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