u Switching algebrau Representations of the logic functionu Logic circuit design Chapter 4 Combinational logic design principlesAnalysis: Timing diagram truth tableLogic circuit truth tableSynthesis:Truth table equation circuit Combinational logic From timing diagram to truth tableCombinational logic analysisFrom logic circuit to truth tableCombinational-circuit analysisFrom input wave to output wave !From logic circuit to logic equationCombinational-circuit analysisGet logic equation for each outputCombinational logic synthesisuFrom truth table to logic equationuFrom logic equation to logic circuituMinimization of the logic circuitMinterm mi : A normal productMaxterm Mi : A normal sumrelation: Mi = (mi )Minterm and MaxtermMinterm and MaxtermFor 3 input variables : a b cm1=abc m3=abc m6=abcM1=a+b+c M3=a+b+c M6=a+b+c For 4 input variables : a b c dm1=abc d m3=abcd m6=abcdM1=a+b+c+d M3=a+b+c +d M6=a+b+c+d Properties 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 maxterm must be 0; The sum of any two different maxterm must be 1.Standard logic equationMinterm list (Canonical sum) : list of “1” Maxterm list (Canonical product): list of “0”Standard logic 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 equationFor any logic function, there are only one truth table, minterm list and maxterm list !Standard logic equationFrom logic equation to logic circuitEquivalent in logic , but much faster and use less area ! From 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 ?