Chapter 2 part b boolean soppos
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This document discusses Boolean logic expressions in the forms of Sum of Products (SOP) and Product of Sums (POS). It provides examples of how to write SOP and POS expressions from truth tables. For a given truth table, it shows how to determine the SOP expression by identifying the product terms and ORing them together. Similarly, it demonstrates how to obtain the POS expression by identifying the sum terms and ANDing them together. Exercises are provided for the reader to practice developing SOP and POS expressions and logic diagrams from truth tables.
Chapter 2 part b boolean soppos
- 1. CHAPTER 2: BOOLEAN OPERATION Part B By: Siti Sabariah Salihin sabariah@psa.edu.my
- 2. 2.3 Developing Logic Expression from the Truth Table in the form of a. Sum Of Product , SOP b. Product Of Sum , POS CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 3. A. SUM OF PRODUCT , SOP � Sum Of Product expression ( a.k.a SOP) is one or more product terms (AND) connected by OR operator. The examples for this form are: � 1. AB + AB + AB ( 3 product terms) � 2. ABC + ABC ABC ( 3 product terms) � 3. AB + CD + EF + GK + HL ( 5 product terms) � Each of these sum of products expressions consist of two or more AND terms which are Ored togather. CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 4. A. SUM OF PRODUCT , SOP � Example: Write a Sum of Product, SOP Boolean Expression and draw their Logic Diagram for the following given Truth Table. A B C Y 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 5. A. SUM OF PRODUCT , SOP � Solution: A B C Y 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 ABC ABC ABC The Final SOP for Truth Table is Y = A B C +A B C + A B C and Logic Diagram is shown in following figure: CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 6. A. SUM OF PRODUCT , SOP Y = A B C +A B C + A B C � Logic Diagram is shown in following figure: � A B C CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 7. A. SUM OF PRODUCT , SOP � Exercise 1a: Write a Sum of Product, SOP Boolean Expression and draw their Logic Diagram for the following given truth table. A B C Y 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 8. A. SUM OF PRODUCT , SOP Exercise 2a: Develop the Truth Table for the expression Y = ABC + ABC and draw The Logic Circuit. Solution Exercise 1 and 2: Discuss With your lecturer CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 9. B. PRODUCT OF SUM , POS Product of sums expression (aka POS) is one or more sum (OR) terms connected by AND operator. � The examples for POS form are: ( 2 Sum Terms ) 1. ( A + B + ) . ( A + B + C ) � 2. ( A + B) . ( C + D ) F ( 3 Sum Terms ) 3. (A + B) . (B + D) . (A+B+C) . (A+D+E) ( 4 Sum terms) An POS expression is equal to 0 only if at least one of the sum terms is equal to 0. Convert each binary value to the corresponding sum term by replacing each 1 wuth the corresponding variable complement and each o with the corresponding variable. Example 1001 = A + B + C + D CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 10. B. PRODUCT OF SUM , POS � Example: Write a Product Of Sum, POS Boolean Expression and draw the logic diagram for the given truth table. A B C Y 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 CHAPTER 2 : EE202 DIGITAL ELECTRONICS (A+B+C) (A+B+C)
- 11. B. PRODUCT OF SUM , POS � Solution: Y=(A+B+C) . (A+B+C) The Logic Circuit : Discuss with your lecturer CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 12. B. PRODUCT OF SUM , POS � Example 1b: Develop the Truth Table for ( A + B ) . ( A + B ) . ( A + B ) and Draw Logic circuit. Solution: A B Y 0 0 0 0 1 0 1 0 0 1 1 1 The Logic Circuit: Discuss With Your Lecturer CHAPTER 2 : EE202 DIGITAL ELECTRONICS
- 13. continue chapter 2 Part C 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
- 14. continue chapter 2: Part C.