CSE 140: Components and Design Techniques for Digital Systems

Slides:

Advertisements

Similar presentations

Techniques for Combinational Logic Optimization

Advertisements

CSE20 Lecture 15 Karnaugh Maps Professor CK Cheng CSE Dept. UC San Diego 1.

CS 140 Lecture 16 System Designs Professor CK Cheng CSE Dept. UC San Diego 1.

CSEE 4823 Advanced Logic Design Handout: Lecture #2 1/22/15

1 CK Cheng CSE Dept. UC San Diego CS 140, Lecture 2 Combinational Logic.

CS 140 Lecture 5 Professor CK Cheng 10/10/02. Part I. Combinational Logic 1.Spec 2.Implementation K-map: Sum of products Product of sums.

1 CS 140 Lecture 3 Combinational Logic Professor CK Cheng CSE Dept. UC San Diego.

1 CS 20 Lecture 14 Karnaugh Maps Professor CK Cheng CSE Dept. UC San Diego.

CS 140 Lecture 3 Professor CK Cheng Tuesday 4/09/02.

1 CK Cheng CSE Dept. UC San Diego CS 140, Lecture 2 Combinational Logic.

CS 140 Lecture 4 Professor CK Cheng Tuesday 5/08/02.

CS 140 Lecture 6 Professor CK Cheng Tuesday 10/15/02.

Give qualifications of instructors: DAP

CS 140 Lecture 4 Combinational Logic: K-Map Professor CK Cheng CSE Dept. UC San Diego 1.

1 CS 140 Lecture 3 Combinational Logic Professor CK Cheng CSE Dept. UC San Diego.

CS 140 Lecture 6 Professor CK Cheng UC San Diego.

CS 140 Lecture 4 Professor CK Cheng 4/11/02. Part I. Combinational Logic Implementation K-Map Given F R D Obj: Minimize sum of products Proc: Draw K-Map.

CS 140 Lecture 5 Professor CK Cheng CSE Dept. UC San Diego.

CS 140 Lecture 5 Professor CK Cheng CSE Dept. UC San Diego 1.

Simplifying Boolean Expressions Using K-Map Method

Lecture 3: Incompletely Specified Functions and K Maps CSE 140: Components and Design Techniques for Digital Systems Fall 2014 CK Cheng Dept. of Computer.

1 Simplification of Boolean Functions:  An implementation of a Boolean Function requires the use of logic gates.  A smaller number of gates, with each.

Two-Level Simplification Approaches Algebraic Simplification: - algorithm/systematic procedure is not always possible - No method for knowing when the.

ECE2030 Introduction to Computer Engineering Lecture 8: Quine-McCluskey Method Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering.

1 ECE2030 Introduction to Computer Engineering Lecture 8: Quine-McCluskey Method Prof. Hsien-Hsin Sean Lee School of ECE Georgia Institute of Technology.

1 Quine-McCluskey Method. 2 Motivation Karnaugh maps are very effective for the minimization of expressions with up to 5 or 6 inputs. However they are.

ENEE244-02xx Digital Logic Design Lecture 12. Announcements HW4 due today HW5 is up on course webpage. Due on 10/16. Recitation quiz on Monday, 10/13.

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

CSE 140 Lecture 12 Combinational Standard Modules CK Cheng CSE Dept. UC San Diego 1.

1 Example: Groupings on 3-Variable K-Maps BC F(A,B,C) = A ’ B ’ A BC F(A,B,C) = B ’ A

CSE 140: Components and Design Techniques for Digital Systems Lecture 3: Incompletely Specified Functions and K Maps CK Cheng Dept. of Computer Science.

CEC 220 Digital Circuit Design More Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Slide 1 of 11.

EECS 270 Lecture 10. K-map “rules” – Only circle adjacent cells (remember edges are adjacent!) – Only circle groups that are powers of 2 (1, 2,

Lecture 4: Four Input K-Maps CSE 140: Components and Design Techniques for Digital Systems CK Cheng Dept. of Computer Science and Engineering University.

CSE 140: Components and Design Techniques for Digital Systems Lecture 6: Universal Gates CK Cheng Dept. of Computer Science and Engineering University.

CEC 220 Digital Circuit Design Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Slide 1 of 10.

Lecture 5: K-Map minimization in larger input dimensions and K-map minimization using max terms CSE 140: Components and Design Techniques for Digital Systems.

CHAPTER 6 Quine-McCluskey Method

Lecture 6 Quine-McCluskey Method

Lecture 3: Incompletely Specified Functions and K Maps

Lecture 4 Nand, Nor Gates, CS147 Circuit Minimization and

ELEC Digital Logic Circuits Fall 2014 Logic Minimization (Chapter 3)

Computer Organisation

Lecture #6 EGR 277 – Digital Logic

CSE 140 Lecture 12 Combinational Standard Modules

Plotting functions not in canonical form

CSE 140 Lecture 12 Combinational Standard Modules

CSE 140 Lecture 11 Standard Combinational Modules

Lecture 3: Incompletely Specified Functions and K Maps

Optimized Implementation of Logic Function

CSE140 HW2 Preparation Xinyuan Wang 04/20/2018.

