Chapter 2 boolean part c

CHAPTER 2 :

BOOLEAN OPERATIONSPart C

2.4 Simplify combinational Logic Circuits using:

a. Boolean Laws ( Already Discuss in Part B notes) b. Karnough Map b. Karnough Map b. Karnough Map b. Karnough Map

Review:Boolean SimplificationQuestion: 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 Do and pass up Do and pass up Do and pass up to me tomorrow in my class. This is to HELPHELPHELPHELP u to COVER COVER COVER COVER your QUIZ 1 MARK.QUIZ 1 MARK.QUIZ 1 MARK.QUIZ 1 MARK.

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

Two variables K-map with assume A and B as variable

Three variable K-map with assume A, B and C as variable

� LoopingLoopingLoopingLooping 1.1.1.1. Looping of Looping of Looping of Looping of PAIR/TWOPAIR/TWOPAIR/TWOPAIR/TWO� Looping a PAIRPAIRPAIRPAIR of adjacent 1s in a K-map

eliminates the variable that appears in complemented and uncomplemented form

2.2.2.2. Looping group of Looping group of Looping group of Looping group of FOUR/QUAD FOUR/QUAD FOUR/QUAD FOUR/QUAD� Looping a QUADQUADQUADQUAD of adjacent 1s eliminate the two

variables that appear in both complemented and uncomplemented form

3.3.3.3. Looping group of Looping group of Looping group of Looping group of EIGHT/OCTETEIGHT/OCTETEIGHT/OCTETEIGHT/OCTET� Looping an OCTETOCTETOCTETOCTET of adjacent 1s eliminates the

three variables that appear in the both complemented and uncomplemented form

� Examples Examples Examples Examples Simplify this Boolean equation by using K-maps

F = X Y Z+ X Y Z + X Y Z

� ExamplesExamplesExamplesExamplesFind out the equation based on the given

� Solution

More Exercises in K-Map

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

� Discuss the answer with your lecturer.� Do exercises in Tutorials.

END OF CHAPTER 2

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: ]REFERENCES: ]REFERENCES: ]REFERENCES: ]

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