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2.3 Developing Logic Expression from the Truth Table in the form of a. Sum Of Product , SOP
b. Product Of Sum , POS
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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. DEE2034 : DIGITAL ELECTRONICS
Example: Write a Sum of Product, SOP Boolean
Expression and draw their Logic Diagram for the following given Truth Table.
A. SUM OF PRODUCT , SOP
A B C Y0 0 0 10 0 1 00 1 0 00 1 1 11 0 0 01 0 1 11 1 0 01 1 1 0
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Solution:
A. SUM OF PRODUCT , SOP
A B C Y0 0 0 10 0 1 00 1 0 00 1 1 11 0 0 01 0 1 11 1 0 01 1 1 0
A B C
A B C
A B C
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:
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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
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Exercise 1a: Write a Sum of Product, SOP Boolean Expression and draw their Logic Diagram for the following given truth table.
A. SUM OF PRODUCT , SOP
A B C Y0 0 0 10 0 1 00 1 0 10 1 1 01 0 0 11 0 1 01 1 0 01 1 1 1
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A. SUM OF PRODUCT , SOP
Solution Exercise 1 and 2:Discuss With your lecturer
Exercise 2a: Develop the Truth Table for the expression Y = ABC + ABC and drawThe Logic Circuit.
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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: 1. ( A + B + ) . ( A + B + C ) ( 2 Sum
Terms )
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
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Example: Write a Product Of Sum, POS Boolean Expression and draw the logic diagram for the given truth table.
B. PRODUCT OF SUM , POS
A B C Y0 0 0 10 0 1 10 1 0 10 1 1 11 0 0 01 0 1 11 1 0 11 1 1 0
(A+B+C)
(A+B+C)
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Solution: Y = ( A + B + C ) . ( A + B + C )
The Logic Circuit : Discuss with your lecturer
B. PRODUCT OF SUM , POS
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Example 1b: Develop the Truth Table for ( A + B ) . ( A + B ) . ( A + B ) and Draw
Logic circuit. Solution:
The Logic Circuit: Discuss With Your Lecturer
B. PRODUCT OF SUM , POS
A B Y0 0 00 1 01 0 01 1 1
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continue chapter 2 Part C
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.
REFERENCES:
Download Tutorials Chapter 2: Boolean Operations http://www.portal.cidos.edu.my
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continue chapter 2: Part C.
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