The document introduces the Karnaugh Map (K-map) as a method for simplifying Boolean algebra expressions, emphasizing its advantages such as reduced calculation needs and fewer error risks. It outlines the steps to solve expression using K-map and discusses the types of implicants. While effective for expressions with three to six variables, the K-map process becomes complex with more variables and the resulting expression may not always be unique.

1. Karnaugh
Map(K-Map)

2. Hello!
I am Abdulla Al Moin
Department of CSE
Section: PC – B [Fall-20]
Daffodil International University
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Mohammad Monirul Islam
Lecturer (Senior Scale)
Department of CSE
Daffodil International University
Under Course
Course Name: Digital Electronics
Course Code: CSE-223

4. Introduction to (K-Map)
method
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5. Definations
The Karnaugh map (KM or K-map) is a method of
simplifying Boolean algebra expressions.
The Karnaugh map reduces the need for extensive calculations by
taking advantage of humans' pattern-recognition capability.
Take two forms
◎Sum of Product (SOP)
◎Product of Sum (POS)
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6. Steps to solve expression using K-map
i. Select K-map according to the number of variables.
ii. Identify min-terms or max-terms as given in problem.
iii. For SOP put 1’s in blocks of K-map respective to the min-terms (0’s elsewhere).
iv. For POS put 0’s in blocks of K-map respective to the maxterms(1’s elsewhere).
v. Make rectangular groups containing total terms in power of two like 2,4,8 ..(except
1) and try to cover as many elements as you can in one group.
vi. From the groups made in step 5 find the product terms and sum them up for SOP
form.

7. Represent Variables
Using K-map

8. The 3 Variable K-map
Z= ∑A,B,C(1,3,6,7)

9. The 4-Variable K- Map
F(P,Q,R,S)=∑(0,2,5,7,8,10,13,15)

10. Various Implicants
in K-Map

11. Various Implicants in K-Map
 Prime Implicants  Essential Prime Implicants

12. Various Implicants in K-Map
 Redundant Prime
Implicants
 Selective Prime Implicants

13. Importance And Advantage
1. The K-map simplification technique is simpler
and less error-prone compared to the method
of solving the logical expressions using Boolean
laws.
2. It prevents the need to remember each and
every Boolean algebraic theorem.
3. It involves fewer steps than the algebraic
minimization technique to arrive at a simplified
expression.
4. K-map simplification technique always results
in minimum expression if carried out properly.

14. Disadvantage
1. As the number of variables in the logical expression
increases, the K-map simplification process becomes
complicated.
2. The minimum logical expression arrived at by using the K-
map simplification procedure may or may not be unique
depending on the choices made while forming the groups.
For example, for the output variable Y shown by the K-map in
Figure 10, we can obtain two different, but accurate logical
expressions

15. “
Karnaugh maps are used to
simplify real-world logic
requirements so that they can be
implemented using a minimum
number of physical logic gates..
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16. Conclution
Having analyzed the structure of K-maps, we
may arrive at the conclusion that the K-map
simplification process is an effective reduction
technique when dealing with logical
expressions which contain around three to six
input variables.
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17. Thanks!
Any questions?
You can find me at:
abdulla15-2838@diu.edu.bd.me
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