《电子技术数字基础 Digital Fundamentals》双语课件PPT-第04章 Boolean Algebra and Logic Simplification.ppt

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《电子技术数字基础 Digital Fundamentals》双语课件PPT-第04章 Boolean Algebra and Logic Simplification.ppt

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《电子技术数字基础 Digital Fundamentals》双语课件PPT-第04章 Boolean Algebra and Logic Simplification

Boolean Algebra and Logic Simplification Contents Boolean Operations and Expressions Law and Rules of Boolean Algebra DeMorgan’s Theorems Boolean Analysis of Logic Circuits Simplification Using Boolean Algebra Standard Forms of Boolean Expressions Boolean Expressions and Truth Tables The Karnaugh Map Karnaugh Map SOP Minimization 4-1 Boolean Operations and Expressions Boolean algebra (布尔代数） is the mathematics of digital systems. Sum term （和的形式）: is a sum of literals (文字) ( a variable or the complement of a variable), produced by an OR gate. A sum term is equal to 1 when one or more of the literals in the term are 1. A sum term is equal to 0 only if each of the literals is 0. 4-1 Boolean Operations and Expressions Product term （积的形式）: is the product of literals, produced by an AND gate. 4-1 Boolean Operations and Expressions 4-2 Laws and Rules of Boolean Algebra4-2-1 Laws of Boolean Algebra (布尔代数常用公式） Commutative laws (交换律）for addition and multiplication A+B=B+A; AB=BA 4-2-2 Rules of Boolean Algebra (基本公式） 1. A+0= A variable ORed with 0 is always equal to the variable. 4-2-2 Rules of Boolean Algebra 5. A+A= A variable ORed with itself is always equal to the variable. 4-2-2 Rules of Boolean Algebra 4-2-2 Rules of Boolean Algebra 9. The double complement of a variable is always equal to the variable. 4-2-2 Rules of Boolean Algebra 11. (A+B)(A+C)=A+BC 4-2-2 Rules of Boolean Algebra 4-3 Basic Theorems 1. Replacement theorem (代入定理） 4-3 Basic Theorems 2. Demorgan’s theorem （摩尔定理） 4-3 Basic Theorems 4-3 Basic Theorems 3. Duality theorem （对偶定理） 4-4 Boolean Analysis of Logic Circuits（逻辑电路分析） 1. Logic Circuit (逻辑电路图） 4-4 Boolean Analysis of Logic Circuits4-7 Boolean Expressions and Truth Table 3. Truth Table （真值表） Constructing the truth table from a logic expression. 4-4 Boolean Analysis of Logic Circuits 4-4 Boolean Analysis of Logic Circuits Ex. X=A(B+CD) 4-4 Boolean Analysis of Logic Circuits 4-7 Boolean Expressions and Truth Table Determini