数字逻辑第三章,英文ppt课件

1、Chapter 4Combinational Logic Design PrinciplesPrefaceCombinational Logic CircuitSequential Logic CircuitCombinational Logic CircuitInputOutputLogic GatesCombinational Logic CircuitCombinational Logic CircuitInputOutputFeedback LogicSequential Logic CircuitLogic AbstractGet Truth Table or Logic Funct

2、ionSimplify Logic FunctionDraw Logic Circuit Program by VHDL or ABEL Using PLD or CPLD Using Logic IC Module Design StepEmphasis4.1 Switching AlgebraBoolean Algebra(1854)1.AxiomsPositive-LogicNegative-Logic1-High 0-Low0-High 1-LowDefault as Positive-LogicGeorge Boole1815-1864(A1) 0000001111100110Xif

3、X1, 0XthenXif0, 1XthenXif0011001XifX(A2) (A3) 111(A4) (A5) 2.TheoremsXX0XX111X(T1) Identities 00 XXXXXXX1 XXXX)(0 XX(T2) Null elements(T3) Idempotency(T4) Involution(T5) ComplementsSingle-Variable TheoremsXYYX)()(ZYXZYX)()(ZYXZYXZYXYZXXXZXYX)()(ZYXZYYZX)1 (XYYX)()(ZXYXZYXZXYXZYX)(ZYYXZXX(T6) Commuta

4、tivity(T7) Associativity(T8) Distributivity(T9) CombiningXYXYXXYXYXXXYXYX)()(YYXYYXXXYXYX)()()(YYZXZZYX)()(YZXYZXZYXZYX)()()(XZYXZYYZXYZXZYXZYX)()()()(XXZYYYZXZZYXZYZXYX)()(ZXYXXYXXXYXX)(ZXYXZYZXYX (T10) Covering(T11) ConsensusZXYXBAZYZXYX ZYXZYXZXYX ZXYX )()()()()(ZXYXZYZXYXZYXXZXYXZYZXYX )(T12) De

5、MorgansYXYX )(YXYX )(YXYXX )(YX)(YXYXYXYX )(YXYX )(YX YXYXX)(Prove by using Truth TableX Y0 00 11 01 11111111100000000(T13) Extending 1Augustus De Morgan1806-18713.Rules)()(321321XXXXXXnnXXXXXX2121)(32XXAnnXXXXXX2121)(AXAX11)(I. ReplacingEx.4-1Ifthenn-Variable DeMorgans theoremsnXXX21), 0(), 1 (),(2

6、12121nnnXXFXXXFXXXXF), 1 (), 0(),(212121nnnXXFXXXFXXXXFII. Shannons ExpansionClaude Elwood Shannon1916-20191937Prove?F)(BCA),(CBAFFF)()()(),(CBABCABACBAF CBABCABACBAF )(),(BA FCBAIII. InversionwholeBe knownAsk forPrinciple of Inversion:Swapping “+” and “”.Swapping “1” and “0”.Complementing all Uncom

7、plemented variables,and Uncomplementing all Complemented ones. Ex.4-2Retain of original Sequence ofOperationFirst “” and Secend “+”() ()OrDFF)()(ZXYXZYXZXYXZYX)(IV. DualityPositive LogicNegative LogicPrinciple of Duality:Swapping “+” and “”.Swapping “1” and “0”.Retain of original Sequence ofOperatio

8、nEx.4-3Distributivity)( CABA)()(CABA)()(CABABA)( CABA)()( CABA)()( CABA)()()(CBCABACABACBAF ),(4.Standard Representations of Logic FunctionsSum of productsAND-ORProduct of sumsOR-ANDNAND-NAND) )()( CABANOR-NORAND-OR-NOTBase Rpresentations5.Minterm and MaxtermAn n-variable minterm is a normal product

9、 term with n literals.An n-variable maxterm is a normal sum term with n literals.2n such product terms.2n such sum terms.mii=0,1, ,2n-1Mii=0,1, ,2n-1CBABCA70iimji 0jimmCBAEx.4-43-variablesA,B,C23(8) mintermsA B C0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1CBA CBACBACAB ABC1111111100000000000000000000000

10、00000000000000000000000000000000011111111m0m1m2m3m4m5m6m7Every minterm is exclusive.ifCBACBA70iiMji 1jiMMCBAEx.4-53-variablesA,B,C23(8) maxtermsA B C0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1CBACBACBACBACBA111111111111110111111011110111110111011110110111011111111111111100000000M7M6M5M4M3M2M1M0Every ma

