数字电路第四章

1、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 Outp

2、uts (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

3、),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 Ci

4、rcuit（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 00 = 0 1+1 = 1 11 = 1 0+0 = 0 01 = 10 = 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

5、 + 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(BC) = (AB)C A+(B+C) = (A+B)+CDistributivity (分配律) A(B+C) = AB+BC A+BC = (A+B)

6、(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 AAA 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 + XY = X X(X+Y) = XCombining (组合律)XY + XY = X (X+Y)(X+Y) = XConsensus 添加律（一致性定理）XY + XZ + YZ = XY + XZ(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,

7、XY + XY = 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)： XY + XZ + YZ = XY + XZ,YZ = 1YZ = (X+X)YZ,XY + XZ + (X+X)YZ,= XY + XZ + XYZ +XYZ,= XY(1+Z) + XZ(1+Y),= XY + XZ,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)： AD + AC + CD + ABCD =

8、AD + AC,= A ( 1D + 1C + CD + 1BCD ) + A ( 0D + 0C + CD + 0BCD ),= A ( D + CD + BCD ) + A ( C + CD ),= AD( 1 + C + BC ) + AC( 1 + D ),= AD + AC,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 (AB + AC) = AB + AC,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),

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