department of management school of business, economics and informatics boolean algebra eva szatmari...
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Department of ManagementSchool of Business, Economics and Informatics
Boolean AlgebraEva Szatmari
School of BEI Study Skills in Mathematics
http://moodle.bbk.ac.uk/
http://www.dcs.bbk.ac.uk/~sjmaybank/introduction%20to%20computer%20systems.html
Learning Objectives
• Basic Boolean Operations• Truth Table • Examples• Practice Questions• Evaluating Boolean Expressions• Examples• Practice Questions
Basic Boolean Operations
What are the basic Boolean operations?
What do you know about them?
Truth Table
What is a truth table?
How do you construct one?
What are the key steps when constructing one?
Example 1
(A AND B) OR NOT(A)
Example 2
(NOT(A) OR B) AND C
Example 3
(A AND NOT(B)) XOR C
Example 4
(A IMPLIES B) OR (A IMPLIES C)
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)
Practice Question 1 – Answer
A B NOT(B)
NOT(B) AND A
A OR (NOT(B) AND A)
0 0 1 0 0
0 1 0 0 0
1 0 1 1 1
1 1 0 0 1
Practice Question 2 – Answer
A B A OR B A AND B
(A OR B) IMPLIES (A AND B)
0 0 0 0 1
0 1 1 0 0
1 0 1 0 0
1 1 1 1 1
Practice Question 3 – Answer
A B C B AND C A OR (B AND C)0 0 0 0 00 0 1 0 00 1 0 0 00 1 1 1 11 0 0 0 11 0 1 0 11 1 0 0 11 1 1 1 1
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?
Example 1
Evaluate the value of the following Boolean expression, if A = 1 and B = 0
A OR NOT(B)
Example 2
Evaluate the value of the following Boolean expression, if A = 1, B = 0 and C = 1
(A AND NOT(B)) IMPLIES C
Example 3
Evaluate the value of the following Boolean expression, if A = 1 and B = 0
A OR NOT(B AND C)
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)
Practice Questions – Answers
1) NOT(A XOR B) = NOT (0 XOR 1) = NOT(0) = 1
2) A OR (NOT(B) AND C) If C = 00 OR (NOT(1) AND 0) = 0 OR (0 AND 0) = 0 OR 0 = 0If C = 10 OR (NOT(1) AND 1) = 0 OR (0 AND 1) = 0 OR 0 = 0
Any Other Questions?