11、xterm is exclusive.ifiiMmRelationship between minterms and maxterms:ABCCABBCACBACAABFXX),(7631mmmmFABCAEx.4-6)()(5420mmmmFF),(5420mmmmFA B C0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1F01010011m1m3m6m7“0”“1”),(5420MMMM5420mmmm5420MMMMiiMm)()()(CBACBACBACBA)(BACABCCAABCAABXX“0”“1”MaxtermMintermM0M2M4M5CB

12、A,)5 , 4 , 2 , 0(CBA,)7 , 6 , 3 , 1 (F10101100m0m2m4m5BABCACBACABABCCBCACBACAB AABCBCACBACABABCF4.2 Combinational Circuit AnalysisABCFABCBBACCBehave of the circuit. Get different circuit structure. 3 Invertors 4 AND Gates 3 OR Gates )(CABAFCAABFBCACBACABABCFABCFAND-OR ABCFOR-AND1 Invertor2 AND Gates

13、 1 OR Gate1 Invertor1 AND Gate2 OR Gates )()( CAABFNAND-NAND1 Invertor3 NAND Gates ABCF)()( CABAFABCFNOR-NOR1 Invertor3 NOR Gates FasterFasterAND-OR ABCFDe Morgan Theorems:)(YXYXNAND-NAND HOMEWORK: P2314.9 4.14(Using Theorems)4.3 Combination-Circuit SynthesisLogic AbstractGet Truth Table or Logic Fu

14、nctionSimplify Logic FunctionDraw Logic Circuit Program by VHDL or ABEL Using PLD or CPLD Using Logic IC Module Design StepABCCABCBACBAF,)7 , 6 , 5(ABAC Ex.4-7Design a circuit for vote. One manager, and two clerks.If the manager dissents, then the proposal isnt passed .If the manager agrees, and any

15、 other clerk agrees too, then the proposal is passed.Assume: manager is A, clerks are B and C.agreeing-1,and disagreeing-0passing-1,and not passing-0A B C0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1F00000111Ouput is F.ABCFAND-ORNAND-NANDCombinational-Circuit MinimizationMinimizing the number of first-le

16、vel gate. Minimizing the number of inputs on each first-level gate. Minimizing the number of inputs on the second-level gate. ABCFABCFInputs on first-level gate First-level gate BCACBACABABCFCAABF1.Minimization using Boolean TheoremsCombiningXYXYXXYXYX)()(CoveringXYXXXYXX)(ConsensusZXYXZYZXYX )()()(

17、)()(ZXYXZYZXYXExtending 1YXYXX YXYXX)(2.Karnaugh MapsMaurice Karnaugh1953Truth FigureCCCDCBAABBA BABABAABCDCDBACAB ABCABCBABDCBAACCDBA DCBACBA DCBADABC ABCDDCAB DBCABCDADCBADCBADCABCBABCACBABACBAABm0 m1 m2 m3 0 1 0 1 CCBBDCBADADCBABDDBCADAB0 1 00 01 11 10 m0 m1 m3 m2 m4 m5 m7 m6 00 00 01 01 11 11 10

18、 10m4 m1 m3 m2 m0 m5 m7 m6 m12 m13 m15 m14 m8 m9 m11 m10 2-variables3-variables4-variablesGray CodesFor usingCombining!1951Edward W VeitchZYXZYXUsing Method of Karnaugh MapsCovering Logic Adjacent 1-cellsOnly one variable is different.For Using Combination Theorem.Logic Adjacent 1-cells:Immediately

19、adjacentWraparoundSymmetricalCovering Principles:Each circle covers has 2i 1-cells.Range of each circle covers is the largest possible.Quantity of circle covers is the least possible.Each circle covers has one 1-cell different from others at least.Remove i-variables from product term.DBBCADACCBAFCBA

20、BCADDB ACACBCADCBABDCADCBAF),(Ex.4-8SimplifyingCDAB00 00 01 01 11 11 10 10Truth TableA B C D0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1F11001011011111111111110000Distinguished 1-cell111111XX“0”“1”Sum of products)(DCBA)(CBA)()(DCBADCBACBAF)(DCBACDAB00 00 01 01 11 11 10 101111111111110000XX“0”“1”Product of sumsDistinguished 0-cellDCBAd,)15,14,12,11(DCBAmF,)10, 8 , 6 , 4 , 3 , 2 , 0(“Dont care” Input Combinations In