{"id":3200,"date":"2025-06-07T03:49:51","date_gmt":"2025-06-07T03:49:51","guid":{"rendered":"https:\/\/diznr.com\/?p=3200"},"modified":"2025-06-07T03:49:51","modified_gmt":"2025-06-07T03:49:51","slug":"digital-electronics-2-valued-boolean-algebra-and-its-theorem-in-digital-logic-with-explanation-easy","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/digital-electronics-2-valued-boolean-algebra-and-its-theorem-in-digital-logic-with-explanation-easy\/","title":{"rendered":"Digital Electronics\/ 2-valued Boolean algebra and it&#8217;s theorem in Digital Logic with easy explanation."},"content":{"rendered":"<p>Digital Electronics\/ 2-valued Boolean algebra and it&#8217;s theorem in Digital Logic with easy explanation.<\/p>\n<p>[fvplayer id=&#8221;296&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"68\"><strong data-start=\"3\" data-end=\"66\">\u00a02-Valued Boolean Algebra &amp; Its Theorems in Digital Logic<\/strong><\/h3>\n<h3 data-start=\"70\" data-end=\"116\"><strong data-start=\"74\" data-end=\"114\">\ud83d\udd39 What is 2-Valued Boolean Algebra?<\/strong><\/h3>\n<p data-start=\"117\" data-end=\"285\"><strong data-start=\"117\" data-end=\"136\">Boolean Algebra<\/strong> is a mathematical system used in <strong data-start=\"170\" data-end=\"193\">digital electronics<\/strong> where variables take only <strong data-start=\"220\" data-end=\"234\">two values<\/strong>:<br data-start=\"235\" data-end=\"238\" \/>\u2705 <strong data-start=\"240\" data-end=\"259\">0 (False \/ LOW)<\/strong><br data-start=\"259\" data-end=\"262\" \/>\u2705 <strong data-start=\"264\" data-end=\"283\">1 (True \/ HIGH)<\/strong><\/p>\n<p data-start=\"287\" data-end=\"385\">All digital circuits (AND, OR, NOT gates) use <strong data-start=\"333\" data-end=\"352\">Boolean algebra<\/strong> to simplify logic expressions.<\/p>\n<h3 data-start=\"392\" data-end=\"428\"><strong data-start=\"395\" data-end=\"426\">\u00a0Basic Boolean Operations<\/strong><\/h3>\n<h3 data-start=\"429\" data-end=\"458\"><strong data-start=\"433\" data-end=\"458\">1\ufe0f\u20e3 AND Operation (\u22c5)<\/strong><\/h3>\n<ul data-start=\"459\" data-end=\"693\">\n<li data-start=\"459\" data-end=\"498\">Symbol: <span class=\"katex\"><span class=\"katex-mathml\">A\u22c5BA \\cdot B<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span> or <span class=\"katex\"><span class=\"katex-mathml\">ABAB<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"499\" data-end=\"635\">Truth Table:<br \/>\n<table data-start=\"518\" data-end=\"635\">\n<thead data-start=\"518\" data-end=\"535\">\n<tr data-start=\"518\" data-end=\"535\">\n<th data-start=\"518\" data-end=\"522\">A<\/th>\n<th data-start=\"522\" data-end=\"526\">B<\/th>\n<th data-start=\"526\" data-end=\"535\">A \u22c5 B<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"558\" data-end=\"635\">\n<tr data-start=\"558\" data-end=\"575\">\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr data-start=\"578\" data-end=\"595\">\n<td>0<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr data-start=\"598\" data-end=\"615\">\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr data-start=\"618\" data-end=\"635\">\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li data-start=\"636\" data-end=\"693\"><strong data-start=\"638\" data-end=\"650\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">1\u22c51=1,1 \\cdot 1 = 1,<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span> <span class=\"katex\"><span class=\"katex-mathml\">0\u22c51=00 \\cdot 1 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"695\" data-end=\"723\"><strong data-start=\"699\" data-end=\"723\">2\ufe0f\u20e3 OR Operation (+)<\/strong><\/h3>\n<ul data-start=\"724\" data-end=\"934\">\n<li data-start=\"724\" data-end=\"747\">Symbol: <span class=\"katex\"><span