Microsoft Word - Digital Logic Design v_4_6a

 Example of plotting, filling and reducing a compressed K-map directly from the compressed K-

map and expanding to an uncompressed form.

 A 6-variable example of compressed K-map is described by:

F ABC,,,( DY,, Z)=∑ Y Y Z Y Z).15,14,.12,7,.6,5,4,.1,.0( +∑md )13(

Where m = m(A,B,C,D)

Minimize the function.

AB CD (^) 00 01 11 10

00

01

11

10

Y^0

Y^0

1 1

1 Z

Y Z

• 1

0 0

0 0

• 
  

AB CD (^) 00 01 11 10
00
01
11
Step1. Compressed K-Map Step 3.^10
Map-entered variable  0
Complementary-covered 1  don’t care
1  1 & 0  0
Step 2.
1  don’t care
0  0
No change to Variables
Implicants: Group variables
Individually
AB CD (^) 00 01 11 10
00
01
11
10
Y^0
Y^0

• 
  
  
  
  • 
    
    
    
    • Z
    
    
    
    
  
  
  
  

Y Z

• 
  
  
  
  • 
    
  
  
  
  

0 0

0 0

p2 p3

p1

0 0

0 0

- 1

- 0

0 0

- 1

0 0

(^0 0) P4
p5

0

Z

1

Z

XY

00

01

11

10

0

0

1

1

XY Z

00

01

11

10

0

1

1

0

0 1

Compressed K-Map Uncompressed K-

Map

Definition: A complementary covered 1 in a compressed K-map is a 1 that is covered

with a map-entered variable and covered again with the complement same map-

entered variable.

p3 = X.Y

(Redundant Prime Implicant)

p1 = Y.Z

p2 = X.Z

F(X,Y,Z)= Y.Z+X.Z