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.

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.