class=\"katex-mathml\">A+BA + B<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"748\" data-end=\"884\">Truth Table:<br \/>\n<table data-start=\"767\" data-end=\"884\">\n<thead data-start=\"767\" data-end=\"784\">\n<tr data-start=\"767\" data-end=\"784\">\n<th data-start=\"767\" data-end=\"771\">A<\/th>\n<th data-start=\"771\" data-end=\"775\">B<\/th>\n<th data-start=\"775\" data-end=\"784\">A + B<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"807\" data-end=\"884\">\n<tr data-start=\"807\" data-end=\"824\">\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr data-start=\"827\" data-end=\"844\">\n<td>0<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr data-start=\"847\" data-end=\"864\">\n<td>1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr data-start=\"867\" data-end=\"884\">\n<td>1<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li data-start=\"885\" data-end=\"934\"><strong data-start=\"887\" data-end=\"899\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">1+0=1,1 + 0 = 1,<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span> <span class=\"katex\"><span class=\"katex-mathml\">0+0=00 + 0 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"936\" data-end=\"970\"><strong data-start=\"940\" data-end=\"970\">3\ufe0f\u20e3 NOT Operation (\u00ac or &#8216;)<\/strong><\/h3>\n<ul data-start=\"971\" data-end=\"1117\">\n<li data-start=\"971\" data-end=\"1007\">Symbol: <span class=\"katex\"><span class=\"katex-mathml\">A\u2032A&#8217;<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> or <span class=\"katex\"><span class=\"katex-mathml\">\u00acA\\neg A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1008\" data-end=\"1073\">Truth Table:<br \/>\n<table data-start=\"1027\" data-end=\"1073\">\n<thead data-start=\"1027\" data-end=\"1037\">\n<tr data-start=\"1027\" data-end=\"1037\">\n<th data-start=\"1027\" data-end=\"1031\">A<\/th>\n<th data-start=\"1031\" data-end=\"1037\">A&#8217;<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1052\" data-end=\"1073\">\n<tr data-start=\"1052\" data-end=\"1061\">\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr data-start=\"1064\" data-end=\"1073\">\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li data-start=\"1074\" data-end=\"1117\"><strong data-start=\"1076\" data-end=\"1088\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">1\u2032=0,1&#8242; = 0,<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span> <span class=\"katex\"><span class=\"katex-mathml\">0\u2032=10&#8242; = 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">0<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1124\" data-end=\"1160\"><strong data-start=\"1127\" data-end=\"1158\">\u00a0Boolean Algebra Theorems<\/strong><\/h3>\n<p data-start=\"1161\" data-end=\"1215\">These theorems help in <strong data-start=\"1184\" data-end=\"1214\">simplifying logic circuits<\/strong>.<\/p>\n<h3 data-start=\"1217\" data-end=\"1243\"><strong data-start=\"1221\" data-end=\"1241\">1\ufe0f\u20e3 Identity Law<\/strong><\/h3>\n<ul data-start=\"1244\" data-end=\"1287\">\n<li data-start=\"1244\" data-end=\"1263\"><span class=\"katex\"><span class=\"katex-mathml\">A+0=AA + 0 = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1264\" data-end=\"1287\"><span class=\"katex\"><span class=\"katex-mathml\">A\u22c51=AA \\cdot 1 = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1289\" data-end=\"1311\"><strong data-start=\"1293\" data-end=\"1309\">2\ufe0f\u20e3 Null Law<\/strong><\/h3>\n<ul data-start=\"1312\" data-end=\"1355\">\n<li data-start=\"1312\" data-end=\"1331\"><span class=\"katex\"><span class=\"katex-mathml\">A+1=1A + 1 = 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1332\" data-end=\"1355\"><span class=\"katex\"><span class=\"katex-mathml\">A\u22c50=0A \\cdot 0 