Chapter 15 - State Minimization-2x2(1)

Nonequivalent assignments for 3 and 4 states table 15

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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 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 15-14b 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 graph: Q3+ = X1Q0 + X2Q1 + X3Q2 + X4Q3 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.

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