姜書艷數(shù)字邏輯設計及應用8

1、1,Chapter 4 Combinational Logic Design Principles(組合邏輯設計原理),Basic Logic Algebra (邏輯代數(shù)基礎) Combinational-Circuit Analysis (組合電路分析) Combinational-Circuit Synthesis (組合電路綜合),Digital Logic Design and Application (數(shù)字邏輯設計及應用),2,Review of Chapter 3,Electronic Behavior of CMOS Circuits Logic Voltage Levels (

2、邏輯電壓電平) DC Noise Margins (直流噪聲容限) Fan-In（扇入） Fun-Out (扇出),Digital Logic Design and Application (數(shù)字邏輯設計及應用),3,Review of Chapter 3,Transmission Gates (傳輸門) Schmitt-Trigger Inputs （Hysteresis） Three-State Outputs (Tri-State output) Open-Drain Outputs (Open-Collector Gate),Digital Logic Design and Appli

3、cation (數(shù)字邏輯設計及應用),4,Review of Chapter 3,Logic Levels CMOS(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 (數(shù)字邏輯設計及應用),5,Review of Chapter 3,Wired AND (線與) Open-Drain Outputs (Open-Collector Gate) Wired OR (線或) Emitter-Coupled Logic Gate

4、（ECL, 發(fā)射極耦合邏輯門）,Digital Logic Design and Application (數(shù)字邏輯設計及應用),6,Digital Logic Design and Application (數(shù)字邏輯設計及應用),Review of Chapter 3,Positive Logic and Negative Logic (正邏輯和負邏輯) Three basic logic functions: AND, OR, and NOT (三種基本邏輯：與、或、非),7,Review of Chapter 3 (第三章內容回顧),Digital Logic Design and Ap

5、plication (數(shù)字邏輯設計及應用),Three kinds of Description Method (三種描述方法)： Truth Table (真值表) Logic Expression (邏輯表達式) Logic Circuit (邏輯符號) NAND and NOR (與非和或非),8,8,Introduction,Lets learn to design digital circuits, starting with a simple form of circuit: Combinational circuit Outputs depend solely on the pr

6、esent combination of the circuit inputs values,2.1,Digital,System,if b=0, then F=0,if b=1, then F=1,b=1,F=1,(a),Vs. sequential circuit: Has “memory” that impacts outputs too,Digital,System,b=0,F=1,Cannot determine value of F solely from present input value,(b),9,Digital Logic Design and Application

7、(數(shù)字邏輯設計及應用),Basic Concepts (基本概念),Two Types of Logic Circuits(邏輯電路分為兩大類): Combinational Logic Circuit（組合邏輯電路） Sequential Logic Circuit（時序邏輯電路）,Outputs depend only on its Current Inputs. (任何時刻的輸出僅取決與當時的輸入),Outputs depends not only on the current Inputs but also on the Past sequence of Inputs. (任一時刻的輸

8、出不僅取決與當時的輸入， 還取決于過去的輸入序列),電路特點：無反饋回路、無記憶元件,10,Digital Logic Design and Application (數(shù)字邏輯設計及應用),4.1 Switching Algebra (開關代數(shù)),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 1,11,4.1.2 Single-Variable Theo

9、rems(單變量開關代數(shù)定理),Identities (自等律)：X + 0 = X X 1 = X Null Elements (0-1律)：X + 1 = 1 X 0 = 0 Involution (還原律)：( X ) = X Idempotency(同一律)：X + X = X X X = X Complements(互補律)：X + X = 1 X X = 0,Digital Logic Design and Application (數(shù)字邏輯設計及應用),12,Digital Logic Design and Application (數(shù)字邏輯設計及應用),4.1.3 Two-an

10、d Three-Variable Theorems (二變量或三變量開關代數(shù)定理),Similar Relationship with General Algebra (與普通代數(shù)相似的關系) Commutativity (交換律) A B = B A A + B = B + A Associativity (結合律) A(BC) = (AB)C A+(B+C) = (A+B)+C Distributivity (分配律) A(B+C) = AB+AC A+BC = (A+B)(A+C),可以利用真值表證明公式和定理,13,Perfect induction of the theorem,Us

11、e the truth table to prove the functions on both side are same !,To prove, just evaluate all possibilities,14,14,Example uses of the properties,Show abc equivalent to cba. Use commutative property: a*b*c = a*c*b = c*a*b = c*b*a Show abc + abc = ab. Use first distributive property abc + abc = ab(c+c)

