{"id":18539,"date":"2016-10-28T19:50:43","date_gmt":"2016-10-28T19:50:43","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=18539"},"modified":"2016-10-28T19:50:43","modified_gmt":"2016-10-28T19:50:43","slug":"octal-logic-6-and-5-4","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/octal-logic-6-and-5-4\/","title":{"rendered":"Octal logic:  6 AND 5 = 4"},"content":{"rendered":"<h1>The tutor explains a consequence of octal logic.<\/h1>\n<p>Octal logic focuses on numbers in base 8.  An octal number has the following form:<\/p>\n<p>p(2<sup>0<\/sup>)+q(2<sup>1<\/sup>)+r(2<sup>2<\/sup>)<\/p>\n<p>which evaluates to<\/p>\n<p>p(1)+q(2)+r(4)<\/p>\n<p>where p,q,r have possible values 0 or 1 (&#8220;off&#8221; or &#8220;on&#8221;).<\/p>\n<p>The number 6 is<\/p>\n<p>0(1)+1(2)+1(4):  q,r=1<\/p>\n<p>The number 5 is<\/p>\n<p>1(1)+0(2)+1(4):  p,r=1<\/p>\n<p>The AND operation puts a 1 only where both inputs already equal 1.  From above, we see that for 6 and 5, only r is 1 in both.  Since r is the coefficient of 4, we have 6 AND 5 = (1)4 = 4.<\/p>\n<p>Source:<\/p>\n<p>Grimaldi, Ralph P.  <u>Discrete and Combinatorial Mathematics<\/u>.  Don Mills:  Addison-Wesley, 1994.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor explains a consequence of octal logic. Octal logic focuses on numbers in base 8. An octal number has the following form: p(20)+q(21)+r(22) which evaluates to p(1)+q(2)+r(4) where p,q,r have possible values 0 or 1 (&#8220;off&#8221; or &#8220;on&#8221;). The &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/octal-logic-6-and-5-4\/\"> <span class=\"screen-reader-text\">Octal logic:  6 AND 5 = 4<\/span> Read More &raquo;<\/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":[1425,1992],"class_list":["post-18539","post","type-post","status-publish","format-standard","hentry","category-math","tag-logic","tag-octal-numbers"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18539","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=18539"}],"version-history":[{"count":10,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18539\/revisions"}],"predecessor-version":[{"id":18549,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18539\/revisions\/18549"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=18539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=18539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=18539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}