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Karnaugh map or K-map discussion

2,3,4,5 variables K-map are ways of minimizing the Boolean functions using diagrams which are made up of squares. By minimization we imply a function with minimum number of terms and each term with lowest number of literals.

Following k-map for 2-5 variables are discussed in this section:

1) Two variables K-map

Two variable Karnaugh map (K-map) and 2 var kmap example discussed below.

First write the Truth Table for 2 variables x and y. Once we know all the values in table its easier to plot the 2 var k-map.

2 variable K– map plot below : - Each element (0-3) from above table is plotted in k-map below. Var x is horizontal row and y is vertical column.  There intersection denotes output function element.

 

K-map location number
x
y
Output function
0
0
0
x’y’
1
0
1
x’y
2
1
0
xy’
3
1
1
xy

0

1

0

1

x

y

x’y’
x’y
xy’
xy
Prdt of Maxterms.
3 var K-map.

2 variable solved k-map example link.

A solved example of 2 variable k-map below.

F(x,y)=sum(0,2,3)

Minimization solution to above function.

 

= y’(x + x’) + xy + xy’ = y’ + x (y+y’) = y’ + x

 

K-map Trick : From the elements in enclosed box, we can minimize by only keeping the element which is not changing. In this example its y’ and x.   

0

1

0

1

x

y

x’y’ =1

xy’ = 1
xy = 1

 

 

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2 variable K– map plot is mapped in table below.

Three variables K-map

Four variables K-map

Five variables K-map

Prime Implicant and Gate level minimization examples

2) Three variable Kmap

3) Four variables Kmap

4) Five variables K-map

5) Prime Implicant and Gate level minimization examples