1 / 7

Boolean Algebra Essentials: Canonical Forms and Conversions

Understand Boolean algebra canonical forms, conversions, truth tables, and simplification methods with examples in lecture slides. Learn to express Boolean functions in the sum-of-products and product-of-sums forms. Review exam results and grading criteria.

gstewart
Download Presentation

Boolean Algebra Essentials: Canonical Forms and Conversions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CS 3501 - Chapter 3 (3A and 10.2.2) Dr. Clincy Professor of CS • Today: Brief lecture • Today: Cover Exam 1 Dr. Clincy Lecture Slide 1

  2. Boolean Algebra • Through our exercises in simplifying Boolean expressions, we see that there are numerous ways of stating the same Boolean expression. • These “synonymous” forms are logically equivalent. • Logically equivalent expressions have identical truth tables. • In order to eliminate as much confusion as possible, designers express Boolean functions in standardized or canonical form. Lecture

  3. Boolean Algebra • There are two canonical forms for Boolean expressions: sum-of-products and product-of-sums. • Recall the Boolean product is the AND operation and the Boolean sum is the OR operation. • In the sum-of-products form, ANDed variables are ORed together. • For example: • In the product-of-sums form, ORed variables are ANDed together: • For example: Lecture

  4. Boolean Algebra • It is easy to convert a function to sum-of-products form using its truth table. • We are interested in the values of the variables that make the function true (=1). • Using the truth table, we list the values of the variables that result in a true function value. • Each group of variables is then ORed together. • The sum-of-products form for our function is: We note that this function is not in simplest terms. Our aim is only to rewrite our function in canonical sum-of-products form. Lecture

  5. Boolean Algebra • It is easy to convert a function to sum-of-products form using its truth table. • We are interested in the values of the variables that make the function true (=1). • Using the truth table, we list the values of the variables that result in a true function value. • Each group of variables is then ORed together. • The sum-of-products form for our function is: We note that this function is not in simplest terms. Our aim is only to rewrite our function in canonical sum-of-products form. Lecture

  6. Boolean Algebra • It is easy to convert a function to product-of-sums form. • We are interested in the values of the variables that make the function true (=0). • Using the truth table, we list the values of the variables that result in a false function value. • Each group of variables is then ANDed together. • The product-of-sum form for our function is: f(x,y,z)=(x+y+z)(x+y+z’)(x’+y+z’) Lecture

  7. CS3501 Exam 1 Results Average Score = 38 (Average Grade = 75) Score SD = 20 (extremely large) Grading Scaled Used: 90-70 A-grade (3 students) 69-49 B-grade (5 students) 48-28 C-grade (11 students) 27-7 D-grade (10 students) 6-0 F-grade (1 student) In getting your grade logged, be sure and pass back the exam after we go over them – Exam Policy – lose points for not passing back Dr. Clincy 7

More Related