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1357\" data-end=\"1385\"><strong data-start=\"1361\" data-end=\"1383\">3\ufe0f\u20e3 Idempotent Law<\/strong><\/h3>\n<ul data-start=\"1386\" data-end=\"1429\">\n<li data-start=\"1386\" data-end=\"1405\"><span class=\"katex\"><span class=\"katex-mathml\">A+A=AA + A = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1406\" data-end=\"1429\"><span class=\"katex\"><span class=\"katex-mathml\">A\u22c5A=AA \\cdot A = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1431\" data-end=\"1459\"><strong data-start=\"1435\" data-end=\"1457\">4\ufe0f\u20e3 Involution Law<\/strong><\/h3>\n<ul data-start=\"1460\" data-end=\"1479\">\n<li data-start=\"1460\" data-end=\"1479\"><span class=\"katex\"><span class=\"katex-mathml\">(A\u2032)\u2032=A(A&#8217;)&#8217; = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1481\" data-end=\"1509\"><strong data-start=\"1485\" data-end=\"1507\">5\ufe0f\u20e3 Complement Law<\/strong><\/h3>\n<ul data-start=\"1510\" data-end=\"1555\">\n<li data-start=\"1510\" data-end=\"1530\"><span class=\"katex\"><span class=\"katex-mathml\">A+A\u2032=1A + A&#8217; = 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1531\" data-end=\"1555\"><span class=\"katex\"><span class=\"katex-mathml\">A\u22c5A\u2032=0A \\cdot A&#8217; = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1557\" data-end=\"1587\"><strong data-start=\"1561\" data-end=\"1585\">6\ufe0f\u20e3 Distributive Law<\/strong><\/h3>\n<ul data-start=\"1588\" data-end=\"1691\">\n<li data-start=\"1588\" data-end=\"1641\"><span class=\"katex\"><span class=\"katex-mathml\">A\u22c5(B+C)=(A\u22c5B)+(A\u22c5C)A \\cdot (B + C) = (A \\cdot B) + (A \\cdot C)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1642\" data-end=\"1691\"><span class=\"katex\"><span class=\"katex-mathml\">A+(B\u22c5C)=(A+B)\u22c5(A+C)A + (B \\cdot C) = (A + B) \\cdot (A + C)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1693\" data-end=\"1721\"><strong data-start=\"1697\" data-end=\"1719\">7\ufe0f\u20e3 Absorption Law<\/strong><\/h3>\n<ul data-start=\"1722\" data-end=\"1781\">\n<li data-start=\"1722\" data-end=\"1751\"><span class=\"katex\"><span class=\"katex-mathml\">A+(A\u22c5B)=AA + (A \\cdot B) = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1752\" data-end=\"1781\"><span class=\"katex\"><span class=\"katex-mathml\">A\u22c5(A+B)=AA \\cdot (A + B) = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1783\" data-end=\"1817\"><strong data-start=\"1787\" data-end=\"1815\">8\ufe0f\u20e3 De Morgan&#8217;s Theorems<\/strong><\/h3>\n<ul data-start=\"1818\" data-end=\"1883\">\n<li data-start=\"1818\" data-end=\"1850\"><span class=\"katex\"><span class=\"katex-mathml\">(A\u22c5B)\u2032=A\u2032+B\u2032(A \\cdot B)&#8217; = A&#8217; + B&#8217;<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1818\" data-end=\"1850\"><span class=\"katex\"><span class=\"katex-mathml\">(A+B)\u2032=A\u2032\u22c5B\u2032(A + B)&#8217; = A&#8217; \\cdot B&#8217;<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1890\" data-end=\"1932\"><strong data-start=\"1893\" data-end=\"1932\">\u00a0Example: Simplify the Expression<\/strong><\/h3>\n<p data-start=\"1933\" data-end=\"2030\"><strong data-start=\"1933\" data-end=\"1948\">Expression:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">A+(A\u22c5B)A + (A \\cdot B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><br data-start=\"1970\" data-end=\"1973\" \/><strong data-start=\"1973\" data-end=\"1998\">Using Absorption Law:<\/strong><br data-start=\"1998\" data-end=\"2001\" \/><span class=\"katex\"><span class=\"katex-mathml\">A+(A\u22c5B)=AA + (A \\cdot B) = A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2032\" data-end=\"2131\">So, instead of using a circuit with AND and OR gates, we can directly use <strong data-start=\"2106\" data-end=\"2111\">A<\/strong>, saving hardware.