{"id":2671,"date":"2021-09-29T02:55:38","date_gmt":"2021-09-29T10:55:38","guid":{"rendered":"http:\/\/wonghoi.humgar.com\/blog\/?p=2671"},"modified":"2021-09-29T03:31:53","modified_gmt":"2021-09-29T11:31:53","slug":"descriptive-names-for-logic-operations-on-a-pair-x-y","status":"publish","type":"post","link":"https:\/\/wonghoi.humgar.com\/blog\/2021\/09\/29\/descriptive-names-for-logic-operations-on-a-pair-x-y\/","title":{"rendered":"Descriptive names for logic operations on a pair (x, y)"},"content":{"rendered":"\n<p><\/p>\n\n\n\n<p>It reads as &#8220;The output is TRUE only when the reduction <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-72da2435088fbe9b14ead71eb20d8d7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#120;&#44;&#121;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"\/> meets the description of the operations below&#8221;<\/p>\n\n\n\n<p>0 inputs:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span style=\"text-decoration: underline;\">Constant<\/span><\/strong>: gives the same <em>hard-coded<\/em> result regardless of inputs<\/li><\/ul>\n\n\n\n<p>1 input:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span style=\"text-decoration: underline;\">Transfer<\/span><\/strong>: <em>Hardwired <\/em>to one of the inputs<\/li><li><strong><span style=\"text-decoration: underline;\">Complement<\/span><\/strong>: NOT<\/li><\/ul>\n\n\n\n<p>2 inputs (symmetric):<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span style=\"text-decoration: underline;\">Comparison<\/span><\/strong>: <em>different <\/em>(XOR), <em>identical <\/em>(NXOR or <em>equivalence<\/em>)<\/li><li><strong><span style=\"text-decoration: underline;\">Arithmetic<\/span><\/strong>: AND, OR and its complements NAND, NOR<\/li><\/ul>\n\n\n\n<p>2 inputs (asymmetric):<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span style=\"text-decoration: underline;\">Inhibition<\/span><\/strong>: ONLY 1 followed by 0 is an inhibition. It&#8217;s a WHITE-list: anything else is not an inhibition (starting with 0 doesn&#8217;t inhibit)<\/li><li><strong><span style=\"text-decoration: underline;\">Implication<\/span><\/strong>: ANYTHING GOES as long as 1 is be followed by 1. It&#8217;s a BLACK-list: anything else qualifies as an implication (starting with 0 does not break the implication)<\/li><\/ul>\n\n\n\n<p>Implication is the complement of Inhibition, as the only case that breaks an implication is inhibition.<\/p>\n\n\n\n<p>This &#8216;operator&#8217; instead of truth-table view is more often used in electrical engineering than in computer science. There are many names for the same thing, but I put in some thought to find the intuitive words to make it easy to understand and remember<\/p>\n\n\n\n<p>WARNING: Those there are tempting faint similarities between logic and set theory, there&#8217;s no direct tight duality between the two. Whitelist\/Blacklist in inhibition\/implication do not make sense with set-diff\/subset as we are talking about a one-shot relationship here in logic, while set theory talks about the relationship between elements picked after it is quantified by &#8220;for all&#8221; vs &#8220;there is&#8221;. i.e. Truth table do not mix with sets<\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_2671\" class=\"pvc_stats all  \" data-element-id=\"2671\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div>","protected":false},"excerpt":{"rendered":"<p>It reads as &#8220;The output is TRUE only when the reduction meets the description of the operations below&#8221; 0 inputs: Constant: gives the same hard-coded result regardless of inputs 1 input: Transfer: Hardwired to one of the inputs Complement: NOT &hellip; <a href=\"https:\/\/wonghoi.humgar.com\/blog\/2021\/09\/29\/descriptive-names-for-logic-operations-on-a-pair-x-y\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_2671\" class=\"pvc_stats all  \" data-element-id=\"2671\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2671","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts\/2671","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/comments?post=2671"}],"version-history":[{"count":14,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts\/2671\/revisions"}],"predecessor-version":[{"id":2691,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts\/2671\/revisions\/2691"}],"wp:attachment":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/media?parent=2671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/categories?post=2671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/tags?post=2671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}