4-2-2 Rules of Boolean Algebra A The double complement of a variable is al ways equal to the variable B AB A+AB 10.A+AB= A 0 0 0 001 0 0 0 (用真值表证明左右式等价)11 equal A AB= A(1 t B) Factoring(distributive law) =A·1 Rule2:(1+B)=1 Rule4:A·1=A 16
16 4-2-2 Rules of Boolean Algebra 9. The double complement of a variable is always equal to the variable. A = 10. A+AB= （用真值表证明左右式等价） A A
4-2-2 Rules of Boolean Algebra 11. (A+B)(A+C=A+BC A C A+B a+C A+B)(A +C BC A+BC B00 0 0 0 0 0 0 0 0 0 111 0 000 12. A+AB=atB A+AB=(A+A(A+B)=A+B 注意:根据公式特点进行记忆
17 4-2-2 Rules of Boolean Algebra 11. (A+B)(A+C)=A+BC 注意：根据公式特点进行记忆。 12. A+ AB = A+ B A+ AB = (A+ A)(A+ B) = A+ B
4-2-2 Rules of Boolean Algebra 13. Ab+ac+bc=ab+ac AB+AC+BCX AB+AC+(A+ A)BC X Ab+ABo+ AC+ABC X AB+Ac
18 4-2-2 Rules of Boolean Algebra 13. AB + AC + BC = AB + AC AB AC AB ABC AC ABC AB AC BC AB AC A A BC = + = + + + + + X= + + ( + ) X X X
4-2-2 Rules of Boolean algebra ◆总结 1用真值表证明等式成立的好方法。 2以上公式反映了逻辑关系,而不是数量之间的 关系。所以,在运算中不能简单套用初等代数 的运算规则
4-2-2 Rules of Boolean Algebra 总结 1.用真值表证明等式成立的好方法。 2.以上公式反映了逻辑关系，而不是数量之间的 关系。所以，在运算中不能简单套用初等代数 的运算规则。 19
4-3 Demorgan s theorem(摩根定 理) 厂,厂 The complement of two or more ANDed variables is equivalent to the or of the complements of the individual variables Inputs Output X Y XY X+Y X XY X 00 X y 0 01 00 NAND Negative-OR 20
20 4-3 Demorgan’s theorem （摩根定 理） X Y = X + Y The complement of two or more ANDed variables is equivalent to the OR of the complements of the individual variables