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1、1Digital Logic Design and ApplicationJin YanhuaLecture #7Other CMOS Input and Output StructuresBasic Logic AlgebraUESTC, Spring 2014Jin. UESTC2答疑安排第317周周二 3、4節(jié)，7、8節(jié)周四 3、4節(jié)周五 1、2節(jié)A教1樓教室休息室 電梯/(A102)旁邊或2樓 A202旁邊的教師休息室Jin. UESTC3Last TimeOther CMOS Input and Output StructruesENEN_LABSchmitt-Trigger Inp

2、utsVOUTVIN5.02.12.95.0VT+VT-Transmission GatesAENOUTThree-State OutputsJin. UESTC44. Open-Drain OutputsABZVCCVCCR pull-up resistanceABZLogic SymbolAs small as possible, to minimize the rise time. Cannot be arbitrarily small, it is determined by IOLmaxpassive pull-up無源上拉Applications: driving multisou

3、rce buses; driving LEDs; performing wired logic. Jin. UESTC5Driving LEDsVOLmaxILED = 10 mAJin. UESTC6Multi-source BusesJin. UESTC7輸出電平？造成邏輯混亂很大的負(fù)載電流同時流過輸出級可使門電路損壞VCCAZactive pull-up有源上拉VCCB低高有源上拉的CMOS器件其輸出端不能直接相聯(lián)1001M1001MJin. UESTC8Wired Logic of Open-Drain OutputsABZVCCVCCRCDVCCZ = Z1 Z2 = (AB) (C

4、D) = (AB + CD)Z1Z2Wired AND (線與) 第4章 反演定理 Jin. UESTC93.8 CMOS Logic FamiliesElectrical Characteristics (P.144-147 Table3-5/6/7)Symmetric output drive: output can sink or source equal amounts of current.Jin. UESTC103.9 Low-Voltage CMOS Logic and InterfacingP.152 Figure 3-62P.155 3.9.4 SummaryJin. UES

5、TC11TTL Logic FamiliesTTL Logic Levels and Noise MarginsTTL fanoutAsymmetric output drive A TTL Data Sheet P167 Table3-10IILmax=0.4 mA IIHmax=20 uAIOLmax=8 mA IOHmax=400 uAJin. UESTC12CMOS/TTL InterfacingConsider: Noise Margin, Fan-out, Capacitance LoadsabnormalVOLmax0.5VOHmin2.7VIHmin2.0VOLmax0.8TT

6、LabnormalVOLmax0.33VOLmax0.8VIHmin2.0VOHmin3.84CMOS74HCT driving 74LS H-state: |VOHmin VIHmin| = 1.84V L-state: |VOLmin VILmin| = 0.47V74LS driving 74HCT High: 2.7 2.0 = 0.7V Low: | 0.5 0.8 | = 0.3VJin. UESTC13Logic Families3.8 CMOS FamiliesHC, HCTHigh-speed CMOSTTL compatibleVHC, VHCT (very)AHC, AH

7、CT (advanced)FCT, FCT-T3.10.6 TTL FamiliesH (high-speed)S (Schottky)L, LS (low-power)A, AS, ALS (advanced) F (fast)7454Part Number: FAM nn function Jin. UESTC14Review of Chapter 3Logic Signals and GatesPositive Logic and Negative LogicBasic building blocks AND, OR, NOTCMOS LogicInverter, NAND, NOR,

8、AND-OR-INVERTFan-in, non-inverting GatesSteady-State Electrical BehaviorLogic levels and noise marginsEffects of loading, Nonideal inputs, Unused InputsJin. UESTC15Review of Chapter 2Steady-State Electrical BehaviorCurrent Driving CapabilityDynamic Electrical BehaviorSpeed and Power ConsumptionOther

9、 CMOS Input and Output StructuresTransmission Gates, Schmitt-Trigger InputsThree-State Outputs, Open-Drain OutputsLogic Family: CMOS and TTLResistive LoadsGate Loads, Fanout16Jin. UESTCChapter 4 Combinational Logic Design PrinciplesBasic Logic AlgebraCombinational-Circuit AnalysisCombinational-Circu

10、it SynthesisDigital Logic Design and ApplicationJin. UESTC17Basic ConceptsTwo types of logic circuits:combinational logic circuitsequential logic circuitOutputs depend only on its current inputs.Outputs depends not only on the current inputs but also on the past sequence of inputs.A combinational ci

11、rcuit dont contain feedback loops which generally create sequential circuit behavior.Jin. UESTC184.1 Switching Algebra4.1.1 AxiomsX = 0, if X 1X = 1, if X 00 = 11 = 000 = 01+1 = 111 = 10+0 = 001 = 10 = 01+0 = 0+1 = 1F = 0 + 1 ( 0 + 1 0 ) = 0 + 1 1= 0a.k.a. “Boolean algebra”Jin. UESTC194.1.2 Single-V

12、ariable TheoremsIdentities(自等律): X+0=XX1=XNull Elements(0-1律): X+1=1X0=0Involution(還原律): ( X ) = XIdempotency(同一律): X+X=XXX=XComplements(互補律): X+X=1XX=0The relationship between variable and constantThe relationship between variable and itselfJin. UESTC204.1.3 Two- and Three-Variable TheoremsSimilar

