Chapter 10.1 and 10.2: Boolean Algebra

Slides:

Advertisements

Similar presentations

Solving Quadratic Equations Using the Zero Product Property

Advertisements

Morgan Kaufmann Publishers

Chapter 2 Logic Circuits.

Logic Gate Level Part 2. Constructing Boolean expression from truth table First method: write nonparenthesized OR of ANDs Each AND is a 1 in the result.

1 Section 10.1 Boolean Functions. 2 Computers & Boolean Algebra Circuits in computers have inputs whose values are either 0 or 1 Mathematician George.

Boolean Algebra and Logic Gates

Logic Functions and their Representation. Slide 2 Combinational Networks x1x1 x2x2 xnxn f.

Lecture 3. Boolean Algebra, Logic Gates

Chapter 2: Combinatorial Logic Circuits Illustration Pg. 32 Logic Circuit Diagrams - Circuit Optimization -2,3,4 level maps 48 elements Optimized to 25.

Fall 2002CMSC Discrete Structures1 Yes, No, Maybe... Boolean Algebra.

Simplifying a Variable Expression

Chapter 2: Boolean Algebra and Logic Functions

Boolean Functions.

Chapter 10.1 and 10.2: Boolean Algebra Based on Slides from Discrete Mathematical Structures: Theory and Applications.

Applied Discrete Mathematics Week 13: Boolean Algebra

Switching functions The postulates and sets of Boolean logic are presented in generic terms without the elements of K being specified In EE we need to.

Discrete Mathematics CS 2610 February 19, Logic Gates: the basic elements of circuits Electronic circuits consist of so-called gates connected.

Variables Tutorial 3c variable A variable is any symbol that can be replaced with a number to solve a math problem. An open sentence has at least one.

Dr. Eng. Farag Elnagahy Office Phone: King ABDUL AZIZ University Faculty Of Computing and Information Technology CPCS 222.

COE 202: Digital Logic Design Combinational Logic Part 4

Discrete Mathematics CS 2610 February 12, Agenda Previously Finished functions Began Boolean algebras And now Continue with Boolean algebras.

Discrete Mathematics CS 2610 September Equal Boolean Functions Two Boolean functions F and G of degree n are equal iff for all (x 1,..x n )  B.

Ahmad Almulhem, KFUPM 2010 COE 202: Digital Logic Design Combinational Logic Part 4 Dr. Ahmad Almulhem ahmadsm AT kfupm Phone: Office:

CHAPTER 1 SETS, FUNCTIONs, ELEMENTARY LOGIC & BOOLEAN ALGEBRAs

BOOLEAN ALGEBRA Kamrul Ahsan Teacher of

Discrete Mathematics CS 2610 February 10, Agenda Previously Functions And now Finish functions Start Boolean algebras (Sec. 11.1)

Chapter-3: BOOLEAN ALGEBRA & LOGIC GATES Analysis and logical design.

R. Johnsonbaugh Discrete Mathematics 5 th edition, 2001 Chapter 9 Boolean Algebras and Combinatorial Circuits.

Lecture 18: Boolean Algebra Boolean Functions. w = Chris is allowed to watch television x = Chris's homework is finished y = it is a school night z =

Solving Quadratic Equations Using the Zero Product Property March 18, 2014.

Solving Linear Equations and Inequalities Chapter 2.

CHAPTER 5 Combinational Logic Analysis

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Real Numbers and Introduction to Algebra.

(have students make a chart of 4 x 11

CSE 461. Binary Logic Binary logic consists of binary variables and logical operations. Variables are designated by letters such as A, B, C, x, y, z etc.

Lecture 21: Combinatorial Circuits II Discrete Mathematical Structures: Theory and Applications.

Boolean Algebra.

Mu.com.lec 9. Overview Gates, latches, memories and other logic components are used to design computer systems and their subsystems Good understanding.

CHAPTER 2 Boolean algebra and Logic gates

Boolean Constants and Variables Boolean 0 and 1 do not represent actual numbers but instead represent the state, or logic level. Closed switchOpen switch.

Table 2.1 Postulates and Theorems of Boolean Algebra

Chapter 11 (Part 1): Boolean Algebra

Chapter 2: Boolean Algebra and Logic Functions

Algebra 1 Notes: Lesson 1-5: The Distributive Property

… and now for the Final Topic:

CHAPTER 3 SETS AND BOOLEAN ALGEBRA

September 7 Notes Boolean Algebra.

Algebra 1 Section 8.2.

Digital Systems: Logic Gates and Boolean Algebra

Discrete Mathematics CS 2610

CMSC Discrete Structures

Solving Quadratic Equations by Factoring March 16, 2015

Representing Boolean functions

Yes, No, Maybe... BooleanAlgebra 12/10/2018.

Lecture 20: Combinatorial Circuits I

Chapter 10.1 and 10.2: Boolean Algebra

Chapter 10.1 and 10.2: Boolean Algebra

Chapter 10.1 and 10.2: Boolean Algebra

Applied Discrete Mathematics Week 4: Functions

Representing Boolean Functions

Gates Type AND denoted by X.Y OR denoted by X + Y NOR denoted by X + Y

Table 2.1 Postulates and Theorems of Boolean Algebra

Chapter 10.3 and 10.4: Combinatorial Circuits

Analysis of Logic Circuits Example 1

2 Chapter Chapter 2 Equations, Inequalities and Problem Solving.

Problems of the Day 2  x 24x2y

Expression: An expression is a mathematical "phrase" that stands for a single number; for example (3x + 1) : is an expression whose value is three times.

Solving Quadratic Equations by Factoring March 11, 2016

CMSC Discrete Structures

Boolean Algebra.

Presentation transcript:

Chapter 10.1 and 10.2: Boolean Algebra Discrete Mathematical Structures: Theory and Applications

Learning Objectives Learn about Boolean expressions Become aware of the basic properties of Boolean algebra Discrete Mathematical Structures: Theory and Applications

Two-Element Boolean Algebra Let B = {0, 1}. Discrete Mathematical Structures: Theory and Applications

Two-Element Boolean Algebra Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Two-Element Boolean Algebra Discrete Mathematical Structures: Theory and Applications

Two-Element Boolean Algebra Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Boolean Algebra Discrete Mathematical Structures: Theory and Applications

Boolean Algebra Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Find a midterm that equals 1 if x1 = x3 = 0 and x2 = x4 = x5 =1, and equals 0 otherwise. Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Therefore, the set of operators {. , +, ‘} is functionally complete. Discrete Mathematical Structures: Theory and Applications

Sum of products expression Example 3, p. 710 Find the sum of products expansion of F(x,y,z) = (x + y) z’ Two approaches: Use Boolean identifies Use table of F values for all possible 1/0 assignments of variables x,y,z Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Discrete Mathematical Structures: Theory and Applications

Functional Completness The set of operators {. , +, ‘} is functionally complete. Can we find a smaller set? Yes, {. , ‘}, since x + y = (x’ + y’)’ {NAND}, {NOR} are functionally complete: NAND: 1|1 = 0 and 1|0 = 0|1 = 0|0 = 1 NOR: {NAND} is functionally complete, since {. , ‘} is so and x’ = x|x xy = (x|y)|(x|y) Discrete Mathematical Structures: Theory and Applications