数字电路第四章
1,Chapter 4 Combinational Logic Design Principles(组合逻辑设计原理),Basic Logic Algebra (逻辑代数基础) Combinational-Circuit Analysis (组合电路分析) Combinational-Circuit Synthesis (组合电路综合),Digital Logic Design and Application (数字逻辑设计及应用),2,Review of Chapter 3,Electronic Behavior of CMOS CircuitsLogic Voltage Levels (逻辑电压电平)DC Noise Margins (直流噪声容限)Fan-In(扇入)Fun-Out (扇出),Digital Logic Design and Application (数字逻辑设计及应用),3,Review of Chapter 3,Transmission Gates (传输门)Schmitt-Trigger Inputs (Hysteresis)Three-State Outputs (Tri-State output)Open-Drain Outputs (Open-Collector Gate),Digital Logic Design and Application (数字逻辑设计及应用),4,Review of Chapter 3,Logic LevelsCMOS(0-1.5V, 3.5-5V)TTL(0-0.8V, 2-5V)ECL(L=-1.8V, H=-0.9V)(L=3.6V, H=4.4V),Digital Logic Design and Application (数字逻辑设计及应用),5,Review of Chapter 3,Wired AND (线与)Open-Drain Outputs (Open-Collector Gate)Wired OR (线或)Emitter-Coupled Logic Gate (ECL, 发射极耦合逻辑门),Digital Logic Design and Application (数字逻辑设计及应用),6,Digital Logic Design and Application (数字逻辑设计及应用),Review of Chapter 3,Positive Logic and Negative Logic(正逻辑和负逻辑)Three basic logic functions: AND, OR, and NOT (三种基本逻辑:与、或、非),7,Review of Chapter 3 (第三章内容回顾),Digital Logic Design and Application (数字逻辑设计及应用),Three kinds of Description Method (三种描述方法): Truth Table (真值表) Logic Expression (逻辑表达式) Logic Circuit (逻辑符号)NAND and NOR (与非和或非),8,Digital Logic Design and Application (数字逻辑设计及应用),Basic Concepts (基本概念),Two Types of Logic Circuits(逻辑电路分为两大类):Combinational Logic Circuit(组合逻辑电路)Sequential Logic Circuit(时序逻辑电路),Outputs depend only on its Current Inputs.(任何时刻的输出仅取决与当时的输入),Outputs depends not only on the current Inputs but also on the Past sequence of Inputs.(任一时刻的输出不仅取决与当时的输入,还取决于过去的输入序列),电路特点:无反馈回路、无记忆元件,9,Digital Logic Design and Application (数字逻辑设计及应用),4.1 Switching Algebra (开关代数),4.1.1 Axioms (公理)X = 0 , if X 1 X = 1, if X 0 0 = 1 1 = 0 0·0 = 0 1+1 = 1 1·1 = 1 0+0 = 0 0·1 = 1·0 = 0 1+0 = 0+1 = 1,F = 0 + 1 · ( 0 + 1 · 0 ) = 0 + 1 · 1,10,4.1.2 Single-Variable Theorems(单变量开关代数定理),Identities (自等律):X + 0 = X X · 1 = XNull Elements (0-1律):X + 1 = 1 X · 0 = 0Involution (还原律):( X ) = XIdempotency(同一律):X + X = X X · X = XComplements(互补律):X + X = 1 X · X = 0,Digital Logic Design and Application (数字逻辑设计及应用),11,Digital Logic Design and Application (数字逻辑设计及应用),4.1.3 Two-and Three-Variable Theorems (二变量或三变量开关代数定理),Similar Relationship with General Algebra (与普通代数相似的关系)Commutativity (交换律) A · B = B · A A + B = B + AAssociativity (结合律) A·(B·C) = (A·B)·C A+(B+C) = (A+B)+CDistributivity (分配律) A·(B+C) = A·B+B·C A+B·C = (A+B)·(A+C),可以利用真值表证明公式和定理,12,Notes (几点注意),不存在变量的指数 A·A·A A3允许提取公因子 AB+AC = A(B+C)没有定义除法 if AB=BC A=C ?,没有定义减法 if A+B=A+C B=C ?,A=1, B=0, C=0AB=AC=0, AC,A=1, B=0, C=1,错!,错!,Digital Logic Design and Application (数字逻辑设计及应用),13,Some Special Relationships(一些特殊的关系),Covering (吸收律)X + X·Y = X X·(X+Y) = XCombining (组合律)X·Y + X·Y = X (X+Y)·(X+Y) = XConsensus 添加律(一致性定理)X·Y + X·Z + Y·Z = X·Y + X·Z(X+Y)·(X+Z)·(Y+Z) = (X+Y)·(X+Z),Digital Logic Design and Application (数字逻辑设计及应用),14,对上述的公式、定理要熟记,做到举一反三,(X+Y) + (X+Y) = 1,A + A = 1,X·Y + X·Y = X,(A+B)·(A·(B+C) + (A+B)·(A·(B+C) = (A+B),Digital Logic Design and Application (数字逻辑设计及应用),15,Prove (证明): X·Y + X·Z + Y·Z = X·Y + X·Z,Y·Z = 1·Y·Z = (X+X)·Y·Z,X·Y + X·Z + (X+X)·Y·Z,= X·Y + X·Z + X·Y·Z +X·Y·Z,= X·Y·(1+Z) + X·Z·(1+Y),= X·Y + X·Z,Digital Logic Design and Application (数字逻辑设计及应用),16,4.1.4 n-Variable Theorems (n变量定理),Generalized idempotency theorem ( 广义同一律 )X + X + + X = X X · X · · X = XShannons expansion theorems ( 香农展开定理 ),Digital Logic Design and Application (数字逻辑设计及应用),17,Prove (证明): A·D + A·C + C·D + A·B·C·D = A·D + A·C,= A · ( 1·D + 1·C + C·D + 1·B·C·D ) + A · ( 0·D + 0·C + C·D + 0·B·C·D ),= A · ( D + C·D + B·C·D ) + A · ( C + C·D ),= A·D·( 1 + C + B·C ) + A·C·( 1 + D ),= A·D + A·C,Digital Logic Design and Application (数字逻辑设计及应用),18,4.1.4 n-Variable Theorems ( n变量定理 ),Demorgans Theorems (摩根定理), Complement Theorems (反演定理),(A · B) = A + B,(A + B) = A · B,Digital Logic Design and Application (数字逻辑设计及应用),19,Complement Rules (反演规则): · +,0 1,Complementing Variables ( 变量取反 )Follow the Priority Sequence as Before ( 遵循原来的运算优先次序 )Keep the complement Symbol of Non-single variables ( 不属于单个变量上的反号应保留不变 ),Digital Logic Design and Application (数字逻辑设计及应用),20,Example 1:Write the Complement function for each of The Following Logic functions. (写出下面函数的反函数 ) F1 = A · (B + C) + C · D F2 = (A · B) + C · D · E,Example 2:Prove (A·B + A·C) = A·B + A·C,合理地运用反演定理能够将一些问题简化,21,合理地运用反演定理能够将一些问题简化,Digital Logic Design and Application (数字逻辑设计及应用),