数字电子技术pp4.ppt

Digital Fundamentals CHAPTER 4 Boolean Algebra and Logic Simplification （布尔代数和逻辑化简） 马克思曾经说过：一门学科只有成功地运用数学语言进行描述时，才算达到了完善的地步。 数学模型的意义。 /view/27896.htm?fr=ala0_1_1 4-1 Boolean Operations and Expressions Boolean Operations and Expressions Addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1 Multiplication 0 * 0 = 0 0 * 1 = 0 1 * 0 = 0 1 * 1 = 1 4-2 Laws and Rules of Boolean Algebra Laws Boolean Algebra Commutative Laws（交换律） Associative Laws（结合律） Distributive Laws（分配律） Laws of Boolean Algebra Associative Law of Multiplication: A * (B * C) = (A * B) * C Laws of Boolean Algebra Distributive Law: A(B + C) = AB + AC Rules of Boolean Algebra Rules of Boolean Algebra Rule 10: A + AB = A Rules of Boolean Algebra Rule 11: Rules of Boolean Algebra Rule 12: (A + B)(A + C) = A + BC 4-3 DeMorgan’s Theorem （德·摩根定理） DeMorgan’s Theorems Theorem 1 Theorem 2 4-8 The Karnaugh Map（卡诺图） This chapter you should master: Adjacency cells Adjacency cells can be grouped,so that we could reduce some variables. 将n个输入变量的全部最小项与输出量之间的关系用小方块阵列图表示，并且将逻辑相邻的最小项放在相邻的几何位置上，所得到的阵列图就是n变量的卡诺图。 Examples :2-variable, 3-variable, 4-variable. Form of Karnaugh map： A B Y 0 0 1 0 1 1 1 0 1 1 1 0 A B 0 1 0 1 0 1 1 1 The value of output variables Example 1：2-variable Karnaugh map Adjacency cell：there is only a single-variable change。 0 1 00 01 11 10 A BC 0 0 0 0 0 1 1 1 variables The value of output A B C Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Example 2：3-variable Karnaugh map Tip ：00 and 10 are adjacency cells。 00 01 11 10 AB CD 00 01 11 10 1 1 0 1 1 0 X 1 0 X 0 1 1 1 0 1 4-variable Karnaugh map The cell 0010: The value of output While ABCD= 0100 The binary value can be 0 or 1，this term is called don’t care。 Adjacen-cy cells Example 3: 4-variable Karnaugh map F( A , B , C )=?( m1,m2,m4,m7 )