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1、Truth table and logic equationChapter 4 Combinational logic design principlesCombinational logic The output is determined only by its input. Output can be changed when input changed.Representations of logic functionsTruth tableTiming diagramLogic equationsLogic circuitsTruth tableLeft: the input com
2、binations 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
3、 (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 tableMinterm mi : A normal productMaxterm Mi : A normal sum , Mi = (mi )Minterm and Maxte
4、rmProperties of mintermFor any input combinations, there is one and only one minterm will be 1;The sum of all the minterm must be 1; The product of any two different minterm must be 0.Properties of maxtermFor any input combinations, there is one and only one maxterm will be 0;The product of all the
5、maxterm must be 0; The sum of any two different maxterm must be 1.Shannons expansion theoremsMinterm list (Canonical sum) :Maxterm list (Canonical product):Standard logic equationStandard logic equationMinterm list (Canonical sum) : list of “1” Maxterm list (Canonical product): list of “0”Standard l
6、ogic equationAny logic can be realized in two level circuit :Minterm list , Canonical sum, sum of product; Maxterm list , Canonical product, product of sum; Standard logic equationAny logic can be realized in two level circuit :Standard logic equationFrom logic equation to logic circuitHow to make a circuit better ? One logic function may have many equivalent equations and circuitfigure 4-11 12 13 How to make a better one ?
