11.1 - 1 FINITE STATE MACHINES - II STATE MINIMIZATION...

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Unformatted text preview: 1 FINITE STATE MACHINES - II STATE MINIMIZATION PARTITIONING MINIMIZATION PROCEDURE VENDING MACHINE EXAMPLE ANALYSIS OF SYNCHRONOUS SEQUENTIAL CIRCUITS PROCEDURE EXAMPLE ALGORITHMIC STATE MACHINES (ASM) CHARTS COMPLETE FSM DESIGN EXAMPLE PARALLEL-TO-SERIAL CONVERTER WITH PARITY GENERATOR __________________________________________________ ECSE-323/Department of Electrical and Computer Engineering/McGill University/ Prof. Marin. Figures taken from Fundamentals of Digital Logic with VHDL Design, S. Brown and Z. Vranesic, 2 nd Edition, McGraw Hill. 2 FINITE STATE MACHINES - II STATE MINIMIZATION PARTITIONING MINIMIZATION PROCEDURE DEFINITION: Two states S i and S j are said to be equivalent if and only if for every input sequence , the same output sequence will be produced regardless of whether S i or S j are the initial states. DEFINITION OF 1-SUCCESSOR : If the machine moves from state S i to state S v when input w = 1, then we say that S v is a 1-successor of S i DEFINITION OF 0-SUCCESSOR : If the machine moves from state S j to state S u when input w = 0, then we say that S u is a 0-successor of S i IF STATES S i AND S j ARE EQUIVALENT, THEN THEIR CORRESPONDING K-SUCCESSORS (FOR ALL K) ARE ALSO EQUIVALENT. __________________________________________________ ECSE-323/Department of Electrical and Computer Engineering/McGill University/ Prof. Marin. Figures taken from Fundamentals of Digital Logic with VHDL Design, S. Brown and Z. Vranesic, 2 nd Edition, McGraw Hill. 3 FINITE STATE MACHINES - II STATE MINIMIZATION PARTITIONING MINIMIZATION PROCEDURE (CONTINUES) DEFINITION : A PARTITION CONSISTS OF ONE OR MORE BLOCKS, WHERE EACH BLOCK COMPRISES A SUBSET OF STATES THAT MAY BE EQUIVALENT, BUT THE STATES IN A GIVEN BLOCK ARE DEFINITELY NOT EQUVALENT TO THE STATES IN THE OTHER BLOCK. __________________________________________________ ECSE-323/Department of Electrical and Computer Engineering/McGill University/ Prof. Marin. Figures taken from Fundamentals of Digital Logic with VHDL Design, S. Brown and Z. Vranesic, 2 nd Edition, McGraw Hill. 4 FINITE STATE MACHINES - II STATE MINIMIZATION PARTITIONING MINIMIZATION PROCEDURE (CONTINUES) PROCEDURE: 1) ALL STATES BELONG TO THE INITIAL PARTITION P 1 2) P 1 IS PARTITIONED IN BLOCKS SUCH THAT THE STATES IN EACH BLOCK GENERATE THE SAME OUTPUT....
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11.1 - 1 FINITE STATE MACHINES - II STATE MINIMIZATION...

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