Basic Digital Design Discussion D2.3. Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms.

Slides:

Advertisements

Similar presentations

Basic Logic Gates Discussion D5.1 Section Sections 13-3, 13-4.

Advertisements

Combinational Logic Circuits Chapter 2 Mano and Kime.

Morgan Kaufmann Publishers

Introduction to Computer Engineering by Richard E. Haskell Basic Digital Design Module M1.2 Section 3.2.

Chapter 2 Logic Circuits.

A Programmable Logic Device Lecture 4.3. A Programmable Logic Device Multiple-input Gates A 2-Input, 1-Output PLD.

Gate-Level Minimization. Digital Circuits The Map Method The complexity of the digital logic gates the complexity of the algebraic expression.

CS 151 Digital Systems Design Lecture 11 NAND and XOR Implementations.

Basic Digital Design Discussion D5.4 Section 13.6.

Basic Logic Gates and De Morgan's Theorem Discussion D5.1 Appendix D.

ENGIN112 L11: NAND and XOR Implementation September 26, 2003 ENGIN 112 Intro to Electrical and Computer Engineering Lecture 11 NAND and XOR Implementations.

Boolean Algebra and Logic Gates

Basic Digital Design Discussion D5.4 Appendix F. Basic Digital Design Sum-of-Products Design Product-of-Sums Design.

COMBINATIONAL LOGIC CIRCUITS C.L. x1 x2 xn Z Z = F (x1, x2, ……., Xn) F is a Binary Logic (BOOLEAN ) Function Knowing F Allows Straight Forward Direct Implementation.

Basic Digital Design Discussion D2.3. Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms.

Introduction to Computer Engineering by Richard E. Haskell Basic Logic Gates Module M1.1 Section 3.1.

Boolean Algebra and Logic Gates1 DIGITAL LOGIC DESIGN by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN.

Combinational Logic Circuits Chapter 2 Mano and Kime.

AOI Logic Implementation © 2014 Project Lead The Way, Inc.Digital Electronics.

Chapter Two Boolean Algebra and Logic Gate

Digital Logic Gates. Sum of Products (Review) Procedure: 1.Form a minterm for each combination of the variables that produces a 1 2.OR all the minterms.

AOI Logic Implementation

Logic Design CS221 1 st Term Boolean Algebra Cairo University Faculty of Computers and Information.

1 Why study Boolean Algebra? 4 It is highly desirable to find the simplest circuit implementation (logic) with the smallest number of gates or wires. We.

F = ∑m(1,4,5,6,7) F = A’B’C+ (AB’C’+AB’C) + (ABC’+ABC) Use X’ + X = 1.

Combinational Logic 1.

Switching Theory and Logic Design

AOI Logic Implementation

Logic Gates Shashidhara H S Dept. of ISE MSRIT. Basic Logic Design and Boolean Algebra GATES = basic digital building blocks which correspond to and perform.

Boolean Logic and Circuits ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning.

ACOE1611 Combinational Logic Circuits Reference: M. Mano, C. Kime, “Logic and Computer Design Fundamentals”, Chapter 2.

CE1110 :Digital Logic Design lecture 02 Digital Logic Gates Dr. Atef Ali Ibrahim 1.

CS 1110 Digital Logic Design

Boolean Algebra and Logic Gates

Boolean Algebra AND gate A B | AB 0 0 | | | | 1 OR gate A B | A + B 0 0 | | | | 1 NOT gate _ A | A or A’ 0 | 1 1 |

Lecture 09 NAND and XOR Implementations. Overview °Developing NAND circuits °Two-level implementations Convert from AND/OR to NAND (again!) °Multi-level.

CHAPTER 1 SETS, FUNCTIONs, ELEMENTARY LOGIC & BOOLEAN ALGEBRAs

1 Lect # 2 Boolean Algebra and Logic Gates Boolean algebra defines rules for manipulating symbolic binary logic expressions. –a symbolic binary logic expression.

Boolean Algebra & Logic Circuits Dr. Ahmed El-Bialy Dr. Sahar Fawzy.

Conversion from one number base to another Binary arithmetic Equation simplification DeMorgan’s Laws Conversion to/from SOP/POS Reading equations from.