<\/p>\n<h3 data-start=\"2138\" data-end=\"2155\"><strong data-start=\"2141\" data-end=\"2155\">\u00a0Summary<\/strong><\/h3>\n<p data-start=\"2156\" data-end=\"2329\">\u2714 <strong data-start=\"2158\" data-end=\"2177\">Boolean Algebra<\/strong> is used in <strong data-start=\"2189\" data-end=\"2217\">Digital Logic &amp; Circuits<\/strong>.<br data-start=\"2218\" data-end=\"2221\" \/>\u2714 <strong data-start=\"2223\" data-end=\"2251\">2-Valued Boolean Algebra<\/strong> uses only <strong data-start=\"2262\" data-end=\"2271\">0 &amp; 1<\/strong>.<br data-start=\"2272\" data-end=\"2275\" \/>\u2714 <strong data-start=\"2277\" data-end=\"2297\">Boolean Theorems<\/strong> help simplify logic circuits.<\/p>\n<p data-start=\"2331\" data-end=\"2396\" data-is-last-node=\"\" data-is-only-node=\"\">Would you like <strong data-start=\"2346\" data-end=\"2390\">circuit diagrams or more solved examples<\/strong>?<\/p>\n<h3><a href=\"https:\/\/www.pvpsiddhartha.ac.in\/dep_it\/lecture%20notes\/FDLD_21\/UNIT-2.pdf\" target=\"_blank\" rel=\"noopener\">Digital Electronics\/ 2-valued Boolean algebra and it&#8217;s theorem in Digital Logic with easy explanation.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.madeeasy.in\/uploads\/examsolution\/09.DigitalElectronics_UPPSCTheory.pdf\" target=\"_blank\" rel=\"noopener\">01. Boolean Algebra and Logic Gates.pmd<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.pvpsiddhartha.ac.in\/dep_it\/lecture%20notes\/DSD\/unit2.pdf\" target=\"_blank\" rel=\"noopener\">UNIT-II Boolean algebra and Logic Gates<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/uomustansiriyah.edu.iq\/media\/lectures\/5\/5_2020_09_29!09_37_22_PM.pdf\" target=\"_blank\" rel=\"noopener\">Boolean Algebra and Logic Gate<\/a><\/h3>\n<p class=\"\" data-start=\"0\" data-end=\"200\">Here&#8217;s a clear and easy-to-understand explanation of <strong data-start=\"53\" data-end=\"81\">2-Valued Boolean Algebra<\/strong> and its theorems in <strong data-start=\"102\" data-end=\"141\">Digital Electronics \/ Digital Logic<\/strong>, ideal for students of B.Tech, GATE, or competitive exams.<\/p>\n<hr class=\"\" data-start=\"202\" data-end=\"205\" \/>\n<h2 class=\"\" data-start=\"207\" data-end=\"250\">\ud83d\udca1 What is <strong data-start=\"221\" data-end=\"249\">2-Valued Boolean Algebra<\/strong>?<\/h2>\n<p class=\"\" data-start=\"252\" data-end=\"365\"><strong data-start=\"252\" data-end=\"271\">Boolean Algebra<\/strong> is a <strong data-start=\"277\" data-end=\"303\">mathematical structure<\/strong> used to perform operations on <strong data-start=\"334\" data-end=\"354\">binary variables<\/strong> (0 and 1).<\/p>\n<p class=\"\" data-start=\"367\" data-end=\"443\">In <strong data-start=\"370\" data-end=\"398\">2-valued Boolean algebra<\/strong>, each variable has only two possible values:<\/p>\n<ul data-start=\"444\" data-end=\"487\">\n<li class=\"\" data-start=\"444\" data-end=\"465\">\n<p class=\"\" data-start=\"446\" data-end=\"465\"><code data-start=\"446\" data-end=\"449\">0<\/code> \u2192 <strong data-start=\"452\" data-end=\"465\">False\/Low<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"466\" data-end=\"487\">\n<p class=\"\" data-start=\"468\" data-end=\"487\"><code data-start=\"468\" data-end=\"471\">1<\/code> \u2192 <strong data-start=\"474\" data-end=\"487\">True\/High<\/strong><\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"489\" data-end=\"552\">It forms the backbone of <strong data-start=\"514\" data-end=\"551\">digital circuits and logic design<\/strong>.