Digital Logic & Design Dr. Waseem Ikram Lecture 12.

EECS 465: Digital Systems Lecture Notes # 2

CHAPTER 5 KARNAUGH MAPS 5.1 Minimum Forms of Switching Functions

CSE 140: Components and Design Techniques for Digital Systems

CSE 370 – Winter 2002 – Logic minimization - 1

Optimization Algorithm

Chapter 3 Gate-level Minimization.

Quine-McClusky Minimization Method

EECS 465: Digital Systems Design Lecture Notes #3

Lecture 6: Universal Gates

Optimized Implementation of Logic Function

COE 202: Digital Logic Design Combinational Logic Part 3

Overview Part 2 – Circuit Optimization

CSE 140 Lecture 3 Combinational Logic: Implementation

Professor CK Cheng CSE Dept. UC San Diego

CSE 140 Lecture 4 Combinational Logic: K-Map

Lecture 3: Incompletely Specified Functions and K Maps

CSE 140 Lecture 11 Standard Combinational Modules

Presentation transcript:

CSE 140: Components and Design Techniques for Digital Systems Lecture 5: K-Map minimization in larger input dimensions and K-map minimization using max terms CSE 140: Components and Design Techniques for Digital Systems CK Cheng Dept. of Computer Science and Engineering University of California, San Diego

Part I. Combinational Logic Specification Implementation K-map: Sum of products Product of sums

Implicant: A product term that has non-empty intersection with on-setF and does not intersect with off-set R . Prime Implicant: An implicant that is not a proper subset of any other implicant. Essential Prime Implicant: A prime implicant that has an element in on- set F but this element is not covered by any other prime implicants. Implicate: A sum term that has non-empty intersection with off-set R and does not intersect with on-set F. Prime Implicate: An implicate that is not a proper subset of any other implicate. Essential Prime Implicate: A prime implicate that has an element in offset R but this element is not covered by any other prime implicates.

K-Map to Minimized Product of Sums Sometimes it is easier to reduce the K-map by considering the offset F1=a’b’c’d+abc’d+a’b’cd’+abcd’ F2=(a+b’)(a’+b)(c’+d’)(c+d) ab cd 00 01 11 10 1 iClicker: Which function is simpler for a two level logic implementation? F1 F2 Two are the same

K-Map to Minimized Product of Sums Sometimes it is easier to reduce the K-map by considering the offset F1=a’b’c’d+abc’d+a’b’cd’+abcd’ F2=(a+b’)(a’+b)(c’+d’)(c+d) ab cd 00 01 11 10 1

Another min product of sums example Given R(a,b,c,d) = Σm (3, 11, 12, 13, 14) D (a,b,c,d)= Σm (4, 8, 10) K-map ab 00 01 11 10 cd 0 4 12 8 00 1 5 13 9 01 11 3 7 15 11 2 6 14 10 10

Another min product of sums example Given R(a,b,c,d) = Σm (3, 11, 12, 13, 14) D (a,b,c,d)= Σm (4, 8, 10) ab 00 01 11 10 cd 0 4 12 8 00 1 X 0 X 1 5 13 9 01 1 1 0 1 d 11 3 7 15 11 0 1 1 0 2 6 14 10 10 1 1 0 X a

PI Q: Which of the following is a not an essential prime implicate? Prime Implicates: ΠM(0,8), ΠM(11,15), ΠM(12,13,14,15), ΠM(6,14) PI Q: Which of the following is a not an essential prime implicate? ΠM(0,8) ΠM(11,15) ΠM(12,13,14,15) ΠM(6,14) a d 0 1 0 X 1 1 0 1 1 1 0 0 1 X 0 1 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 ab 00 01 11 10 cd

Five variable K-map a=0 a=1 bc 00 01 11 10 00 01 11 10 de c c 00 01 e 0 4 12 8 16 20 28 24 1 5 13 9 17 21 29 25 01 e e 3 7 15 11 19 23 31 27 11 d d 2 6 14 10 18 22 30 26 10 b b a Neighbors of m5 are: minterms 1, 4, 7, 13, and 21 Neighbors of m10 are: minterms 2, 8, 11, 14, and 26

Reading a Five variable K-map: An example bc 00 01 11 10 00 01 11 10 de c c 00 0 4 12 8 16 20 28 24 1 1 1 1 1 1 1 5 13 9 17 21 29 25 01 e e 3 7 15 11 19 23 31 27 11 1 1 1 1 1 1 1 1 1 1 1 d d 2 6 14 10 18 22 30 26 10 b b 5 EPIs a

Six variable K-map d d f f e e c c d d a f f e e c c b 0 4 12 8 0 4 12 8 16 20 28 24 1 5 13 9 17 21 29 25 f f 3 7 15 11 19 23 31 27 e e 2 6 14 10 18 22 30 26 c c d d 32 36 44 40 48 52 60 56 33 37 45 41 49 53 61 57 a f f 35 39 47 43 51 55 63 59 e e 34 38 46 42 50 54 62 58 c c b