CS151 Introduction to Digital Design Chapter 2: Combinational Logic Circuits 2-9 Exclusive-OR Operator and Gates 1Created by: Ms.Amany AlSaleh.

CHAPTER 5 Combinational Logic Analysis

CEC 220 Digital Circuit Design SOP and POS forms Friday, January 23 CEC 220 Digital Circuit Design Slide 1 of 17.

ECE DIGITAL LOGIC LECTURE 8: BOOLEAN FUNCTIONS Assistant Prof. Fareena Saqib Florida Institute of Technology Spring 2016, 02/11/2016.

Logic Gates Chapter 5 Subject: Digital System Year: 2009.

KU College of Engineering Elec 204: Digital Systems Design 1 Review D: n bit binary number D = (d n-1 ∙ ∙ ∙ d 1 d 0 ) 2 If D is an unsigned binary number.

Figure 5–5 Exclusive-OR logic diagram and symbols. Open file F05-05 to verify the operation. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by.

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

CEC 220 Digital Circuit Design SOP and POS forms Friday, Sept 11 CEC 220 Digital Circuit Design Slide 1 of 17.

Dr. Nermin Hamza. x · y = y · x x + y = y + x x · (y · z) = (x · y) · z x + (y + z) = (x + y) + z x · (y + z) = (x · y) + (x · z) x + (y · z) = (x + y)

CHAPTER 2 Boolean algebra and Logic gates

Digital Logic Circuits, Digital Component and Data Representation Course: BCA-2 nd Sem Subject: Computer Organization And Architecture Unit-1 1.

Computer Architecture CST 250 Logic Gates & Truth Tables Prepared by:Omar Hirzallah.

Table 2.1 Postulates and Theorems of Boolean Algebra

Combinational Logic Circuits

CS 105 Digital Logic Design

Princess Sumaya University

ECE 331 – Digital System Design

Boolean Algebra Why study Boolean Algebra?

Boolean Algebra.

Chapter 2 Boolean Algebra and Logic Gate

Digital Systems Design

Boolean Algebra Logic Gates

AOI Logic Implementation

Table 2.1 Postulates and Theorems of Boolean Algebra

Discussion D5.1 Section Sections 13-3, 13-4

Digital Logic Chapter-2

Digital Logic Chapter-2

Presentation transcript:

Basic Digital Design Discussion D2.3

Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

Exclusive-OR Gate XOR X Y Z Z = X xor Y X Y Z

Sum of Products Design X Y minterms 0 0 m0 = X'Y' 0 1 m1 = X'Y 1 0 m2 = XY' 1 1 m3 = XY

Sum of Products Design X Y Z Design an XOR gate m1 = X'Y m2 = XY' Z = m1 + m2 = (X'Y) + (XY')

Precedence of Logical Operators All not operations are done first All and operations are done next All or operations are done last Z = (X'Y) + (XY') = X'Y + XY'

Basic Digital Design Sum of Products Design –Minterms Product of Sums Design –Maxterms

Product of Sums Design Maxterms: A maxterm is NOT a minterm maxterm M0 = NOT minterm m0 M0 = m0' = (X'Y')' = (X'' + Y'')'' = X + Y

Product of Sums Design X Y minterms maxterms 0 0 m0 = X'Y' M0 = m0' = X + Y 0 1 m1 = X'Y M1 = m1' = X + Y' 1 0 m2 = XY' M2 = m2' = X' + Y 1 1 m3 = XY M3 = m3' = X' + Y'

Product of Sums Design X Y Z Design an XOR gate Z is NOT minterm m0 AND it is NOT minterm m3

Product of Sums Design X Y Z Design an XOR gate M0 = X + Y M3 = X' + Y' Z = M0 * M3 = (X + Y)(X' + Y')

Inverses and Duals X Y Z M0 = X + Y M3 = X' + Y' Z = M0 * M3 = (X + Y)(X' + Y') Z' = m0 + m3 = (X'Y') + (XY) Inverted Duals Z' = M1 * M2 = (X + Y')(X' + Y) Z = m1 + m2 = (X'Y) + (XY') Inverted Duals Equal