PPT: Karnaugh Maps (K-Maps) - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


Karnaugh Maps
Page 2


Karnaugh Maps
Why Karnaugh 
Maps?
Graphical 
Simplification
Karnaugh Maps offer a visual 
method to reduce digital 
circuits to their minimum 
number of gates.
Truth Table 
Alternative
Maps express truth tables or 
complex Boolean expressions 
in a simple table of 1s and 0s.
Practical Application
Useful for circuits with up to 6 inputs, providing quicker 
minimization than Boolean algebra.
Page 3


Karnaugh Maps
Why Karnaugh 
Maps?
Graphical 
Simplification
Karnaugh Maps offer a visual 
method to reduce digital 
circuits to their minimum 
number of gates.
Truth Table 
Alternative
Maps express truth tables or 
complex Boolean expressions 
in a simple table of 1s and 0s.
Practical Application
Useful for circuits with up to 6 inputs, providing quicker 
minimization than Boolean algebra.
Constructing Karnaugh Maps
Map Size
The map's size depends on input count:
2 inputs: 4 cells (2²)
3 inputs: 8 cells (2³)
4 inputs: 16 cells (2t)
Map Structure
Input labels appear at the top-left corner. Edges represent 
all possible input combinations.
For example, a 3-input map has the top edge representing 
4 possible combinations for inputs A and B.
Page 4


Karnaugh Maps
Why Karnaugh 
Maps?
Graphical 
Simplification
Karnaugh Maps offer a visual 
method to reduce digital 
circuits to their minimum 
number of gates.
Truth Table 
Alternative
Maps express truth tables or 
complex Boolean expressions 
in a simple table of 1s and 0s.
Practical Application
Useful for circuits with up to 6 inputs, providing quicker 
minimization than Boolean algebra.
Constructing Karnaugh Maps
Map Size
The map's size depends on input count:
2 inputs: 4 cells (2²)
3 inputs: 8 cells (2³)
4 inputs: 16 cells (2t)
Map Structure
Input labels appear at the top-left corner. Edges represent 
all possible input combinations.
For example, a 3-input map has the top edge representing 
4 possible combinations for inputs A and B.
Using the Karnaugh 
Map
Truth Table Data
Populate the map with data from a truth table or Boolean 
equation.
Boolean Expressions
Each cell corresponds to a specific Boolean expression.
Logic Values
Place 1s in cells that match input combinations producing logic 
1 outputs.
Page 5


Karnaugh Maps
Why Karnaugh 
Maps?
Graphical 
Simplification
Karnaugh Maps offer a visual 
method to reduce digital 
circuits to their minimum 
number of gates.
Truth Table 
Alternative
Maps express truth tables or 
complex Boolean expressions 
in a simple table of 1s and 0s.
Practical Application
Useful for circuits with up to 6 inputs, providing quicker 
minimization than Boolean algebra.
Constructing Karnaugh Maps
Map Size
The map's size depends on input count:
2 inputs: 4 cells (2²)
3 inputs: 8 cells (2³)
4 inputs: 16 cells (2t)
Map Structure
Input labels appear at the top-left corner. Edges represent 
all possible input combinations.
For example, a 3-input map has the top edge representing 
4 possible combinations for inputs A and B.
Using the Karnaugh 
Map
Truth Table Data
Populate the map with data from a truth table or Boolean 
equation.
Boolean Expressions
Each cell corresponds to a specific Boolean expression.
Logic Values
Place 1s in cells that match input combinations producing logic 
1 outputs.
Step (a)
1
Identify Input 
Values
From Table 2.4.1 row 3, inputs 
AMC have values of 010.
2
Check Output
This produces a logic 1 at output 
X, giving Boolean expression M.
3
Place in Map
Place 1 in the cell corresponding 
to A=0 and MC=10.