Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

Slides:

Advertisements

Similar presentations

Advertisements

Instructor Dr Sameh Abdulatif

INTRODUCTION LOGICAL OPERATIONS TRUTH TABLE AND RULES.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

CS 151 Digital Systems Design Lecture 6 More Boolean Algebra A B.

1 Boolean Algebra & Logic Design. 2 Developed by George Boole in the 1850s Mathematical theory of logic. Shannon was the first to use Boolean Algebra.

Chapter 4 Logic Gates and Boolean Algebra. Introduction Logic gates are the actual physical implementations of the logical operators. These gates form.

CS 300 – Lecture 3 Intro to Computer Architecture / Assembly Language Digital Design.

Propositional Equivalence Goal: Show how propositional equivalences are established & introduce the most important such equivalences.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patterson and Hennessy Text.

Computer Science 101 Circuit Design Algorithm. Circuit Design - The Problem The problem is to design a circuit that accomplishes a specified task. The.

Logic gates & Boolean Algebra. Introduction Certain components (called logic elements) of the computer combine electric pulses using a set of rules. Electric.

Lecture 17: Digital Design Today’s topic –Intro to Boolean functions Reminders –HW 4 due Wednesday 10/8/2014 (extended) –HW 5 due Wednesday 10/15/2014.

DeMorgan Theorem, Computer Simulation Exercises

Lecture 7 Topics –Boolean Algebra 1. Logic and Bits Operation Computers represent information by bit A bit has two possible values, namely zero and one.

Lecture 22: 11/19/2002CS170 Fall CS170 Computer Organization and Architecture I Ayman Abdel-Hamid Department of Computer Science Old Dominion University.

Chapter 3: Digital Logic Dr Mohamed Menacer Taibah University

Combination of logic gates  Logic gates can be combined to produce more complex functions.  They can also be combined to substitute one type of gate.

Linear Algebra. Circuits The circuits in computers and other input devices have inputs, each of which is either a 0 or 1, the output is also 0s and 1s.

1 Lecture 6 BOOLEAN ALGEBRA and GATES Building a 32 bit processor PH 3: B.1-B.5.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

ENGIN112 L6: More Boolean Algebra September 15, 2003 ENGIN 112 Intro to Electrical and Computer Engineering Lecture 6 More Boolean Algebra A B.

Floyd, Digital Fundamentals, 10 th ed Digital Fundamentals Tenth Edition Floyd Chapter 5 © 2008 Pearson Education.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patterson and Hennessy Text.

1 Digital Logic Design Week 5&6 cont’d Revision for Quiz 2/Exam.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

Boolean Functions and Boolean Algebra Laxmikant Kale.

BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION

Digital Logic Design Dr. Oliver Faust Chapter 4

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patterson and Hennessy Text.

Standard & Canonical Forms COE 202 Digital Logic Design Dr. Aiman El-Maleh College of Computer Sciences and Engineering King Fahd University of Petroleum.

BOOLEAN ALGEBRA LOGIC GATES. Introduction British mathematician George Boole( ) was successful in finding the link between logic and mathematics.

School of Computer and Communication Engineering, UniMAP DKT 122/3 - DIGITAL SYSTEM I Chapter 4A:Boolean Algebra and Logic Simplification) Mohd ridzuan.

CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC. De Morgan’s Theorem De Morgan’s Theorem.

DE MORGAN’S THEOREM. De Morgan’s Theorem De Morgan’s Theorem.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patterson and Hennessy Text.

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text.

Logic Gates Learning Objectives Learn that there is a one-to-one relationship between logic gates and Boolean expressions Learn how logic gates are combined.

CSIS-110 Introduction to Computer Science

Combinational Circuits Part 1

Logic Gates and Boolean Algebra

Computer Science 210 Computer Organization

Combinational Logic Circuits

DeMorgan’s Theorem DeMorgan’s 2nd Theorem

Propositional Equivalence

Logic Gates and Boolean Algebra

CHAPTER 2 Boolean Algebra

Chapter 2.3 Binary Logic.

Component 1 – 2A, B, C Binary Logic

Computer Science 210 Computer Organization

Dr. Clincy Professor of CS

Agenda – 2/12/18 Questions? Readings: CSI 4, P

Dr. Clincy Professor of CS

BASIC & COMBINATIONAL LOGIC CIRCUIT

Week 7: Gates and Circuits: PART II

Functions Computers take inputs and produce outputs, just like functions in math! Mathematical functions can be expressed in two ways: We can represent.

GCSE Computer Science – Logic Gates & Boolean Expressions

From now on: Combinatorial Circuits:

Lecture 5 Binary Operation Boolean Logic. Binary Operations Addition Subtraction Multiplication Division.

Dr. Clincy Professor of CS

Combinational Logic Circuit

Laws & Rules of Boolean Algebra

Presentation transcript:

Computer Organization CS345 David Monismith Based upon notes by Dr. Bill Siever and notes from the Patternson and Hennessy Text

Review Last time we reviewed for the exam and in particular we covered Boolean Algebra. This time we will continue Boolean algebra by looking at the sum of products representation and we will look at forming logic gates using JLS from a sum of products.

Boolean Algebra A sum of products is a group of Boolean terms that are added (ORed) together where each term is a product (AND) of Boolean variables. For example, the following equation is a sum of products: A*~B*C + ~A*B*~C + A*~B*~C There also exists a product of sums, which is the dual (using DeMorgan's law) of the sum of products. We won't focus much attention on the produce of sums. We can easily convert a truth table to a sum of products and then convert the sum of products to a functioning logic circuit. The algorithm to do so follows below. To do so, examine the following truth table. Look at each row that has a true output (those with a result of 1).

Boolean Algebra: Example For each row with a true output, create a product using all input variables. Variables having a false input for a row are negated in the product. Variables having a true input for a row are not negated in the product. Rows with false outputs are ignored when forming a sum of products. A B C Output

Example Contd. Notice that for the input above, there are four rows with true outputs. Those are as follows: A B C Output So, the products for each row, in the order shown above are: ~A*~B*~C ~A*~B*C ~A*B*C A*B*C We then sum (OR) these products to form our sum of products equation as follows: ~A*~B*~C + ~A*~B*C + ~A*B*C + A*B*C

Boolean Algebra Notice that when using a sum of products, there are only two levels of gates (aside from the NOT gates). There is one level of ANDs, which occur first, and one level of ORs which occur second. In class, diagrams of AND, OR, and NOT gates were shown. It was also shown that you may have multiple inputs to an AND or an OR gate. Gates like AND, OR, and NOT only have one output, unless the outputs are copied.