数电Lecture5.pdf

数字电子技术 Digital Circuits By Bao Qilian 2010/10/27 1 Chapter 4 Boolean Algebra and Logic Simplification Objectives:  Boolean Operation and Expression  Laws and Rules of Boolean Algebra  Boolean Expression of Logic Circuits  Standard Forms of Boolean Expression  Conversion between different forms  Simplification by using algebra rules  Karnaugh map and simplification Reading assignment: Chapter 4:p162- 2010/10/27 2 p213 Digital Circuits By Bao Qilian 4.5 Conversion between Truth table and logic functions The combination of input variable values in truth table can be converted to minterms (product terms) or a maxterms (sum terms). For minterm: 1 is variable, 0 is complement For maxterm: 1 is complement, 0 is 2010/10/27 3 variable Digital Circuits By Bao Qilian Example: m 10 1010 AB CD Minterm=1 1010 A B C D Maxterm=0 1010 M 10 2010/10/27 4 Digital Circuits By Bao Qilian Minterms and Maxterms for Three Binary Variables 2010/10/27 5 Digital Circuits By Bao Qilian  Using m to represent minterms. i Sum of minterms expression: f mi