<\/p>\n<hr class=\"\" data-start=\"554\" data-end=\"557\" \/>\n<h2 class=\"\" data-start=\"559\" data-end=\"593\">\u2699\ufe0f <strong data-start=\"565\" data-end=\"593\">Basic Boolean Operations<\/strong><\/h2>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"595\" data-end=\"844\">\n<thead data-start=\"595\" data-end=\"644\">\n<tr data-start=\"595\" data-end=\"644\">\n<th data-start=\"595\" data-end=\"607\" data-col-size=\"sm\">Operation<\/th>\n<th data-start=\"607\" data-end=\"616\" data-col-size=\"sm\">Symbol<\/th>\n<th data-start=\"616\" data-end=\"630\" data-col-size=\"sm\">Meaning<\/th>\n<th data-start=\"630\" data-end=\"644\" data-col-size=\"sm\">Example<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"695\" data-end=\"844\">\n<tr data-start=\"695\" data-end=\"744\">\n<td data-start=\"695\" data-end=\"707\" data-col-size=\"sm\">AND<\/td>\n<td data-start=\"707\" data-end=\"716\" data-col-size=\"sm\">\u00b7 or \u2227<\/td>\n<td data-start=\"716\" data-end=\"730\" data-col-size=\"sm\">Multiply<\/td>\n<td data-col-size=\"sm\" data-start=\"730\" data-end=\"744\">1\u00b71 = 1<\/td>\n<\/tr>\n<tr data-start=\"745\" data-end=\"794\">\n<td data-start=\"745\" data-end=\"757\" data-col-size=\"sm\">OR<\/td>\n<td data-col-size=\"sm\" data-start=\"757\" data-end=\"766\">+<\/td>\n<td data-col-size=\"sm\" data-start=\"766\" data-end=\"780\">Add<\/td>\n<td data-col-size=\"sm\" data-start=\"780\" data-end=\"794\">1+0 = 1<\/td>\n<\/tr>\n<tr data-start=\"795\" data-end=\"844\">\n<td data-start=\"795\" data-end=\"807\" data-col-size=\"sm\">NOT<\/td>\n<td data-col-size=\"sm\" data-start=\"807\" data-end=\"816\">\u00ac or &#8216;<\/td>\n<td data-col-size=\"sm\" data-start=\"816\" data-end=\"830\">Invert<\/td>\n<td data-col-size=\"sm\" data-start=\"830\" data-end=\"844\">\u00ac1 = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr class=\"\" data-start=\"846\" data-end=\"849\" \/>\n<h2 class=\"\" data-start=\"851\" data-end=\"890\">\ud83d\udcd8 <strong data-start=\"857\" data-end=\"890\">Basic Boolean Theorems \/ Laws<\/strong><\/h2>\n<h3 class=\"\" data-start=\"892\" data-end=\"918\">\u2705 1. <strong data-start=\"901\" data-end=\"918\">Identity Laws<\/strong><\/h3>\n<ul data-start=\"919\" data-end=\"944\">\n<li class=\"\" data-start=\"919\" data-end=\"932\">\n<p class=\"\" data-start=\"921\" data-end=\"932\">A + 0 = A<\/p>\n<\/li>\n<li class=\"\" data-start=\"933\" data-end=\"944\">\n<p class=\"\" data-start=\"935\" data-end=\"944\">A \u00b7 1 = A<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"946\" data-end=\"968\">\u2705 2. <strong data-start=\"955\" data-end=\"968\">Null Laws<\/strong><\/h3>\n<ul data-start=\"969\" data-end=\"994\">\n<li class=\"\" data-start=\"969\" data-end=\"982\">\n<p class=\"\" data-start=\"971\" data-end=\"982\">A + 1 = 1<\/p>\n<\/li>\n<li class=\"\" data-start=\"983\" data-end=\"994\">\n<p class=\"\" data-start=\"985\" data-end=\"994\">A \u00b7 0 = 0<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"996\" data-end=\"1024\">\u2705 3. <strong data-start=\"1005\" data-end=\"1024\">Idempotent Laws<\/strong><\/h3>\n<ul data-start=\"1025\" data-end=\"1050\">\n<li class=\"\" data-start=\"1025\" data-end=\"1038\">\n<p class=\"\" data-start=\"1027\" data-end=\"1038\">A + A = A<\/p>\n<\/li>\n<li class=\"\" data-start=\"1039\" data-end=\"1050\">\n<p class=\"\" data-start=\"1041\" data-end=\"1050\">A \u00b7 A = A<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"1052\" data-end=\"1080\">\u2705 4. <strong data-start=\"1061\" data-end=\"1080\">Complement Laws<\/strong><\/h3>\n<ul data-start=\"1081\" data-end=\"1108\">\n<li class=\"\" data-start=\"1081\" data-end=\"1095\">\n<p class=\"\" data-start=\"1083\" data-end=\"1095\">A + A&#8217; = 1<\/p>\n<\/li>\n<li class=\"\" data-start=\"1096\" data-end=\"1108\">\n<p class=\"\" data-start=\"1098\" data-end=\"1108\">A \u00b7 A&#8217; = 0<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"1110\" data-end=\"1142\">\u2705 5. <strong