Converting decimal (denary) into binary is very simple and can be done by simply remembering the following numbers:<\/p>\n\n\n\n
128, 64, 32, 16, 8, 4, 2, 1<\/strong><\/p>\n\n\n\n Have you noticed anything about these numbers?<\/strong><\/p>\n\n\n\n From right to left they are doubling every time!<\/p>\n\n\n\n So why do we need to remember these numbers?<\/strong><\/p>\n\n\n\n Let me show you with an example.<\/p>\n\n\n\n Convert denary number 198 into binary. <\/p>\n\n\n\n All we need to do to convert this denary number is draw out a table. Put the numbers, 128, 64, 32 etc from above into the top row. <\/p>\n\n\n\n We start from the far left and ask “can 128 be taken away from 198 without leaving a negative number?” As 198 is bigger than 128 we put a 1 under 128 and subtract 128 from 198; <\/p>\n\n\n\n 198 \u2013 128 = 70<\/strong>. <\/p>\n\n\n\n We now carry the remainder across to the next column and ask the same \u2013 “can 64 be taken away from 70 without leaving a negative number?” As 70 is bigger than 64 we put a 1 under 64 and subtract 64 from 70; <\/p>\n\n\n\n 70 \u2013 64 = 6.<\/strong> <\/p>\n\n\n\n We now carry the remainder across to the next column and ask the same \u2013 “can 32 be taken away from 6 without leaving a negative number?” As 6 is not bigger than 32 we put a 0 under 32 and carry 6 across to the next column. <\/p>\n\n\n\n We now carry the remainder across to the next column and ask the same \u2013 “can 16 be taken away from 6 without leaving a negative number?” As 6 is not bigger than 16 we put a 0 under 16 and carry 6 across to the next column. <\/p>\n\n\n\n We now carry the remainder across to the next column and ask the same – “can 8 be taken away from 6 without leaving a negative number?” As 6 is not bigger than 8 we put a 0 under 8 and carry 6 across to the next column. <\/p>\n\n\n\n We now carry the remainder across to the next column and ask the same \u2013 “can 4 be taken away from 6 without leaving a negative number?” As 6 is bigger than 4 we put a 1 under 4 and subtract 4 from 6; <\/p>\n\n\n\n 6 \u2013 4 = 2. <\/strong><\/p>\n\n\n\n We now carry the remainder across to the next column and ask the same \u2013 “can 2 be taken away from 2 without leaving a negative number?”\u00a0 As 2 can be taken away from 2 without leaving a negative we put a 1 under 2 and subtract 2 from 2; <\/p>\n\n\n\n 2 \u2013 2 = 0. <\/strong><\/p>\n\n\n\n As we now have 0 left our calculation must be complete. The remaining column must<\/strong> contain a 0.<\/p>\n\n\n\n 198 in binary is 11000110<\/strong><\/p>\n\n\n\n Work from the left to the right – it doesn’t work the other way around!<\/p>\n\n\n\n The numbers on the top row double each time from right to left don’t write them in the wrong order.<\/p>\n\n\n\n Ensure you learn the method – you will get conversions on an exam paper and they are easy marks. <\/p>\n","protected":false},"excerpt":{"rendered":" Converting decimal (denary) into binary is very simple and can be done by simply remembering the following numbers: 128, 64,…<\/p>\n","protected":false},"author":1,"featured_media":2739,"parent":879,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"disable_featured_image":true,"footnotes":""},"class_list":["post-1561","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\/10\/undraw_Share_opinion_re_4qk7.svg",150,150,true],"full":["https:\/\/computerscienced.co.uk\/site\/wp-content\/uploads\/2021\/10\/undraw_Share_opinion_re_4qk7.svg",965,727,false]},"categories_names":null,"comments_number":"0","_links":{"self":[{"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1561","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=1561"}],"version-history":[{"count":4,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1561\/revisions"}],"predecessor-version":[{"id":6145,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/1561\/revisions\/6145"}],"up":[{"embeddable":true,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/pages\/879"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/media\/2739"}],"wp:attachment":[{"href":"https:\/\/computerscienced.co.uk\/site\/wp-json\/wp\/v2\/media?parent=1561"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nExample 1. <\/strong><\/h2>\n\n\n\n
128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n 128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr> 198 – 128 =<\/strong> 70
Remainder 70<\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr> Remainder 70<\/td> 70 – 64 = 6<\/strong>
Remainder 6<\/td> <\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr> Remainder 70<\/td> Remainder 6<\/td> Remainder 6<\/td> <\/td> <\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> 0<\/td> <\/td> <\/td> <\/td> <\/td><\/tr> Remainder 70<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> <\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> 0<\/td> 0<\/td> <\/td> <\/td> <\/td><\/tr> Remainder 70<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> 0<\/td> 0<\/td> 1<\/td> <\/td> <\/td><\/tr> Remainder 70<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> 6 – 4 = 2<\/strong>
Remainder 2<\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> 0<\/td> 0<\/td> 1<\/td> 1<\/td> <\/td><\/tr> Remainder 70<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 2<\/td> 2 – 2 = 0<\/strong>
Remainder 0<\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n128<\/strong><\/td> 64<\/strong><\/td> 32<\/strong><\/td> 16<\/strong><\/td> 8<\/strong><\/td> 4<\/strong><\/td> 2<\/strong><\/td> 1<\/strong><\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> 0<\/td> 0<\/td> 1<\/td> 1<\/td> 0<\/td><\/tr> Remainder 70<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 6<\/td> Remainder 2<\/td> Remainder 0<\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nRemember<\/h2>\n\n\n\n