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课程主页: https://www.udemy.com/course/boolean-algebra-and-logic-gates-introduction/
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**课程名称：** 数字电子技术中的布尔代数与逻辑门 **课程概述：** 本课程深入探讨了数字电子技术的核心基础——布尔代数和逻辑门。课程从布尔代数的介绍开始，涵盖了数字系统中关键的概念，如二进制量、逻辑运算、逻辑函数和逻辑表达式。学习者将掌握使用真值表来评估布尔表达式，理解重言式和矛盾式。 随后，课程详细介绍了各种逻辑门，包括基本逻辑门（NOT、AND、OR）和派生逻辑门（NOR、NAND、XOR、XNOR），并重点讲解了通用逻辑门。 布尔代数的基本公理、对偶原理以及一系列重要定理（如同一律、互补律、对合律、交换律、结合律、分配律、吸收律）将被逐一剖析。德摩根定理及其应用将在课程中得到重点讲解。 课程还将关注布尔表达式与布尔函数，并通过实例演示布尔表达式的简化。学习者将学习如何推导布尔表达式，并通过二进制到十进制的转换进行回顾。 为了进一步提升简化布尔表达式的能力，课程将深入讲解最小项（Minterms）和最大项（Maxterms）的概念，以及标准形式（SOP和POS）的转换。卡诺图（Karnaugh map）作为一种强大的简化工具将在课程中得到详细阐述，包括如何绘制和填充K图，以及SOP和POS形式下分组最小项/最大项的规则和简化方法。课程将通过大量实例来巩固这些技能。 **核心内容：** * 布尔代数基础：逻辑运算、逻辑函数、真值表 * 逻辑门：基本门、派生门、通用门 * 布尔代数公理与定理：对偶、德摩根定理等 * 布尔表达式简化：最小项、最大项、SOP/POS转换 * 卡诺图（Karnaugh map）：SOP与POS简化实例
The details of the course - Digital Electronics - Boolean Algebra and Logic Gates - are as belowIntroductionIntroduction to Boolean AlgebraNumber System - OverviewBinary Valued Quantities Logical OperationsLogical Function And Logical ExpressionsTruth Table, Tautology, FallacyLogical OperatorsNOTANDOR Evaluation of Boolean Expressions Using Truth TableEvaluation of Boolean Expressions Using Truth Table - ConceptsCreation of Table and Possible Combination of ValuesEvaluation of Boolean Expressions Using Truth Table - ExamplesLogic GatesBasic Logic Gates - IntroductionNOTORANDDerived Logic Gates - IntroductionNOR GateNAND GateXOR GateXNOR GateUniversal Gates Basic Postulates of Boolean AlgebraBasic Postulates of Boolean AlgebraPrinciple of DualityBasic Theorems of Boolean AlgebraProperties of Zero and OneIdempotence law Complementary lawInvolution lawCommutative lawAssociative lawDistributive lawAbsorption lawFew More laws De Morgan's TheoremsDeMorgan's Theorem IntroductionDeMorgan's First theoremDeMorgan's Second theoremApplications of DeMorgan's theoremsBoolean Expression and Boolean FunctionBoolean Expression and Boolean FunctionExamples on Simplification of Boolean ExpressionsDerivation of Boolean ExpressionRecall Few Points - Binary to DecimalMintermsMaxtermsConcepts of Minterms and MaxtermsCanonical ExpressionsConversion for Non Standard SOP to SOP FormConversion for Non Standard POS to POS Form Simplification of Boolean ExpressionsSimplification using Karnaugh mapRecall Few Points - Gray CodeDraw and Fill K-Map for Sum of Product (SOP) formRules for Grouping Minterms in K-MapReduction rules in SOP form using K-mapGrouping and Reduction for Pairs in SOP form Grouping and Reduction for Quads in SOP form Grouping and Reduction for Octet in SOP form Summary of Reduction Rules for SOP using K-mapK-Map Simplification Technique -SOP FormSOP Reduction using Karnaugh Map - ExamplesDraw and Fill K-Map for POS formRules for Grouping Maxterms in K-MapSummary of Reduction Rules for POS using K-mapK-Map Simplification Technique - POS FormPOS Reduction using Karnaugh Map - Examples
