Unformatted text preview: Table 15-10. Nonequivalent Assignments
for 3 and 4 States Table 15-11. Number of Distinct (Nonequivalent)
State Assignments Guidelines for State Assignment
Trying all nonequivalent state assignments is not practical.
The following guidelines will tend to place 1s together on
the next-state maps: 1. States which have the same next state for a given input should be given
2. States which are the next states of the same state should be given
3. States which have the same output for a given input should be given
adjacent assignments. Section 15.8 (p. 490) By guidelines, sets of
adjacent states are
● (S0,S1,S3,S5), (S3,S5),
● (S1,S2), (S2,S3), (S1,
S4), (S2,S5)x2, (S1,S6)
E.g., by Guideline 1, S0, S2, S4, S6 should be
adjacent because all have S1 as next state on input 0
E.g., by Guideline 2, S1 and S2 should be given adjacent
assignments (both are next states of S0). Figure 15-15a: Next-State Maps for Figure 15-14 Adjacencies by Guidelines:
1. (b, d) (c, f) (b, e)
2. (a, c)2x (d, f) (b, d) (b, f) (c, e)
Figure 15-15b: Next-State Maps for Figure 15-14 3. (a, c) (b, d) (e, f)
Figure 15-16: State Table and Assignments Table 15-12. Transition table for Figure 15-16(a) Figure 15-17: Next-State and Output Maps for Table 15-12 Using a One-Hot State Assignment
Sometimes reducing flip-flops is not as important as
reducing logic feeding into the flip-flops.
The one-hot assignment uses one flip-flop for each state,
so a state machine with N states requires N flip-flops.
Exactly one of the flip-flops is set to one in each state.
By simple inspection of the
Q3+ = X1Q0 + X2Q1 + X3Q2 +
Z2 = X2Q1 + X4Q3 Section 15.9 (p. 495)
Figure 15-18: Partial State Graph Equations derived by inspection of Figure 15-19:
Q0+ = Q0St′ + Q3
Q1+ = Q0St + Q1K′M′ + Q2K′
Sh = Q1(K′M′ + KM′) + Q2(K′ + K) = Q1M′ + Q2 Figure 15-19: Multiplier Control State Graph...
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This document was uploaded on 03/16/2014 for the course EE 316 at University of Texas.
- Spring '08