data-start=\"1119\" data-end=\"1142\">Double Negation Law<\/strong><\/h3>\n<ul data-start=\"1143\" data-end=\"1154\">\n<li class=\"\" data-start=\"1143\" data-end=\"1154\">\n<p class=\"\" data-start=\"1145\" data-end=\"1154\">(A&#8217;)&#8217; = A<\/p>\n<\/li>\n<\/ul>\n<hr class=\"\" data-start=\"1156\" data-end=\"1159\" \/>\n<h3 class=\"\" data-start=\"1161\" data-end=\"1190\">\u2705 6. <strong data-start=\"1170\" data-end=\"1190\">Commutative Laws<\/strong><\/h3>\n<ul data-start=\"1191\" data-end=\"1224\">\n<li class=\"\" data-start=\"1191\" data-end=\"1208\">\n<p class=\"\" data-start=\"1193\" data-end=\"1208\">A + B = B + A<\/p>\n<\/li>\n<li class=\"\" data-start=\"1209\" data-end=\"1224\">\n<p class=\"\" data-start=\"1211\" data-end=\"1224\">A \u00b7 B = B \u00b7 A<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"1226\" data-end=\"1255\">\u2705 7. <strong data-start=\"1235\" data-end=\"1255\">Associative Laws<\/strong><\/h3>\n<ul data-start=\"1256\" data-end=\"1313\">\n<li class=\"\" data-start=\"1256\" data-end=\"1285\">\n<p class=\"\" data-start=\"1258\" data-end=\"1285\">A + (B + C) = (A + B) + C<\/p>\n<\/li>\n<li class=\"\" data-start=\"1286\" data-end=\"1313\">\n<p class=\"\" data-start=\"1288\" data-end=\"1313\">A \u00b7 (B \u00b7 C) = (A \u00b7 B) \u00b7 C<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"1315\" data-end=\"1345\">\u2705 8. <strong data-start=\"1324\" data-end=\"1345\">Distributive Laws<\/strong><\/h3>\n<ul data-start=\"1346\" data-end=\"1407\">\n<li class=\"\" data-start=\"1346\" data-end=\"1373\">\n<p class=\"\" data-start=\"1348\" data-end=\"1373\">A \u00b7 (B + C) = A\u00b7B + A\u00b7C<\/p>\n<\/li>\n<li class=\"\" data-start=\"1374\" data-end=\"1407\">\n<p class=\"\" data-start=\"1376\" data-end=\"1407\">A + (B \u00b7 C) = (A + B) \u00b7 (A + C)<\/p>\n<\/li>\n<\/ul>\n<hr class=\"\" data-start=\"1409\" data-end=\"1412\" \/>\n<h3 class=\"\" data-start=\"1414\" data-end=\"1442\">\u2705 9. <strong data-start=\"1423\" data-end=\"1442\">Absorption Laws<\/strong><\/h3>\n<ul data-start=\"1443\" data-end=\"1476\">\n<li class=\"\" data-start=\"1443\" data-end=\"1458\">\n<p class=\"\" data-start=\"1445\" data-end=\"1458\">A + A\u00b7B = A<\/p>\n<\/li>\n<li class=\"\" data-start=\"1459\" data-end=\"1476\">\n<p class=\"\" data-start=\"1461\" data-end=\"1476\">A \u00b7 (A + B) = A<\/p>\n<\/li>\n<\/ul>\n<h3 class=\"\" data-start=\"1478\" data-end=\"1512\">\u2705 10. <strong data-start=\"1488\" data-end=\"1512\">De Morgan\u2019s Theorems<\/strong><\/h3>\n<ul data-start=\"1513\" data-end=\"1556\">\n<li class=\"\" data-start=\"1513\" data-end=\"1535\">\n<p class=\"\" data-start=\"1515\" data-end=\"1535\">(A \u00b7 B)&#8217; = A&#8217; + B&#8217;<\/p>\n<\/li>\n<li class=\"\" data-start=\"1536\" data-end=\"1556\">\n<p class=\"\" data-start=\"1538\" data-end=\"1556\">(A + B)&#8217; = A&#8217; \u00b7 B&#8217;<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1558\" data-end=\"1619\">\ud83d\udca1 <em data-start=\"1561\" data-end=\"1619\">These are extremely important in circuit simplification.<\/em><\/p>\n<hr class=\"\" data-start=\"1621\" data-end=\"1624\" \/>\n<h2 class=\"\" data-start=\"1626\" data-end=\"1651\">\ud83e\udde0 <strong data-start=\"1632\" data-end=\"1651\">Tip to Remember<\/strong><\/h2>\n<p class=\"\" data-start=\"1653\" data-end=\"1710\">Use <strong data-start=\"1657\" data-end=\"1673\">truth tables<\/strong> to verify the theorems. For example:<\/p>\n<p class=\"\" data-start=\"1712\" data-end=\"1737\"><strong data-start=\"1712\" data-end=\"1724\">Theorem:<\/strong> A + A&#8217; = 1<\/p>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"1738\" data-end=\"1817\">\n<thead data-start=\"1738\" data-end=\"1757\">\n<tr data-start=\"1738\" data-end=\"1757\">\n<th