This presentation will help you to learn the basics required to learn the K map. This will help you to solve the questions related to K map. This presentation is actually the whole process of K map. If you want to watch its video then go on https://www.youtube.com/watch?v=s3J0m7aZwGg here I have explained the points mentioned in this presentation

1. K-MAP
Maurice Karnaugh introduced k-map in
1953 as a next edition of Edward
Veitch’s (1952) Veitch diagram

2. ADVANTAGES
• Reduces extensive
calc.
• Reduces expression
without Boolean
theorems
• Used for minimizing
circuits
• Less time consuming
• Less space consuming
DISADVANTAGES
• Tedious for more than
5 variables
• Some examples are
solved in few seconds
by Boolean theorems
easily

3. Gray code
• It is a numerical code used in computing in
which consecutive integers are represented by
binary numbers differing in only one digit
• E.g. Binary Gray
00 00
01 01
10 11
11 10

4. Rules for converting binary code into gray
code
• Write first digit in left side as it is
• A digit in gray code is the addition of
corresponding digit in binary and its previous
digit in binary
• 0+0=0 BINARY 1 0 0 1 0 1 0
• 0+1=1 GRAY 1 1 0 1 1 1 1
• 1+0=1 BINARY 1 0 1 1 1 1 1 0 0 1
• 1+1=0 GRAY 1 1 1 0 0 0 0 1 0 1

5. Rules for converting gray code into binary
code
• Write first digit in left side as it is
• A digit in binary code is the addition of
corresponding digit in gray and its previous
digit in binary
• 0+0=0 GRAY 1 0 1 0 1 0 1 0
• 0+1=1 BINARY 1 1 0 0 1 1 0 0
• 1+0=1 GRAY 1 1 1 1 0 0 1 1 0 1
• 1+1=0 BINARY 1 0 1 0 0 0 1 0 0 1

6. Consider the
following truth
table
Here A,B,C,D are
inputs and Y is
output
magnitude A B C D Y
0 0 0 0 0 0
1 0 0 0 1 0
2 0 0 1 0 1
3 0 0 1 1 0
4 0 1 0 0 1
5 0 1 0 1 1
6 0 1 1 0 0
7 0 1 1 1 1
8 1 0 0 0 0
9 1 0 0 1 0
10 1 0 1 0 1
11 1 0 1 1 1
12 1 1 0 0 0
13 1 1 0 1 0
14 1 1 1 0 0
15 1 1 1 1 0

7. Consider inputs A,B binary gray
A B A B
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
Consider inputs C,D binary gray
C D C D
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0

8. Write down inputs in k-
map as shown in figure
For first block all inputs
are 0 i.e. the input given
is A B C D
Hence
0 is for low input
1 is for high input

9. Write magnitudes in the right corner of the
lower side of each block as shown in figure

10. FINAL K-MAP
Write magnitude at
the centre of each
block
NOTE : using magnitude
is just for simplicity

11. Grouping
Rules of grouping -
1’s & 0’s can
not be grouped
diagonal 1’s can
not be grouped

12. Elements in a group should be 2n

13. Minimum
Groups
should be
formed
For above
rule group
Overlapping
is applicable

14. Groups may
be of
non-complete
polygon
Hierarchy is …….16,8,4,2

17. Examples of k-map
1.Minimize the following equation using k-map
y=ABC+ABC+ABC+ABC
_ _ _ _ _ _
ABC = 000 = 0
_ _ _
ABC = 010 = 2
_ _
ABC = 101 = 5
_
ABC = 111 = 7
Using this fill the k-map
Grouping – here 2 groups of 2 1’s
Is possible

18. For upper group A and C are
constants and B is varying.
Neglect B.A and C both are 0.
Hence output of this group is AC
For upper group A and C are
constants and B is varying.
Neglect B.A and C both are 0.
Hence output of this group is AC
_ _
Y=AC+AC
_ _
Thus output Y is given by ,
=A B⃝.

19. 2. Solve the given
k-map
Step I -grouping
Step II -output of
each group
Step III -final output
Here answer is ,
Y=CD+BC+BD
_ _ _

20. Sop form – sum of product form
Sop form – product of sum form
Example-
Example-
ABC+ABC+ABC+ABC
_ _ _ _ _
(A+B+C)(A+B+C)(A+B+C)
__ _

21. Conversion of given equation to sop -
Example-
AB+A+ABC =AB(C+C)+A(B+B)(C+C)+ABC
=ABC+ABC+ABC+ABC+ABC+ABC+ABC
_ _ _
_ _ _ _ _
=ABC+ABC+ABC+ABC
_ _ _ _

22. Conversion of given equation to pos -
First equation should be converted to sop
Example-
From previous example
Y=AB+A+ABC=ABC+ABC+ABC+ABC
_ ___
Y=ABC+ABC+ABC+ABC
_ _ _ _ _ _ _ __
Y=Y=ABC+ABC+ABC+ABC_ _ _ _ _ _ _ _
__ _________________
Y=(ABC)(ABC)(ABC)(ABC)
Y=(A+B+C)(A+B+C)(A+B+C)(A+B+C)
_ _ _ _ _ _ _ _
____ ____ ____ ____
_ _ _ _