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

Slides:

Advertisements

Similar presentations

Advertisements

Combinational Logic Circuits Chapter 2 Mano and Kime.

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

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

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

Basic Digital Design Discussion D5.4 Section 13.6.

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

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.

SYEN 3330 Digital SystemsJung H. Kim Chapter SYEN 3330 Digital Systems Chapter 2 – Part 1.

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.

7.1 – Multiplying Monomials. x · x = x 1 · x 1 =

Chapter Two Boolean Algebra and Logic Gate

Erik Jonsson School of Engineering and Computer Science FEARLESS Engineeringwww.utdallas.edu/~pervin EE/CE 2310 – HON/002 Introduction to Digital Systems.

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

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.

Boolean Algebra and Logic Gates CE 40 B 18 June 2003.

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

CS 151: Introduction to Digital Design Chapter 2-9 Exclusive-OR Gates.

Chapter 2: Boolean Algebra and Logic Gates. F 1 = XY’ + X’Z XYZX’Y’XY’X’ZF1F

AOI Logic Implementation

Basic logic gates  AND gate:The truth table is given by A.BBA

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

5x 4 – 405 = 5(x 4 – 81) = 5(x 2 + 9)(x 2 – 9) = 5(x 2 + 9)(x + 3)(x – 3) by D. Fisher.

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.

Venn Diagram – the visual aid in verifying theorems and properties 1 E.

Department of Computer Engineering. 2 Engr Ahmad Bilal M IN AND MAX Term Khabi Gharoor Nahi Kiya.

A. Abhari CPS2131 Chapter 2: Boolean Algebra and Logic Gates Topics in this Chapter: Boolean Algebra Boolean Functions Boolean Function Simplification.

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

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

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.

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.

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.

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

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

Basic Gates and ICs 74LS00 Quad 2-Input NAND gate 74LS02 Quad 2-Input NOR gate 74LS04 Quad 2-Input NOT gate 74LS08 Quad 2-Input AND gate 74LS32 Quad 2-Input.

Table 2.1 Postulates and Theorems of Boolean Algebra

Combinational Logic Circuits

Homework Reading Machine Projects Labs

CS 105 Digital Logic Design

Special Products of Polynomials

Princess Sumaya University

ECE 2110: Introduction to Digital Systems

Instructor: Alexander Stoytchev

Boolean Algebra Why study Boolean Algebra?

Digital Systems Design

Boolean Algebra Logic Gates

CSC 220: Computer Organization Logic Gates and Functions

AOI Logic Implementation

13 Digital Logic Circuits.

Divisibility Rules.

Table 2.1 Postulates and Theorems of Boolean Algebra

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

Applications of Boolean Algebra Minterm and Maxterm Expansions

Digital Logic Chapter-2

Digital Logic Chapter-2

Principles & Applications

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')