1. Department of Management School of Business, Economics and Informatics Boolean Algebra Eva Szatmari e.szatmari@bbk.ac.uk

2. School of BEI Study Skills in Mathematics http://moodle.bbk.ac.uk/ http://www.dcs.bbk.ac.uk/~sjmaybank/i ntroduction%20to%20computer%20syste ms.html

3. Learning Objectives Basic Boolean Operations Truth Table Examples Practice Questions Evaluating Boolean Expressions Examples Practice Questions

4. Basic Boolean Operations What are the basic Boolean operations? What do you know about them?

5. Truth Table What is a truth table? How do you construct one? What are the key steps when constructing one?

6. Example 1 (A AND B) OR NOT(A)

7. Example 2 (NOT(A) OR B) AND C

8. Example 3 (A AND NOT(B)) XOR C

9. Example 4 (A IMPLIES B) OR (A IMPLIES C)

10. Practice Questions Construct the truth table of the following Boolean expressions: A OR (NOT(B) AND A) (A OR B) IMPLIES (A AND B) A OR (B AND C)

11. Practice Question 1 – Answer ABNOT(B)NOT(B) AND AA OR (NOT(B) AND A) 00100 01000 10111 11001

12. Practice Question 2 – Answer ABA OR BA AND B(A OR B) IMPLIES (A AND B) 00001 01100 10100 11111

13. Practice Question 3 – Answer ABCB AND CA OR (B AND C) 00000 00100 01000 01111 10001 10101 11001 11111

14. Evaluating Boolean Expressions Which operations are used, how do they work? What are the priorities? What values do I know? Is there any value I don’t know?

15. Example 1 Evaluate the value of the following Boolean expression, if A = 1 and B = 0 A OR NOT(B)

16. Example 2 Evaluate the value of the following Boolean expression, if A = 1, B = 0 and C = 1 (A AND NOT(B)) IMPLIES C

17. Example 3 Evaluate the value of the following Boolean expression, if A = 1 and B = 0 A OR NOT(B AND C)

18. Practice Questions 1)Evaluate the value of the following Boolean expression, if A = 0 and B = 1 NOT(A XOR B) 2)Evaluate the value of the following Boolean expression, if A = 0 and B = 1 A OR (NOT(B) AND C)

19. Practice Questions – Answers 1) NOT(A XOR B) = NOT (0 XOR 1) = NOT(0) = 1 2) A OR (NOT(B) AND C) If C = 0 0 OR (NOT(1) AND 0) = 0 OR (0 AND 0) = 0 OR 0 = 0 If C = 1 0 OR (NOT(1) AND 1) = 0 OR (0 AND 1) = 0 OR 0 = 0

20. Any Other Questions?

21. Contact Details Eva Szatmari 0207 631 6254 Or e.szatmari@bbk.ac.uk GOOD LUCK