ECE 375: Digital Design II
Class 9State Assignment Table
PS | NS X=0 | NS X=1 |
---|---|---|
S0 | S1 | S2 |
S1 | S3 | S2 |
S2 | S1 | S4 |
S3 | S5 | S2 |
S4 | S1 | S6 |
S5 | S5 | S2 |
S6 | S1 | S6 |
Now we optimize the state assignments
Start by grouping by the first guideline
[S0, S2, S4, S6] [S0, S1, S3, S5] [S4, S6] [S3, S5]
Then the second guideline
[S1, S2] [S2, S3] [S1, S4] [S1, S6]x2 [S2, S5]x2
Now we draw a K-Map
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | ||||
1 |
Now we start adding in adjacent states
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | S0 | S2 | S4 | S6 |
1 |
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | S0 | S2 | S4 | S6 |
1 | S5 | S1 |
A\BC | 00 | 01 | 11 | 10 |
---|---|---|---|---|
0 | S0 | S2 | S4 | S6 |
1 | S3 | S5 | X | S1 |
Therefore, our optimal state assignment is:
State | Assignment |
---|---|
S0 | 000 |
S1 | 110 |
S2 | 001 |
S3 | 100 |
S4 | 011 |
S5 | 101 |
S6 | 010 |