lect10 state minimization

lect10 state minimization - CSE140: Components and Design...

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1 1 Sources: TSR, Katz, Boriello, Vahid, Perkowski CSE140: Components and Design Techniques for Digital Systems Tajana Simunic Rosing 2 Sources: TSR, Katz, Boriello, Vahid, Perkowski Announcements HW#5 due, HW#6 assigned – due on MONDAY!!!! Midterm on Tuesday, 11/7 at class time – Everything up to and including chap 8, app. A,B,C Today: – FSM optimization • State minimization using Implicant method • State assignment • FSM partitioning
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2 Sources: TSR, Katz, Boriello, Vahid, Perkowski State tables State minimization State assignment Combinational logic optimization netlist identify and remove equivalent states assign unique binary code to each state use unassigned state-codes as don’t care FSM Optimization Flow Chart 4 Sources: TSR, Katz, Boriello, Vahid, Perkowski Successive partitioning algorithm for state minimization Goal – identify and combine states that have equivalent behavior Algorithm sketch 1. place all states in one set 2. initially partition set based on the output behavior 3. successively partition the resulting subsets based on next state transitions 4. repeat (3) until no further partitioning is possible states left in the same set are equivalent Polynomial time procedure
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3 5 Sources: TSR, Katz, Boriello, Vahid, Perkowski Input Next State Output Sequence Present State X=0 X=1 X=0 X=1 R e s e t S 0 S 1S 20 0 0 S 1 S 3S 40 0 1 S 2 S 5S 60 0 00 S3 S0 S0 0 0 01 S4 S0 S0 1 0 10 S5 S0 S0 0 0 11 S6 S0 S0 1 0 Method of successive partitions 6 Sources: TSR, Katz, Boriello, Vahid, Perkowski Minimized FSM Input Next State Output Sequence Present State X=0 X=1 X=0 X=1 R e s e t S 0 S 0 0 S 1 S 0 1 S 2 S 0 00 S3 S0 S0 0 0 01 S4 S0 S0 1 0 10 S5 S0 S0 0 0 11 S6 S0 S0 1 0 ( S0 ) ( S1 S2 ) ( S3 S5 ) ( S4 S6 )
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4 7 Sources: TSR, Katz, Boriello, Vahid, Perkowski Implication chart method: Basic Concepts 1 0 0 3 2 3 6 1 2 5 1 0 0 5 1 6 4 1 0 6 6 3 0 4 2 1 1 1 2 4 3 1 d c b a d c b a x S Compatiblity: Si, Sj are compatible if for each input they have consistent outputs, and their successors are the same or compatible. Conditionally compatible : S i , S j are conditionally compatible if their outputs and next states are consistent for some pairs of successors (S i , S j ) (S k , S l ) 8 Sources: TSR, Katz, Boriello, Vahid, Perkowski Implication chart method: Triangular table definition 4 3 2 1 5 4 3 2 We fill the cells of triangular table as follows: v – if pair of states is compatible, v x – if pair of states in incompatible, x (i,j) – pair (pair of successors), if the pair is conditionally compatible.
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This note was uploaded on 02/14/2008 for the course CSE 140 taught by Professor Rosing during the Fall '06 term at UCSD.

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lect10 state minimization - CSE140: Components and Design...

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