Alright
ladies and gents, today we’ll be learning about the Karnaugh Map otherwise
known as the KMap. The KMap is an alternative method for simplifying a
Boolean expression. It is suitable for inputs of 2 to 4 variables. This method
is much simpler compared to using the Boolean algebra. There are 4 steps
involved when making a karnaugh map which are:
1. By referring to the truth table, fill in all of the 1’s
from the minterms in the truth table.
2. Group the 1’s following a simple set of rules. (We’ll get
more in depth about those rules later).
3. List the groups, analyze it and simptuylify.
4. The simplified expressions are add together (*ORed). * Read as OR in
pasttense form.
Let’s do some examples to help you get a clearer picture on
what I’m rambling on about.
Example 1:
Let’s say we are given 2 variables. Find the simplified
Boolean expression.
Step 1: Make a truth table and a KMap.
A

B

F

Minterms

0

0

0

A’B’

0

1

1

A’B

1

0

1

AB’

1

1

1

AB

B
A

B’
(0)

B
(1)

A’
(0)

O

1

A
(1)

1

1

* In the Karnaugh Map, each cells is filled with
values that corresponds with the “F” column.
Step 2: Group the 1’s in the KMap using a set of rules
stated below.
 Each groups can consists of only 1’s.
 Only adjacent cells are allowed to be grouped.
 The group must be as large as possible meaning that it can have 2, 4, 8 or 16 of 1’s in it.
 The least number of grouhgvps formed the better.
 All 1’s must belong to a group even if it’s a group of one.
 Wrap around is allowed.
 Overlapping groups are allowed.
B
A

B’

B

A’

o

1

A

1

1

 The first group is B as variable B is the only
variable that remains constant
B
A

B’

B

A’

o

1

A

1

1

 The second group is A
since A is the only variable that
remains constant.
Step 3: Skipping this step as we havjnkle already found the
simplest Boolean expression.
Step 4: Add together
the groups.
Answer
= B + A or A
+ B
Example 2: Given 3 variables. Find the simplified Boolean
expression.
Step 1: Build a truth
table and a KMap.
A

B

C

F

Minterms

0

0

0

1

A’B’C’

0

0

1

1

A’B’C

0

1

0

1

A’BC’

0

1

1

1

A’BC

1

0

0

0

AB’C’

1

0

1

0

AB’C

1

1

0

1

ABC’

1

1

1

1

ABC

BC
A

B’C’

B’C

BC

BC’

A’

1

1

1

1

A

0

0

1

1

Step 2: Group the 1’s.
BC
A

B’C’

B’C

BC

BC’

A’

1

1

1

1

A

0

0

1

1


A’B’C’  A’B’C

A’BC A’BC’
BC
A

B’C’

B’C

BC

BC’

A’

1

1

1

1

A

0

0

1

1


A’BC  A’BC’

ABC  ABC’
Step 3: Analyze.
For same letters in a column they will be brought down. For
different letters in a column they will cancel each other out.
Group 1:
Group 2:
A’ B’ C’  A’
B C
A’ B’ C
 A B C
A’ B
C  A B
C’
A’ B C’  A’
B C’
A’ B
Step 4: Add the groups together.
Answer
= A’ + B or B
+ A’
Below are some links that i found to be very helpful when learning about KMaps:
2 comments:
Great Tutorial easy to follow. Just one question, when you have done stage 3 'analyse' how to you know whether they are AND/OR gates etc?
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