{"id":1096,"date":"2012-03-04T09:00:53","date_gmt":"2012-03-04T13:00:53","guid":{"rendered":"http:\/\/www.paleotechnologist.net\/?p=1096"},"modified":"2013-02-02T15:13:17","modified_gmt":"2013-02-02T19:13:17","slug":"the-periodic-table-of-2-input-logic-gates","status":"publish","type":"post","link":"https:\/\/www.paleotechnologist.net\/?p=1096","title":{"rendered":"The Periodic Table of 2-Input Logic Gates"},"content":{"rendered":"<p>For a two-input, one-output digital logic gate (assuming no state memory or feedback), there are a total of sixteen possible behaviors, since for each combination of inputs (00, 01, 10, and 11), the gate must output either a zero or a one. Combining these four behaviors allows description of the gate with four bits, meaning there are sixteen possibilities (0000 through 1111).<\/p>\n<p>Not all of these &#8220;gate types&#8221; are interesting, however. For example, the &#8220;Type 0&#8221; gate (whose descriptor is 0000) always outputs a zero, no matter what the inputs are. Similarly, the &#8220;Type 15&#8221; gate (descriptor 1111) will always output a one.<\/p>\n<p>Some interesting properties that some of the gates have are:<\/p>\n<ul>\n<li><em>Symmetry<\/em>: If you swap inputs A and B, will the gate act the same way?<\/li>\n<li><em>Triviality: <\/em>Is the &#8220;gate&#8221; so trivial that a simple wire will suffice?<\/li>\n<li><em>Commonality: <\/em>Is the gate a &#8220;standard&#8221; or commonly-used gate?<\/li>\n<li><em>Inversion: <\/em>Can the gate invert one or both inputs in at least some cases?<\/li>\n<li><em>Two-input: <\/em>Do both inputs affect the gate&#8217;s output?<\/li>\n<li><em>Universality: <\/em>Can several of this gate be used to emulate any other gate?<\/li>\n<\/ul>\n<p>Here is a chart showing the properties of all of the possible behaviors a simple two-input-one-output digital logic gate could exhibit. Some of these are not true &#8220;gates&#8221;; others are, but lack universality. Interestingly, six of the gate types are universal &#8212; meaning that given a sufficient number of them, any other gate type could be created. An entire computer could be created using nothing but NOR gates, for instance.<\/p>\n<div id=\"attachment_2073\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.paleotechnologist.net\/wp-content\/uploads\/2012\/03\/periodic_table_of_two_input_gates.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2073\" class=\"size-full wp-image-2073\" title=\"A similar concept, generally using four to six inputs, is the idea behind FPGAs.\" src=\"https:\/\/www.paleotechnologist.net\/wp-content\/uploads\/2012\/03\/periodic_table_of_two_input_gates_sm.jpg\" alt=\"\" width=\"600\" height=\"211\" \/><\/a><p id=\"caption-attachment-2073\" class=\"wp-caption-text\">A chart of all possible simple two-input logic gates. (Click for larger.) <\/p><\/div>\n<p>Logic gates of various types can sometimes show up in unexpected places. The humble 555 timer IC, for example, turns out to be <a href=\"https:\/\/www.paleotechnologist.net\/?p=530\" target=\"_blank\">capable of functioning as a Type 2 (or Type 4) gate<\/a>. Since these are universal, a computer <a href=\"https:\/\/www.paleotechnologist.net\/?p=548\" target=\"_blank\">using only 555s as active logic<\/a> is possible!<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are exactly sixteen possible behaviors that a two-input, one-output logic gate can have&#8230; <a href=\"https:\/\/www.paleotechnologist.net\/?p=1096\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"footnotes":""},"categories":[210,413,238,266,222],"tags":[],"class_list":["post-1096","post","type-post","status-publish","format-standard","hentry","category-digital","category-eet205","category-electronics","category-fundamentals","category-math"],"_links":{"self":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts\/1096","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1096"}],"version-history":[{"count":15,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts\/1096\/revisions"}],"predecessor-version":[{"id":3192,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts\/1096\/revisions\/3192"}],"wp:attachment":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}