13、relationships with general algebraCommutativity (交換律) AB = BAA+B = B+AAssociativity (結(jié)合律) A(BC) = (AB)CA+(B+C) = (A+B)+CDistributivity (分配律) A(B+C) = AB+BCA+BC = (A+B)(A+C) Proved by truth table.Jin. UESTC21Notices允許提取公因子 AB + AC = A(B+C)不存在變量的指數(shù) AAA A3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=

14、1, B=0, C=0AB=AC=0, ACA=1, B=0, C=1錯！錯！Jin. UESTC224.1.3 Two- and Three-Variable TheoremsCovering (吸收律)X + XY = X X(X+Y) = XCombining (組合律)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)Some Special Relationships 對偶 Jin. UESTC23對上述的公式、定理要熟記，做到舉一反三 (X

15、+Y) + (X+Y) = 1A + A = 1XY + XY = X(A+B)(A(B+C) + (A+B)(A(B+C) = (A+B)代入定理： 在含有變量 X 的邏輯等式中，如果將式中所有出現(xiàn) X 的地方都用另一個表達(dá)式 F 來代替，則等式仍然成立。Jin. UESTC24To prove: XY + XZ + YZ = XY + XZYZ = 1YZ = (X+X)YZXY + XZ + (X+X)YZ= XY + XZ + XYZ +XYZ= XY(1+Z) + XZ(1+Y)= XY + XZJin. UESTC254.1.4 n-Variable TheoremsGeneral

16、ized idempotency theorem 廣義同一律X + X + + X = X X X X = XShannons expansion theorem 香農(nóng)展開定理F(X1, X2, , Xn)= X1 F(1,X2,Xn) + X1 F(0,X2,Xn)= X1 + F(0,X2,Xn) X1 + F(1,X2,Xn) Jin. UESTC26To prove: AD + AC + CD + ABCD = AD + AC= A ( 1D + 1C + CD + 1BCD ) + A ( 0D + 0C + CD + 0BCD )= A ( D + CD + BCD ) + A (

17、 C + CD )= AD( 1 + C + BC ) + AC( 1 + D )= AD + ACJin. UESTC274.1.4 n-Variable TheoremsDeMorgans Theorem 摩根定理 Complement Theorem 反演定理 (A B) = A + B(A + B) = A B回顧線與Jin. UESTC28DeMorgan SymbolsJin. UESTC294.1.4 n-Variable TheoremsComplement of a logic expression: , 0 1, Complementing all VariablesKee

18、p the previous priorityNotice the out of parenthesesExample1: Write the complement function for each of the following logic functions.F1 = A(B+C)+CDF2 = (AB)+CDE 合理地運用反演定理能夠?qū)⒁恍﹩栴}簡化 Example2: Prove that (AB + AC) = AB + ACJin. UESTC30Example1: Write the complement function for each of the following l

19、ogic functions.F1 = A(B+C)+CDF2 = (AB)+CDEF1 = (A+BC)(C+D)F2 = (A+B)(C+D+E)F2 = AB(C+D+E)AB + AC + BC = AB + AC(A+B)(A+C)AA +AC + AB + BCAC + AB AC + AB + BCExample2: Prove (AB + AC) = AB + ACJin. UESTC314.1.5 DualityDuality Rule , 0 1 Keep the previous priorityExample: Write the Duality function fo

20、r each of the following Logic functions. F1 = A+B(C+D) F2 = ( A(B+C) + (C+D) )X(X+Y) = X FD(X1 , X2 , , Xn , + , , ) = F(X1 , X2 , , Xn , , + , ) 回顧公理、定理Counterexample: X+XY = XXX+Y = X X+Y = XJin. UESTC324.1.5 DualityDuality Rule , 0 1Keep the previous priorityPrinciple of Duality Any logic equatio

21、n remains true if the duals of it is true. To prove: A+BC = (A+B)(A+C)A(B+C)AB+ACJin. UESTC33Example: Write the Duality function for each of the following Logic functions. F1 = A+B(C+D)F2 = ( A(B+C) + (C+D) )F1D = A(B+CD)F2D = ( (A+BC) (CD) )Jin. UESTC34Duality and ComplementDuality: FD(X1 , X2 , ,

22、Xn , + , , ) = F(X1 , X2 , , Xn , , + , ) Complement: F(X1 , X2 , , Xn , + , ) = F(X1 , X2, , Xn , , + ) F(X1 , X2 , , Xn) = FD(X1 , X2, , Xn ) The relation between the positive-logic convention and the negative-logic convention is duality.Jin. UESTC35The relation between the positive-logic conventi

23、on and the negative-logic convention is duality.G1ABFA B FL L LL H LH L LH H Helectrical functionA B F0 0 00 1 01 0 01 1 1positive logicA B F1 1 11 0 10 1 10 0 0negative logicF = ABF = A+BJin. UESTC36More definitionsLiteral: a variable or its complement such as X, X, CS_LExpression: literals combined by AND, OR, parentheses, complementation( FREDZ + CS_LABC + Q5 )RESET Product term: PQRSum term: X+Y+ZSum-of-products expression: A + BC + ABC Product-of