电子科大数字电路课件4-1定理 chenyu.ppt

c h a p t e r 4 Combinational Logic Design Principles c h a p t e r 4 Switching Algebra Combinational Circuit Analysis Combinational Circuit Synthesis Timing Hazards Basic Concept (基本概念) Logic circuits are classified into two types（逻辑电路分为两大类） combinational logic circuit（组合逻辑电路） A combinational logic circuit is one whose outputs depend only on its current inputs.（任何时刻的输出仅取决与当时的输入） characteristic：no feedback circuit sequential logic circuit（时序逻辑电路） The outputs of a sequential logic circuit depend not only on the current inputs, but also on the past sequence of inputs, possibly arbitrarily far back in time.（任一时刻的输出不仅取决于当时的输入，还取决于过去的输入顺序） 4.1 Switching Algebra 4.1.1 Axioms（公理 ） P185 （A1）X = 0 if X ? 1, （A1’） X = 1 if X ? 0 （A2）If X = 0,then X’ = 1（A2’）If X = 1,then X’ =0 （A3）0·0 = 0 （A3’） 1+1 = 1 （A4） 1·1 = 1 （A4’） 0+0 = 0 （A5） 0·1 = 1·0 = 0 （A5’） 1+0 = 0+1 = 1 4.1.2 Single-Variable Theorems (单变量开关代数定理) P188 Identities (自等律)： (T1) X + 0 = X (T1’) X · 1 = X Null Elements(0-1律)： (T2) X + 1 = 1 (T2’) X · 0 = 0 Idempotency (同一律): (T3) X + X = X (T3’) X · X = X Involution (还原律)：(T4) ( X’ )’ = X Complements (互补律): (T5) X + X’ = 1 (T5’) X · X’ =0 4.1.3 Two- and Three-Variable Theorems(1) Commutativity (交换律) (T6)X + Y = Y + X (T6’) X · Y= Y ·X Associativity (结合律) (T7) X·(Y·Z) = (X·Y)·Z (T7’) X+(Y+Z) = (X+Y)+Z Distributivity (分配律) (T8) X·(Y+Z) = X·Y+X·Z (T8’) X+Y·Z = (X+Y)·(X+Z) 4.1.3 Two- and Three-VariableTheorems(2) Covering(吸收律) (T9) X + X·Y = X (T9’) X·(X+Y) = X Combining(合并律) (T10) X·Y + X·Y’ = X (T10’) (X+Y)·(X+Y’) = X Consensus（添加律（一致性定理）） (T11) X·Y + X’·Z + Y·Z = X·Y + X’·Z (T11’) (X+Y)·(X’+Z)·(Y+Z