L13 - Machine Minimization ECE 152A Fall 2006 Reading...

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1 Machine Minimization ECE 152A – Fall 2006 November 30, 2006 ECE 152A - Digital Design Principles 2 Reading Assignment ± Brown and Vranesic ² 8 Synchronous Sequential Circuits ± 8.6 State Minimization ² 8.6.1 Partitioning Minimization Procedure ² 8.6.2 Incompletely Specified FSMs
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2 November 30, 2006 ECE 152A - Digital Design Principles 3 Reading Assignment ± Roth ² 15 Reduction of State Tables / State Assignment ± 15.1 Elimination of Redundant States ± 15.2 Equivalent States ± 15.3 Determination of State Equivalence Using an Implication Table ± 15.4 Equivalent Sequential Circuits ± 15.5 Incompletely Specified State Tables November 30, 2006 ECE 152A - Digital Design Principles 4 Elimination of Redundant States ± Row Matching ² Recall CD player controller ± Mealy implementation contained two sets of rows with same next state and output ± Eliminate redundant states ± Row matching doesn’t identify “equivalent states” ² Row matching identifies “same state” ² Equivalent states are the more general case
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3 November 30, 2006 ECE 152A - Digital Design Principles 5 Equivalent States ± Definitions of equivalent states ² Roth : 2 states equivalent iff for every single input x, outputs are the same and next states are equivalent (as opposed to row matching) ± Pairwise comparison using implication table ² Kohavi : Iff for every possible input sequence the same output sequence will be produced regardless of whether S i or S j is the initial state ± Moore reduction procedure to find equivalence partition November 30, 2006 ECE 152A - Digital Design Principles 6 Determination of State Equivalence using an Implication Table ± Find Equivalent Pairs 1 G C H 0 H B G 1 B F F 1 A C E 0 E A D 1 D E C 0 H F B 0 C D A z x=1 x=0 PS NS
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4 November 30, 2006 ECE 152A - Digital Design Principles 7 Determination of State Equivalence using an Implication Table (1) Construct Implication Table for Pairwise Comparison (2) First Pass ± Compare outputs ² For states to be equivalent, next state and output must be the same ² Put “X’s” where outputs differ November 30, 2006 ECE 152A - Digital Design Principles 8 Implication Table (first pass) B C D E F G H ABCDEFG XX X X X X X X 1 G C H 0 H B G 1 B F F 1 A C E 0 E A D 1 D E C 0 H F B 0 C D A z x=1 x=0 PS NS
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5 November 30, 2006 ECE 152A - Digital Design Principles 9 Determination of State Equivalence using an Implication Table (3) One column (or row) at a time, find implied pairs November 30, 2006 ECE 152A - Digital Design Principles 10 Implication Table (second pass) B C D E F G H ABCDEFG D-F C-H X A-D C-E B-D C-H A-F E-H B-F H-H C-E A-D E-F B-D C-E D-G A-B E-H C-F A-B C-C A-G C-F B-G X X XX X X X X X 1 G C H 0 H B G 1 B F F 1 A C E 0 E A D 1 D E C 0 H F B 0 C D A z x=1 x=0 PS NS
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6 November 30, 2006 ECE 152A - Digital Design Principles 11 Determination of State Equivalence using an Implication Table (3) One column (or row) at a time, find implied pairs (cont) ± Remove self implied pairs ² A-D in cell A-D ² C-E in cell C-E ±
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This note was uploaded on 02/19/2012 for the course ENGR 361 taught by Professor Drexel during the Spring '12 term at Bloomsburg.

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L13 - Machine Minimization ECE 152A Fall 2006 Reading...

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