The concept of compressing around a variable using Shannon’s Expansion Theorem also applies
to K-maps. The example below uses C as the reference variable: 4-variable (multivariable) expression of K-map Compression. Plotting, Filling, and Reducing Compressed K-maps
The steps to compress a K-map are:
(1) Plot the truth table and then compressed K-map.
(2) Choose cube sizes that result in minimum expressions for the function by covering each
map-entered variable separately, treating other map-entered variables as 0s and all 1s as
“don’t cares”.
(3) Choose cube sizes that result in minimum expressions for the function by covering the 1s
in the map that are not complementary-covered.
WX F
0 0 (^) Y
0 1 (^) Y.Z+Y.Z
1 1 (^) Y.Z+Y.Z
1 0 (^) Y.Z
W X Y Z F
0 0 0 0 1
0 0 0 1 1
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 1
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 1
1 1 0 1 0
1 1 1 0 0
1 1 1 1 1
1 1
1 0
00 01 11 10
00
01
11
10
YZ
WX
0 0
1 0
1 0
1 0
1 0
0 0
1 0
Z Z
0 1
Y
WX
Z
0
00
01
11
10
Compare CompareZZCompare0 0
0 1
0 1
C
AB
1 0
1 1
00
01
11
10
O
C
AB
C
100
01
11
10
K-mapCompressed K-mapCompare