3. Index
The map method
Rules for map
Present technique.
Types of variables
Uses of k-map
Application of k-map.
4. WHAT IS K-MAP?
The pictorial representation of variables
from which the Boolean expression or
truth table can be identified.
It avoids ambiguity during logic designing.
Since there is number of probability in
mapping the answer would be same and
avoid confusion.
It is denoted as k-map since it is found by
the person karnaugh.
5. THE MAP
Straight procedure for minimizing Boolean
functions
Considered as pictorial form of a truth
table
It is a diagram made of squares
It consists of minterms[0] & maxterms[1]
In Some cases don’t care conditions are
used [represented by ‘x’] .
6. Rules
Mapping can be done horizontally or
vertically but not in diagonally.
Wrapping technique can be done only
form three variable map.
Only the maxterms can be mapped to form
a Boolean expression.
Overlapping of maxterms is possible,
utmost once.
7. present technique
Maxterms are grouped together to derive
the expression.
Don’t care conditions alone cannot be
mapped to form a group.
The mapping can be selected depending
on the variable used
Corresponding variables should be written
for the mapped values.
The grouping is done in even numbers.
8. Basic’s
The frequently used variable mappings are
Two variable map
Three variable map
Four variable map
Five variable map
Let’s see this in detail
9. Two variable-map
Four minterms for two
variables
It consists of four squares
Y
The 0 and 1 marked in X
row and column
designate the values of 0 0
variables
A two variable is shown
And the expression for
the group is 1 1
=X+Y
10. Three variable map
It consists of eight minterms for three
binary variables
It has eight squares
Minterms are not arranged in binary
sequence but similar to gray code
Wrapping technique can start using only
from the three variable mapping
Consider the following truth table for which
the mapping can be done.
11. Truth table
D.NO A B C S C
0 0 0 0 0 0
1 0 0 1 1 0
2 0 1 0 1 0
3 0 1 1 0 1
4 1 0 0 1 0
5 1 0 1 0 1
6 1 1 0 0 1
7 1 1 1 1 1
13. FOUR VARIABLE MAP
In this method four variables are used.
The map contains 16 squares.
Grouping can be done only for the
maxterms
Wrapping can be done by folding the map.
Adjacent groups cannot be formed since it
contains single map.
The representation of four variable map is.
14. Four variable map
C
CD
AB 00 01 10 11
Adjacent
1 1 1 groups
00
can’t be
formed
01 1
B
10
A Wrapping
can be
11 1 1 1 cone
15. Five variable map
It consists of five variables (A,B,C,D,E)
Left hand four variable consists of 16 squares
and right consists of 16 squares
Actually it is the combination of two four variable
map
The left table represents the variable value A=0
and right table represents the A value as ‘1’.
Adjacent group in the tables can be represented
once
Consider the following truth table for which the
mapping is done.
16. Five variable map
A=0 A=1
D D
DE
BC
0 2 2 3 16 17 19 18
4 5 7 6 20 21 23 22
C C
12 13 15 14 28 29 31 30
B B
8 9 11 10 24 25 27 26
17. Representation of five variable
map without using two four
variable map Adjacent
groups
can’t be
ABC
000 001 010 011 110 111 100 101 formed
DE
but it
00 0 1 2 3 6 7 4 5 gives
the
same
01 8 9 10 11 14 15 12 13 answer
24 25 26 27 30 31 28 29
10
11 16 17 18 19 22 23 20 21
18. DON’T CARE CONDITIONS
Y
CD
00 01 11 11
AB
00 x 1 1 X
01 0 x 1 0
X
10
0 0 1 0
W
11
0 0 1 0
19. DON’T CARE CONDITION
The ‘x’ represents the position of don’t care
conditions.
The value of ‘x’ may 1 or 0 it depends on
grouping.
The expression for the previous k-map is:
A=c +a +bd +bd.
Note that all the don’t care cannot be mapped as
a single group.
20. OUR METHOD
Check the maxterms in the truth table
itself.
Write the corresponding expression.
Simplify the expression with the help of
DEMORGAN’S theory.
The is no need of k-map in this method.
21. uses
K-map is used to derive any form of logical
circuit
It is used in design and analysis procedure
It is used in Quine-McCluskey method
Simplification of Boolean expression is
easier
It is used in sum of product and in product
of sum method.
22. Application
The k-map can be used in combinational
circuit and in sequential circuit.
Full adder and half adder can be easily
analyzed with the help of k-map.
It is used in the in tabular method to
simplify the Boolean expression even
simpler than that.
23. conclusion
Thus k-map is a major topic in electronics
It is used in simplification of Boolean
expression & logic gates
It is used in the conversion of truth table to
Boolean expression and vice versa.
It is better to use a k-map than the tabular
method.