data-start=\"1738\" data-end=\"1742\" data-col-size=\"sm\">A<\/th>\n<th data-start=\"1742\" data-end=\"1747\" data-col-size=\"sm\">A&#8217;<\/th>\n<th data-start=\"1747\" data-end=\"1757\" data-col-size=\"sm\">A + A&#8217;<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1778\" data-end=\"1817\">\n<tr data-start=\"1778\" data-end=\"1797\">\n<td data-start=\"1778\" data-end=\"1782\" data-col-size=\"sm\">0<\/td>\n<td data-start=\"1782\" data-end=\"1787\" data-col-size=\"sm\">1<\/td>\n<td data-col-size=\"sm\" data-start=\"1787\" data-end=\"1797\">1<\/td>\n<\/tr>\n<tr data-start=\"1798\" data-end=\"1817\">\n<td data-start=\"1798\" data-end=\"1802\" data-col-size=\"sm\">1<\/td>\n<td data-col-size=\"sm\" data-start=\"1802\" data-end=\"1807\">0<\/td>\n<td data-col-size=\"sm\" data-start=\"1807\" data-end=\"1817\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p class=\"\" data-start=\"1819\" data-end=\"1830\">\u2705 Verified!<\/p>\n<hr class=\"\" data-start=\"1832\" data-end=\"1835\" \/>\n<h2 class=\"\" data-start=\"1837\" data-end=\"1864\">\ud83d\udd27 Real-Life Application<\/h2>\n<p class=\"\" data-start=\"1866\" data-end=\"1988\">All logic gates (AND, OR, NOT, NAND, NOR, XOR) are <strong data-start=\"1917\" data-end=\"1945\">physical implementations<\/strong> of Boolean operations.<br data-start=\"1968\" data-end=\"1971\" \/>Using these laws:<\/p>\n<ul data-start=\"1989\" data-end=\"2094\">\n<li class=\"\" data-start=\"1989\" data-end=\"2023\">\n<p class=\"\" data-start=\"1991\" data-end=\"2023\">We <strong data-start=\"1994\" data-end=\"2023\">simplify digital circuits<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"2024\" data-end=\"2058\">\n<p class=\"\" data-start=\"2026\" data-end=\"2058\">We <strong data-start=\"2029\" data-end=\"2058\">design efficient hardware<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"2059\" data-end=\"2094\">\n<p class=\"\" data-start=\"2061\" data-end=\"2094\">We <strong data-start=\"2064\" data-end=\"2094\">minimize logic expressions<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr class=\"\" data-start=\"2096\" data-end=\"2099\" \/>\n<h2 class=\"\" data-start=\"2101\" data-end=\"2126\">\ud83d\udcdd Summary Cheat-Sheet<\/h2>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"2128\" data-end=\"2930\">\n<thead data-start=\"2128\" data-end=\"2193\">\n<tr data-start=\"2128\" data-end=\"2193\">\n<th data-start=\"2128\" data-end=\"2150\" data-col-size=\"sm\">Law\/Rule Name<\/th>\n<th data-start=\"2150\" data-end=\"2193\" data-col-size=\"sm\">Expression(s)<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"2261\" data-end=\"2930\">\n<tr data-start=\"2261\" data-end=\"2327\">\n<td data-start=\"2261\" data-end=\"2283\" data-col-size=\"sm\">Identity<\/td>\n<td data-start=\"2283\" data-end=\"2327\" data-col-size=\"sm\">A + 0 = A, A \u00b7 1 = A<\/td>\n<\/tr>\n<tr data-start=\"2328\" data-end=\"2394\">\n<td data-start=\"2328\" data-end=\"2350\" data-col-size=\"sm\">Null<\/td>\n<td data-col-size=\"sm\" data-start=\"2350\" data-end=\"2394\">A + 1 = 1, A \u00b7 0 = 0<\/td>\n<\/tr>\n<tr data-start=\"2395\" data-end=\"2461\">\n<td data-start=\"2395\" data-end=\"2417\" data-col-size=\"sm\">Idempotent<\/td>\n<td data-start=\"2417\" data-end=\"2461\" data-col-size=\"sm\">A + A = A, A \u00b7 A = A<\/td>\n<\/tr>\n<tr data-start=\"2462\" data-end=\"2528\">\n<td data-start=\"2462\" data-end=\"2484\" data-col-size=\"sm\">Complement<\/td>\n<td data-col-size=\"sm\" data-start=\"2484\" data-end=\"2528\">A + A&#8217; = 1, A \u00b7 A&#8217; = 0<\/td>\n<\/tr>\n<tr data-start=\"2529\" data-end=\"2595\">\n<td data-start=\"2529\" data-end=\"2551\" data-col-size=\"sm\">Double Negation<\/td>\n<td data-col-size=\"sm\" data-start=\"2551\" data-end=\"2595\">(A&#8217;)&#8217; = A<\/td>\n<\/tr>\n<tr data-start=\"2596\" data-end=\"2662\">\n<td