4-1 Boolean Operations and Expressions ◆ Product term(积的形式): is the product of literals, produced by an and gate X=AB. X=AB.X=ACD a product term is equal to I only if each of the literals in the term is 1. A product term is equal to O when one or more of the literals are 0 EX.X=ACD=0.1.0=1 Only if a=0. C=l, and d=0, then x1
11 4-1 Boolean Operations and Expressions Product term （积的形式）: is the product of literals, produced by an AND gate. X = AB, X = AB, X = ACD A product term is equal to 1 only if each of the literals in the term is 1. A product term is equal to 0 when one or more of the literals are 0. Ex. X = ACD = 0 1 0 =1 Only if A=0,C=1, and D=0, then X=1
4-2 Laws and rules of boolean algebra 4-2-1 Laws of Boolean Algebra(布尔代数常用公式) ◆ Commutative laws(交换律) for addition and multiplication A+B=B+A: AB=BA ◆ Associative laws(结合律) A+(B+C=(A+B)+C A(BC=(AB)C ◆ Distributive law(分配律) A(B+C=AB+AC
12 4-2 Laws and Rules of Boolean Algebra 4-2-1 Laws of Boolean Algebra (布尔代数常用公式） Commutative laws (交换律）for addition and multiplication A+B=B+A; AB=BA Associative laws (结合律） A+(B+C)=(A+B)+C A(BC)=(AB)C Distributive Law (分配律） A(B+C)=AB+AC
4-2-2 Rules of Boolean algebra(基本公式) 1.A+0=A a variable ored with o is always equal to the variable 2.A+1=1 a variable ored with I is always equal to I 3.A0=0 a variable anded with o is al ways equal to o 4.A·1=A a variable ANded with I is al ways equal to the variable 13
13 4-2-2 Rules of Boolean Algebra (基本公式） 1. A+0= A variable ORed with 0 is always equal to the variable. 2. A+1= A variable ORed with 1 is always equal to 1. 3. A·0= A variable ANDed with 0 is always equal to 0. 4. A·1= A variable ANDed with 1 is always equal to the variable. A 1 0 A
4-2-2 Rules of Boolean Algebra 5.A+A=A(A+A+A+A+.=A) a variable ored with itself is always equal to the variable 6.AA=A (AAA.=A a variable anded with itself is always equal to the variable
14 4-2-2 Rules of Boolean Algebra 5. A+A= （A+A+A+A+…=A) A variable ORed with itself is always equal to the variable. 6. A·A= (AAA…=A) A variable ANDed with itself is always equal to the variable. A A
4-2-2 Rules of Boolean Algebra 7.A+A=1 a variable ored with its complement is always equal to I 8.A.A=0 a variable aNDed with its complement is always equal to o 15
15 4-2-2 Rules of Boolean Algebra 7. A variable ORed with its complement is always equal to 1. A A + = 8. A variable ANDed with its complement is always equal to 0. A A = 1 0