ECE 275: Digital Design I
Class 13K-Maps (Karnough Maps)
Allows you to simplify expressions without using the theorems
F(A, B)
Truth table
A | B | F |
---|---|---|
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 0 |
1 | 0 | 0 |
F = A'B' + A'B If you simplify using theorems, then you would find F= A'
K-map for F
A\B | 0 | 1 |
---|---|---|
0 | 1 | 1 |
1 | 0 | 0 |
You can pair up the ones so you get A'
3 Variable K-Maps
(A, B, C) Only have one bit change
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | ||||
1 |
Could also do this
AB\C | 0 | 1 |
---|---|---|
00 | ||
01 | ||
11 | ||
10 |
Solve a problem
Truth table:
A | B | C | F |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 |
F = AC' + A'B
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 1 | 0 |
F = C
4 Variable K-Maps
AB\CD | 00 | 01 | 11 | 10 |
---|---|---|---|---|
00 | ||||
01 | ||||
11 | ||||
10 |
AB\CD | 00 | 01 | 11 | 10 |
---|---|---|---|---|
00 | m0 | m1 | m3 | m2 |
01 | m4 | m5 | m7 | m6 |
11 | m12 | m13 | m15 | m14 |
10 | m8 | m9 | m11 | m10 |
F = âm(0, 2, 3, 5, 6, 7, 8, 10, 11, 14, 15)
AB\CD | 00 | 01 | 11 | 10 |
---|---|---|---|---|
00 | 1 | 1 | 1 | |
01 | 1 | 1 | 1 | |
11 | 1 | 1 | ||
10 | 1 | 1 | 1 |
F = C + A'BD + B'D'
F= âm(1, 3, 5, 7, 9) + âd(6, 12, 13);
AB\CD | 00 | 01 | 11 | 10 |
---|---|---|---|---|
00 | 1 | 1 | ||
01 | 1 | 1 | X | |
11 | X | X | ||
10 | 1 |
F = A'D + C'D