This document discusses Boolean operations and Karnaugh maps. It introduces Boolean laws and how they can be used to simplify logic expressions. It then explains what a Karnaugh map is and how it provides a systematic way to simplify Boolean expressions and truth tables by grouping adjacent 1s. The document provides examples of using Karnaugh maps, including how to loop pairs, quads and octets. It includes exercises for students to practice minimizing Sum of Products expressions using Karnaugh maps. References for further reading are also provided.

1. CHAPTER 2 :
BOOLEAN OPERATIONS
Part C
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2. 2.4 Simplify combinational Logic
Circuits using:
a. Boolean Laws
( Already Discuss in Part B notes)
b. Karnough Map
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3. Review:Boolean Simplification
Question: Using Boolean Rules/Laws/De Morgan
Theorem, simplify the expression below:
a. Y = AC (A B D) + A B C D + A B C (5m)
b. Y = ABC (BD + CDE) + AC (5m)
NOTES: Do and pass up to me tomorrow in my class.
This is to HELP u to COVER your QUIZ 1 MARK.
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4. KARNAUGH MAP
 Provides a systematic method for
simplifying a Boolean expression or a
truth table function
 The K-map is a table consisting of N = 2n
cells, where n is the number of input
variables.
 The table format is such that there is a
single variable change between any
adjacent cells
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5. Two variables K-map with
assume A and B as variable
Three variable K-map with
assume A, B and C as variable
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6.  Looping
1. Looping of PAIR/TWO
 Looping a PAIR of adjacent 1s in a K-map
eliminates the variable that appears in
complemented and uncomplemented form
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7. 2. Looping group of FOUR/QUAD
 Looping a QUAD of adjacent 1s eliminate the two
variables that appear in both complemented and
uncomplemented form
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8. 3. Looping group of EIGHT/OCTET
 Looping an OCTET of adjacent 1s eliminates the
three variables that appear in the both
complemented and uncomplemented form
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9.  Examples
Simplify this Boolean equation by using K-maps
F = X Y Z+ X Y Z + X Y Z
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10.  Examples
Find out the equation based on the given
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11.  Solution
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12. More Exercises in K-Map
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13. Question:
Use a K-map to minimize the following SOP
Boolean Expression
a. A B C + A B C + A B C + A B C + A B C
b. A B C D + A B C D + A B C D + A B C D + A B C D +
A B C D + A B C D + A B C D + A B C D
c. C ( A B + B ) + A B C + A B
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14.  Discuss the answer with your lecturer.
 Do exercises in Tutorials.
END OF CHAPTER 2
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15. 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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