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©2004 Brooks/Cole FIGURES FOR CHAPTER 15 REDUCTION OF STATE TABLES STATE ASSIGNMENT Click the mouse to move to the next page. Use the ESC key to exit this chapter. This chapter in the book includes: Objectives Study Guide 15.1Elimination of Redundant States 15.2Equivalent States 15.3Determination of State Equivalence Using an Implication Table 15.4Equivalent Sequential Circuits 15.5Incompletely Specified State Tables 15.6Derivation of Flip-Flop Input Equations 15.7Equivalent State Assignments 15.8Guidelines for State Assignment 15.9Using a One-Hot State Assignment Problems

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©2004 Brooks/Cole Table 15-1: State Table for Sequence Detector

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©2004 Brooks/Cole Table 15-2. State Table for Sequence Detector

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©2004 Brooks/Cole Figure 15-1a: Reduced State Table for Sequence Detector

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©2004 Brooks/Cole Figure 15-1b: Reduced State Graph for Sequence Detector

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©2004 Brooks/Cole Figure 15-2

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©2004 Brooks/Cole Table 15-3.

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©2004 Brooks/Cole Figure 15-3: Implication Chart for Table 15-3

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©2004 Brooks/Cole Figure 15-4: Implication Chart After First Pass

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©2004 Brooks/Cole Figure 15-5: Implication Chart After Second Pass

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©2004 Brooks/Cole Table 15-4.

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©2004 Brooks/Cole Figure 15-6a: Graphs for Equivalent Circuits

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©2004 Brooks/Cole Figure 15-6b: Graphs for Equivalent Circuits

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©2004 Brooks/Cole Figure 15-7: Implication Tables for Determining Circuit Equivalence

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©2004 Brooks/Cole Figure 15-8

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©2004 Brooks/Cole Table 15-5. Incompletely Specified State Table (c)

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©2004 Brooks/Cole Table 15-6. X

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©2004 Brooks/Cole Figure 15-9a: Next- State Maps for Table 15-6

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©2004 Brooks/Cole Figure 15-9b: Next- State Maps for Table 15-6

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©2004 Brooks/Cole Table 15-7.

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©2004 Brooks/Cole Figure 15-10: Next-State Maps for Table 15-7

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©2004 Brooks/Cole Figure 15-11: Derivation of S-R Equations for Table 15-7

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©2004 Brooks/Cole Table 15-8. State Assignments for 3-Row Tables

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©2004 Brooks/Cole Figure 15-12: Equivalent Circuits Obtained by Complementing Q k

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©2004 Brooks/Cole Figure 15-13: Equivalent Circuits Obtained by Complementing Q k

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©2004 Brooks/Cole Table 15-9. A3A3 B3B3 C3C3

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©2004 Brooks/Cole Assignment AAssignment B"Assignment C" J 1 = XQ' 2 J 2 = XQ 1 'K 1 = XQ 2 K 1 = X'K 2 = X'J 1 = X' J 2 = X'Q 1 J 1 = X'Q 2 K 2 = X'Q 1 ' K 2 = X K 1 = X J 2 = X Z = X'Q 1 + XQ 2 Z = X'Q 2 + XQ 1 Z = X'Q 1 ' + XQ 2 D 1 = XQ 2 'D 2 = XQ 1 'D 1 = X' + Q 2 ' D 2 = X'(Q 1 +Q 2 )D 1 = X'(Q 2 + Q 1 )D 2 = X + Q 1 Q 2 Flip-Flop Input Equations

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©2004 Brooks/Cole Table 15-10. Nonequivalent Assignments for 3 and 4 States

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©2004 Brooks/Cole Table 15-11. Number of Distinct (Nonequivalent) State Assignments

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©2004 Brooks/Cole Figure 15-14b

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©2004 Brooks/Cole Figure 15-15a: Next-State Maps for Figure 15-14

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©2004 Brooks/Cole Figure 15-15b: Next-State Maps for Figure 15-14

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©2004 Brooks/Cole Figure 15-16: State Table and Assignments

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©2004 Brooks/Cole Table 15-12. Transition table for Figure 15-16(a)

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©2004 Brooks/Cole Figure 15-17: Next-State and Output Maps for Table 15-12

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©2004 Brooks/Cole Figure 15-18: Partial State Graph

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