1、u Switching algebrau Representations of the logic functionu Logic circuit design Chapter 4 Combinational logic design principlesPrinciple of Switching algebraBasic value of any variable or function:1/0 Basic operation in logic algebra:AND(),OR(+),NOT()Axiom of switching algebra if x1,then x=0;if x=1
2、,then x0;if x=0,then x=1;if x=1,then x=0;00=0 11=1 01=0 10=0 0+0=0 1+1=1 1+0=1 0+1=1Some important theoremSome important theoremPerfect induction of the theoremUse the truth table to prove the functions on both side are same!zxyxzyzxyxTwo kind of logic Positive logic:1(high level)0(low level)Negativ
3、e 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.The difference from duality logic When a logic changed to its duality,the only change is 0 and 1 are swapped,and+are swapped!,0,1,)(,1,0,()xfxFxfxFD B
4、e careful to keep the operation orders of the logic functions.pDPNNxFxFPrinciple of Duality:Duality of the function is the negative logic form of the function.Some important theoremDeMorgans theorem:(Complimentary theorem)The complimentary of the function is the duality of the function with complime
5、ntary variables pDPpNxFxFSome important theoremDeMorgans theorem:(x1+x2)=x1 x2 (x1 x2)=x1+x2 Some important theoremCombinational logic The output is determined only by its input.Output can be changed when input changed.Representations of logic functionsTruth tableTiming diagramLogic equationsLogic c
6、ircuitsTruth tableLeft:the input combinations in binary order Right:the output for the inputLogic design:Construct a Truth table A device with majority judge function output the majority input state.Full adder add three input numbers to get their sum.Logic design:Construct a Truth table 4-bits prime-number detector when input is(1,2,3,5,7,11,13),the output is 1,otherwise the output is 0.Logic design:Construct a Truth table 4-bit Binary to Gray code converter change binary input to Gray code output.Logic design:Construct a Truth table
