lecture_5_karnaugh_maps.pdf - Lecture 5 Karnaugh Maps •...

This preview shows page 1 - 9 out of 34 pages.

Chap 5 C-H 1 Lecture 5 Karnaugh Maps Algebraic procedures: Difficult to apply in a systematic way. Difficult to tell when you have arrived at a minimum solution. Karnaugh map (K-map) can be used to minimize functions of up to 6 variables. K-map is directly applied to two- level networks composed of AND and OR gates. Sum-of-products, (SOP) Product-of-sum, (POS).
Image of page 1

Subscribe to view the full document.

Chap 5 C-H 2 Minimum SOP It has a minimum no. of terms. That is, it has a minimum number of gates. It has a minimum no. of gate inputs. That is, minimum no. of literals. Each term in the minimum SOP is a prime implicant, i.e., it cannot be combined with others. It may not be unique. Depend on the order in which terms are combined or eliminated.
Image of page 2
Chap 5 C-H 3 Minimum SOP Example: vertical input scheme Fan-in reduction 1 2 3 1 2 3 4
Image of page 3

Subscribe to view the full document.

Chap 5 C-H 4 Minimum POS It has a minimum no. factors. It has a minimum no. of literals. It may not be unique. – Use (X+Y) (X+Y’) = X – Use (X +C) (X’ + D)(C+D) = (X+C)(X’+D) to eliminate term.
Image of page 4
Chap 5 C-H 5 Minimum POS Example: Vertical input scheme
Image of page 5

Subscribe to view the full document.

Chap 5 C-H 6 2-Variable K-map Place 1s and 0s from the truth table in the K-map. Each square of 1s = minterms. Minterms in adjacent squares can be combined since they differ in only one variable. Use XY’ + XY = X.
Image of page 6
Chap 5 C-H 7 3-Variable K-map Note BC is listed in the order of 00, 01, 11, 10. (Gray code) Minterms in adjacent squares that differ in only one variable can be combined using XY’ + XY = X.
Image of page 7

Subscribe to view the full document.

Chap 5 C-H 8 Location of Minterms Adjacent terms in 3-variable K map.
Image of page 8
Chap 5 C-H 9 K Map Example K-map of F(a,b,c) = m(1,3,5) = M(0,2,4,6,7)
Image of page 9
You've reached the end of this preview.
  • Fall '16
  • JANE SMITH
  • Karnaugh map, Canonical form, Minimum Solutions

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern