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# Chapter 2 ee202 boolean part a

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### Chapter 2 ee202 boolean part a

1. 1. EE 202 : DIGITAL ELECTRONICS CHAPTER 2 : BOOLEAN OPERATIONS by : Siti Sabariah Salihin Electrical Engineering Department sabariah@psa.edu.my
2. 2. CHAPTER 2 : BOOLEAN OPERATIONS EE 202 : DIGITAL ELECTRONICS Programme Learning Outcomes, PLO Upon completion of the programme, graduates should be able to: • PLO 1 : Apply knowledge of mathematics, scince and engineering fundamentals to well defined electrical and electronic engineering procedures and practices Course Learning Outcomes, CLO • CLO 1 : Illustrate the knowledge of digital number systems,codes and ligic operations correctly • CLO 2 : Simplify and design combinational and sequential logic circuits by using the Boolean Algebra and the Karnaugh Maps. EE 202 : DIGITAL ELECTRONICS
3. 3. Upon completion of this Topic 2 student should be able to: 2.1 Know the symbols,operations and functions of logic gates. 2.1.1 Draw the symbols, operations and functions of logic gates. 2.1.2 Explain the Function of Logic gates using Truth Table. 2.1.3 Construct AND, OR and NOT gates using only NAND gates. 2.2 2.2.1 2.2.2 2.2.3 2.2.4 Know the basic concepts of Boolean Algebra and use them in Logic circuits analysis and design. Construct the basic concepts of Boolean Algebra and use them in logic circuits analysis and design. State the Boolean Laws. Develop logic expressions from the truth table from the form of SOP and POS Simplify combinatinal Logic circuits using Boolean Laws and Karnaugh Map EE 202 : DIGITAL ELECTRONICS
4. 4. TRUTH TABLES �A truth table is a table that describes the behavior of a logic gate �The number of input combinations will equal 2N for an N-input truth table EE 202 : DIGITAL ELECTRONICS 4
5. 5. LOGIC GATES • Circuits which perform logic functions are called gates • The basic gates are: I. NOT/INVERTER gate II. AND gate III. OR gate IV. NAND gate V. NOR gate VI. XOR gate VII. XNOR gate EE 202 : DIGITAL ELECTRONICS
6. 6. Symbol I. NOT / INVERTER Gate Timing Diagram Truth Table
7. 7. II. AND Gate Symbol Timing Diagram Truth Table
8. 8. Symbol III. OR gate Timing Diagram Truth Table
9. 9. Symbol IV. NAND Gate Truth Table Timing Diagram
10. 10. V. NOR Gate Symbol Truth Table Timing Diagram
11. 11. VI. XOR Gate Symbol Truth Table Timing Diagram
12. 12. VII. XNOR Gate Symbol Truth Table Timing Diagram
13. 13. BOOLEAN ALGEBRA • The Boolean algebra is an algebra dealing with binary variables and logic operation • The variables are designated by: I. Letters of the alphabet II. Three basic logic operations AND, OR and NOT
14. 14. BOOLEAN ALGEBRA • A Boolean function can be represented by using truth table. A truth table for a function is a list of all combinations of 1’s and 0’s that can be assigned to the binary variable and a list that shows the value of the function for each binary combination • A Boolean expression also can be transformed into a circuit diagram composed of logic gates that implements the function
15. 15. • Examples F = A + BC Truth Table Logic circuit
16. 16. Boolean Algebra Exercise Exercise: • Construct a Truth Table for the logical functions at points C, D and Q in the following circuit and identify a single logic gate that can be used to replace the whole circuit.
17. 17. Solution INPUTS A OUTPUT AT B C D Q
18. 18. Answer: INPUTS OUTPUT AT A B C D Q 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1
19. 19. Exercise • Find the Boolean algebra expression for the following system. Solution:
20. 20. BASIC IDENTITIES AND BOOLEAN LAWS
21. 21. BOOLEAN LAWS COMMUTATIVE LAWS ASSOCIATIVE LAWS
22. 22. BOOLEAN LAWS DISTRIBUTIVE LAWS DEMORGAN’S THEOREMS
23. 23. • All these Boolean basic identities and Boolean Laws can be useful in simplifying a logic expression, in reducing the number of terms in the expression • The reduced expression will produce a circuit that is less complex than the one that original expression would have produced. • Examples Simplify this function F=ABC+ABC+AC
24. 24. Solution CHAPTER 2 : EE202 DIGITAL ELECTRONICS
25. 25. Exercise: Using the Boolean laws, simplify the following expression: Q= (A + B)(A + C) Solution: Q = (A + B)(A + C) Q = AA + AC + AB + BC Q = A + AC + AB + BC Q = A(1 + C) + AB + BC Q = A.1 + AB + BC Q = A(1 + B) + BC Q = A.1 + BC Q = A + BC ( Distributive law ) ( Identity AND law (A.A = A) ) ( Distributive law ( Identity OR law (1 + C = 1) ( Distributive law ) ( Identity OR law (1 + B = 1) ) ( Identity AND law (A.1 = A) ) Then the expression: Q= (A + B)(A + C) can be simplified to Q= A + BC CHAPTER 2 : EE202 DIGITAL ELECTRONICS
26. 26. continue chapter 2 Part B REFERENCES: 1. "Digital Systems Principles And Application" Sixth Editon, Ronald J. Tocci. 2. "Digital Systems Fundamentals" P.W Chandana Prasad, Lau Siong Hoe, Dr. Ashutosh Kumar Singh, Muhammad Suryanata. Download Tutorials Chapter 2: Boolean Operations @ CIDOS http://www.cidos.edu.my