1
Lesson 3: Karnaugh Maps
Computer Aided Digital Design
Computer Aided Digital Design
EE 3109
Gopi K. Manne
Fall 2007
Karnaugh Maps
Boolean Algebra – no guarantee minimized expression
–reduction-order dependent
–
still necessary to sanity check results
–
still necessary to sanity check results
Need other more systematic methods
–Karnaugh Maps – graphical representation
–Quine-McCluskey method – computer algorithm
Three Variable Karnaugh Maps – minterm positions
00
A
BC 0 1
4
0
00
01
11
10
3
26
4
0
5
1
7
Three Variable Karnaugh Maps - example
00
A
BC 0 1
Z = A’ B C + A’ B C’ + A B C’
0
0
00
01
11
10
1
11
0
0
0
0
0
Z = A’ B + B C’
Three Variable Karnaugh Maps - legal circles
00
A
BC 0 1
Z = A’ B’ C + A’ B C + A’ B C’
0
0
00
01
11
10
1
10
0
0
0
1
0
Z = A’ C + A’ B
Three Variable Karnaugh Maps - example
00
A
BC 0 1
Z = A’ B’ C’ + A’ B’ C
+ A’ B C + A’ B C’
0
1
00
01
11
10
1
10
0
1
0
1
0
Z = A’
