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