12、. Complement property Replace c+c by 1: ab(c+c) = ab(1). Identity property ab(1) = ab*1 = ab.,a,15,15,Example uses of the properties,Show x + xz equivalent to x + z. Second distributive property Replace x+xz by (x+x)*(x+z). Complement property Replace (x+x) by 1, Identity property replace 1*(x+z) by

13、 x+z.,a,16,Notes (幾點注意),不存在變量的指數(shù) AAA A3 允許提取公因子 AB+AC = A(B+C) 沒有定義除法 if AB=BC A=C ?,沒有定義減法 if A+B=A+C B=C ?,A=1, B=0, C=0 AB=AC=0, AC,A=1, B=0, C=1,錯！,錯！,Digital Logic Design and Application (數(shù)字邏輯設計及應用),17,Some Special Relationships(一些特殊的關系),Covering (吸收律) X + XY = X X(X+Y) = X Combining (組合律) XY +

14、 XY = X (X+Y)(X+Y) = X Consensus 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 (數(shù)字邏輯設計及應用),18,對上述的公式、定理要熟記，做到舉一反三,(X+Y) + (X+Y) = 1,A + A = 1,XY + XY = X,(A+B)(A(B+C) + (A+B)(A(B+C) = (A+B),Digital Logic Design and Application (數(shù)字邏輯設計及應用),19,Prov

15、e (證明)： 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 (數(shù)字邏輯設計及應用),20,4.1.4 n-Variable Theorems (n變量定理),Generalized idempotency theorem ( 廣義同一律 ) X + X + + X = X X X X = X Shannons expansion theorems

16、 ( 香農(nóng)展開定理 ),Digital Logic Design and Application (數(shù)字邏輯設計及應用),21,Prove (證明)： AD + AC + CD + ABCD = 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 (數(shù)字邏輯設計及應用),22,4.1.4 n

17、-Variable Theorems ( n變量定理 ),Demorgans Theorems (摩根定理), Complement Theorems (反演定理),Digital Logic Design and Application (數(shù)字邏輯設計及應用),23,Complement Rules (反演規(guī)則)： +，0 1，Complementing Variables ( 變量取反 ) Follow the Priority Sequence as Before ( 遵循原來的運算優(yōu)先次序 ) Keep the complement Symbol of Non-single varia

18、bles ( 不屬于單個變量上的反號應保留不變 ),Digital Logic Design and Application (數(shù)字邏輯設計及應用),24,Example 1：Write the Complement function for each of The Following Logic functions. (寫出下面函數(shù)的反函數(shù) ) F1 = A (B + C) + C D F2 = (A B) + C D E,Example 2：Prove (AB + AC) = AB + AC,合理地運用反演定理能夠將一些問題簡化,25,合理地運用反演定理能夠將一些問題簡化,Digital

19、Logic Design and Application (數(shù)字邏輯設計及應用),26,4.1.5 Duality (對偶性),Duality Rule ( 對偶規(guī)則 ) +；0 1 變換時不能破壞原來的運算順序（優(yōu)先級） Principle of Duality ( 對偶原理 ) 若兩邏輯式相等，則它們的對偶式也相等,例： Write the Duality function for each of the following Logic functions. (寫出下面函數(shù)的對偶函數(shù)) F1 = A + B (C + D) F2 = ( A(B+C) + (C+D) ),X + X Y =

20、 X X X + Y = X X + Y = X,X ( X + Y ) = X,FD(X1 , X2 , , Xn , + , , ) = F(X1 , X2 , , Xn , , + , ),Digital Logic Design and Application (數(shù)字邏輯設計及應用),27,4.1.5 Duality (對偶性),證明公式：A+BC = (A+B)(A+C),Digital Logic Design and Application (數(shù)字邏輯設計及應用),Duality Rule ( 對偶規(guī)則 ) +；0 1 變換時不能破壞原來的運算順序（優(yōu)先級） Principle of Duality ( 對偶原理 ) 若兩邏輯式相等，則它們的對偶式也相等,28,Two kind of logic,Positive logic : 1 ( high level ) 0 (low level) Negative logic: 0 ( high level ) 1 (low level),If a logic relation exist in positive logic, it must be exist in negative logic. Both logic are duality for each other.,Positive-Lo