Boolean Algebra Notes Part B

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
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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.
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4.  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 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
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5.  Solution:
A. SUM OF PRODUCT , SOP
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
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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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
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7.  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 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
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8. 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 draw
The Logic Circuit.
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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:
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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10.  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 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
(A+B+C)
(A+B+C)
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11.  Solution:
Y = ( A + B + C ) . ( A + B + C )
The Logic Circuit : Discuss with your lecturer
B. PRODUCT OF SUM , POS
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12.  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 Y
0 0 0
0 1 0
1 0 0
1 1 1
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13. 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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14. continue chapter 2: Part C.
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