ECE 375: Digital Design II

Class 9

State 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