{"id":2382,"date":"2013-09-02T16:23:23","date_gmt":"2013-09-02T16:23:23","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=2382"},"modified":"2013-09-02T16:23:23","modified_gmt":"2013-09-02T16:23:23","slug":"math-hexadecimal-numbers","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-hexadecimal-numbers\/","title":{"rendered":"Math: hexadecimal numbers"},"content":{"rendered":"

Tutoring math, this is an interesting concept. \u00a0Its common application is in computer science.<\/h1>\n

You might have seen numbers like c6 or e9. \u00a0Depending on the context, these may be hexadecimal (aka hex) numbers. \u00a0The hexadecimal system is base 16. \u00a0It uses the following notation:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
decimal<\/strong><\/td>\nhex<\/strong><\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n<\/tr>\n
1<\/td>\n1<\/td>\n<\/tr>\n
2<\/td>\n2<\/td>\n<\/tr>\n
3<\/td>\n3<\/td>\n<\/tr>\n
4<\/td>\n4<\/td>\n<\/tr>\n
5<\/td>\n5<\/td>\n<\/tr>\n
6<\/td>\n6<\/td>\n<\/tr>\n
7<\/td>\n7<\/td>\n<\/tr>\n
8<\/td>\n8<\/td>\n<\/tr>\n
9<\/td>\n9<\/td>\n<\/tr>\n
10<\/td>\na<\/td>\n<\/tr>\n
11<\/td>\nb<\/td>\n<\/tr>\n
12<\/td>\nc<\/td>\n<\/tr>\n
13<\/td>\nd<\/td>\n<\/tr>\n
14<\/td>\ne<\/td>\n<\/tr>\n
15<\/td>\nf<\/td>\n<\/tr>\n<\/table>\n

Since base 16 requires numbers that would be two digits in base ten, the number system is simply expanded to 15 using letters.<\/p>\n

Continuing the logic from my previous post<\/a>, we see that c6 means<\/p>\n

12×161<\/span><\/sup>+6×160<\/span><\/sup>=12×16 + 6×1=192 + 6=198. <\/p>\n

So, c6 in hex is 198 in decimal.<\/p>\n

Since 162<\/span><\/sup>=256, you can represent any number from zero to 255 with two digits in hex. ff=255, as follows:<\/p>\n

ff=15×161<\/span><\/sup>+15×160<\/span><\/sup>=240+15=255.<\/p>\n

Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

Tutoring math, this is an interesting concept. \u00a0Its common application is in computer science. You might have seen numbers like c6 or e9. \u00a0Depending on the context, these may be hexadecimal (aka hex) numbers. \u00a0The hexadecimal system is base 16. …<\/p>\n

Math: hexadecimal numbers<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-2382","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/2382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=2382"}],"version-history":[{"count":10,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/2382\/revisions"}],"predecessor-version":[{"id":2392,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/2382\/revisions\/2392"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=2382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=2382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=2382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}