Unformatted text preview: Table 1510. Nonequivalent Assignments
for 3 and 4 States Table 1511. 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 nextstate maps: 1. States which have the same next state for a given input should be given
adjacent assignments.
2. States which are the next states of the same state should be given
adjacent assignments.
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),
(S4,S6), (S0,S2,S4S6)
● (S1,S2), (S2,S3), (S1,
S4), (S2,S5)x2, (S1,S6)
x2
Figure 1514b
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 1515a: NextState Maps for Figure 1514 Adjacencies by Guidelines:
1. (b, d) (c, f) (b, e)
2. (a, c)2x (d, f) (b, d) (b, f) (c, e)
Figure 1515b: NextState Maps for Figure 1514 3. (a, c) (b, d) (e, f)
Figure 1516: State Table and Assignments Table 1512. Transition table for Figure 1516(a) Figure 1517: NextState and Output Maps for Table 1512 Using a OneHot State Assignment
Sometimes reducing flipflops is not as important as
reducing logic feeding into the flipflops.
The onehot assignment uses one flipflop for each state,
so a state machine with N states requires N flipflops.
Exactly one of the flipflops is set to one in each state.
By simple inspection of the
graph:
Q3+ = X1Q0 + X2Q1 + X3Q2 +
X4Q3
Z2 = X2Q1 + X4Q3 Section 15.9 (p. 495)
Figure 1518: Partial State Graph Equations derived by inspection of Figure 1519:
Q0+ = Q0St′ + Q3
Q1+ = Q0St + Q1K′M′ + Q2K′
Sh = Q1(K′M′ + KM′) + Q2(K′ + K) = Q1M′ + Q2 Figure 1519: 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
 Brown

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