1、u Switching algebrau Representations of the logic functionu Logic circuit design Chapter 4 Combinational logic design principlesAnalysis:Timing diagram truth table Logic circuit truth tableSynthesis:Truth table equation circuit Combinational logic From timing diagram to truth tableCombinational logi
2、c 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 ci
3、rcuituMinimization of the logic circuitMinterm mi:A normal productMaxterm Mi:A normal sumrelation:Mi=(mi)Minterm and MaxtermMinterm and MaxtermFor 3 input variables:a b c m1=abc m3=abc m6=abc M1=a+b+c M3=a+b+c M6=a+b+c For 4 input variables:a b c d m1=abc d m3=abcd m6=abcd M1=a+b+c+d M3=a+b+c+d M6=a
4、+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 th
5、e maxterm must be 0;The sum of any two different maxterm must be 1.Standard logic equationMinterm list(Canonical sum):list of“1”ZYXZYXZYXmmmZYXFXYZ7,6,1,761Maxterm list(Canonical product):list of“0”543205,4,3,2,0,MMMMMZYXFXYZ543205,4,3,2,0,mmmmmZYXFXYZStandard logic equationAny logic can be realized
6、 in two level circuit:Minterm list,Canonical sum,sum of product;Maxterm list,Canonical product,product of sum;xyzxyzzyxmmmXYZ7617,6,1zyxzyxMMXYZ424,2Standard logic equationFor any logic function,there are only one truth table,minterm list and maxterm list!XYZXYZZYXF5,4,3,2,07,6,1,XYZXYZZYXF7,6,15,4,
7、3,2,0,Standard logic equationFrom logic equation to logic circuit131175321mmmmmmmF)(131175321 mmmmmmmFEquivalent in logic,but much faster and use less area!From logic equation to logic circuitHow to make a circuit better?xyzzxyzyxFXYZ7,5,1xyzzyxyzzxyzyxFzxyzxyyFOne logic function may have many equivalent equations and circuitfigure 4-11 12 13 How to make a better one?