data-start=\"2596\" data-end=\"2618\" data-col-size=\"sm\">Commutative<\/td>\n<td data-col-size=\"sm\" data-start=\"2618\" data-end=\"2662\">A + B = B + A, A \u00b7 B = B \u00b7 A<\/td>\n<\/tr>\n<tr data-start=\"2663\" data-end=\"2729\">\n<td data-start=\"2663\" data-end=\"2685\" data-col-size=\"sm\">Associative<\/td>\n<td data-start=\"2685\" data-end=\"2729\" data-col-size=\"sm\">A + (B + C) = (A + B) + C<\/td>\n<\/tr>\n<tr data-start=\"2730\" data-end=\"2796\">\n<td data-start=\"2730\" data-end=\"2752\" data-col-size=\"sm\">Distributive<\/td>\n<td data-col-size=\"sm\" data-start=\"2752\" data-end=\"2796\">A \u00b7 (B + C) = A\u00b7B + A\u00b7C<\/td>\n<\/tr>\n<tr data-start=\"2797\" data-end=\"2863\">\n<td data-start=\"2797\" data-end=\"2819\" data-col-size=\"sm\">Absorption<\/td>\n<td data-col-size=\"sm\" data-start=\"2819\" data-end=\"2863\">A + A\u00b7B = A<\/td>\n<\/tr>\n<tr data-start=\"2864\" data-end=\"2930\">\n<td data-start=\"2864\" data-end=\"2886\" data-col-size=\"sm\">De Morgan\u2019s Laws<\/td>\n<td data-start=\"2886\" data-end=\"2930\" data-col-size=\"sm\">(A \u00b7 B)&#8217; = A&#8217; + B&#8217;, (A + B)&#8217; = A&#8217; \u00b7 B&#8217;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr class=\"\" data-start=\"2932\" data-end=\"2935\" \/>\n<h2 class=\"\" data-start=\"2937\" data-end=\"2975\">\ud83d\udce5 Want a PDF or Video Explanation?<\/h2>\n<p class=\"\" data-start=\"2977\" data-end=\"2992\">I can generate:<\/p>\n<ul data-start=\"2993\" data-end=\"3123\">\n<li class=\"\" data-start=\"2993\" data-end=\"3042\">\n<p class=\"\" data-start=\"2995\" data-end=\"3042\">A <strong data-start=\"2997\" data-end=\"3019\">1-page PDF summary<\/strong> (perfect for revision)<\/p>\n<\/li>\n<li class=\"\" data-start=\"3043\" data-end=\"3084\">\n<p class=\"\" data-start=\"3045\" data-end=\"3084\">A <strong data-start=\"3047\" data-end=\"3063\">video script<\/strong> for YouTube\/Tutorial<\/p>\n<\/li>\n<li class=\"\" data-start=\"3085\" data-end=\"3123\">\n<p class=\"\" data-start=\"3087\" data-end=\"3123\">A <strong data-start=\"3089\" data-end=\"3123\">truth table practice worksheet<\/strong><\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"3125\" data-end=\"3165\">Just let me know what format you prefer!<\/p>\n<h3 data-start=\"3125\" data-end=\"3165\"><a href=\"https:\/\/mrcet.com\/downloads\/digital_notes\/IT\/DIGITAL%20LOGIC%20DESIGN%20(R17A0461).pdf\" target=\"_blank\" rel=\"noopener\">Digital Electronics\/ 2-valued Boolean algebra and it&#8217;s theorem in Digital Logic with easy explanation.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.syedengg.ac.in\/pdf\/TechnicalBooklet\/ECE\/DIGITAL%20ELECTRONICS\/DIGITAL%20PLACEMENT1.pdf\" target=\"_blank\" rel=\"noopener\">DIGITAL ELECTRONICS BOOLEAN ALGEBRA<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/drait.edu.in\/assets\/departments\/ECE\/materials\/18EC32_Notes_Unts_I-III-IV-V.pdf\" target=\"_blank\" rel=\"noopener\">Digital Electronics (18EC32) Notes<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Digital Electronics\/ 2-valued Boolean algebra and it&#8217;s theorem in Digital Logic with easy explanation. [fvplayer id=&#8221;296&#8243;] \u00a02-Valued Boolean Algebra &amp; Its Theorems in Digital Logic \ud83d\udd39 What is 2-Valued Boolean Algebra? Boolean Algebra is a mathematical system used in digital electronics where variables take only two values:\u2705 0 (False \/ LOW)\u2705 1 (True \/ HIGH) [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111],"tags":[],"class_list":["post-3200","post","type-post","status-publish","format-standard","hentry","category-digital-electronics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3200"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3200\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}