数字电路王兢 课件第三章.pdf

Chapter 3 Logic Algebra 逻辑代数基础 §3.1 Operations of Logic Algebra 逻辑代数运算法则 1. Fundamental Theorems of Logic Algebra 基本定律 Every theorem is given in two forms: one for addition and another for multiplication. Two forms are equivalent and are called “Dual” each other. (对偶式) 1 2. Basic Rules 基本规则 1) Substitution 代入规则 2) Complementary Theorem 反演规则 The complement expression is formed by replacing all + operations with • , all • operations with +, all ones with zeros, all zeros with ones, all variables with inversed variables, and all inversed variables with variables. 1 0 + • New function F uncomplemented complemented F variable variable Function F is called the complement of the function F. If the function F is valid, the complement of the function, F , is also valid. 反函数 2 3) Duality 对偶规则 The dual expression is found by replacing all + operation with • , all • operation with +, all ones with zeros, all zeros with ones. + • Function F New function F 1 0 New function F’ is called the dual of the function F. If an expression F is valid in logic algebra, the dual of the expression, F’, is also valid. 如果 F 成立，F’ 也成立 3 Note: 1. Keep the order of the operations (运算顺序不变) 2. Keep the bar which is on a function