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

Consensus Theorem F(x,y,z) = xy + x′z + yz

Consensus Theorem Working backwards and adding a term Dr. Clincy

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. Dr. Clincy Lecture

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: Dr. Clincy Lecture

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. Dr. Clincy Lecture

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’) Dr. Clincy Lecture

CS3503 Exam 1 Results – 2PM Grading Scaled Used: Average Score = 31 (Average Grade = 75) Score SD = 19 (large) Grading Scaled Used: 80-61 A-grade (1 student) 60-41 B-grade (13 students) 40-21 C-grade (11 students) 20-1 D-grade (11 students) 0 F-grade (2 students) 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 8