed in the current column)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nBinary 1 + 1 + 1<\/h2>\n\n\n\n
<\/td> <\/td> 1<\/td> 1<\/td><\/tr> +<\/strong><\/td> <\/td> 1<\/td> 1<\/td><\/tr> =<\/strong><\/td> 1<\/strong><\/td> 1<\/strong><\/td> 0<\/strong><\/td><\/tr> Carry<\/strong><\/td> 1<\/td> 1<\/td> <\/td><\/tr> Explanation<\/strong><\/td> <\/td> (1 + 1 + 1 = 11 the 1 is carried to the next column and the 1 is placed in the current column)<\/td> (1 + 1 = 10 the 1 is carried to the next column and the 0 is placed in the current column)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nBinary addition to 8 digits<\/h2>\n\n\n\n
<\/td> 1<\/td> 0<\/td> 1<\/td> 0<\/td> 1<\/td> 0<\/td> 1<\/td> 0<\/td><\/tr> +<\/strong><\/td> 0<\/td> 0<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td><\/tr> =<\/strong><\/td> 1<\/strong><\/td> 1<\/strong><\/td> 1<\/strong><\/td> 0<\/strong><\/td> 1<\/strong><\/td> 0<\/strong><\/td> 0<\/strong><\/td> 1<\/strong><\/td><\/tr> Carry<\/strong><\/td> <\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> 1<\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nBinary Overflow<\/strong><\/h2>\n\n\n\n