LEC-11 - 11 Finite State Machines I 3/22/2010 Finite State...

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11 Finite State Machines I 3/22/2010 © Copyright Kenneth Short 2003, 2006 1 3/22/2010 © Copyright Kenneth Short 2003, 2006 1 Finite State Machines Kenneth Short 3/22/2010 © Copyright Kenneth Short 2003, 2006 2 Finite State Machine ± A sequential machine, also known as a finite state machine (FSM), is a digital system whose outputs are a function of both its present and past inputs ± A synchronous FSM’s inputs are examined and its outputs change at the triggering edge of its clock ± Accordingly, its input and output sequences are ordered in time by its clock ± A FSM’s present state provides all the information concerning its past history of input values that is needed is to determine its next state and output ± The present state is stored as a binary value in a state register
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11 Finite State Machines I 3/22/2010 © Copyright Kenneth Short 2003, 2006 2 3/22/2010 © Copyright Kenneth Short 2003, 2006 3 FSM Block Diagram Combinational logic Register Inputs Outputs next_state present_state clock 3/22/2010 © Copyright Kenneth Short 2003, 2006 4 Present State – Next State ± A FSM’s outputs are computed by a combinational logic subcircuit from its external inputs and present state. ± Combinational logic computes the next state from the FSM’s inputs and present state ± The next state is the value clocked into the state register at the next triggering clock edge
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11 Finite State Machines I 3/22/2010 © Copyright Kenneth Short 2003, 2006 3 3/22/2010 © Copyright Kenneth Short 2003, 2006 5 Separation of Output and Next State Combinational Logic Combinational Next State Logic Register Inputs Outputs next_state present_state clock Combinational Output Logic 3/22/2010 © Copyright Kenneth Short 2003, 2006 6 Synchronous FSM Operation state 0 state 2 state 1 input a input b input c state 2 state 1 state 3 inputs present state next state clock output q output p output r output
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11 Finite State Machines I 3/22/2010 © Copyright Kenneth Short 2003, 2006 4 3/22/2010 © Copyright Kenneth Short 2003, 2006 7 Mealy and Moore FSMs ± FSMs can be classified as Mealy or Moore machines. These two kinds of FSMs differ in how their outputs are computed ± A Mealy machine’s outputs are a function of both its inputs and present state. The outputs of a Mealy machine can change as soon as any input changes ± A Moore machine’s outputs are a function of its present state only. A Moore machine’s outputs can change only on a triggering clock edge ± The block diagram for the Mealy FSM can be modified to represent a Moore FSM by removing the external inputs from the output combinational circuit 3/22/2010 © Copyright Kenneth Short 2003, 2006 8 Moore FSM Block Diagram Combinational Next State Logic Register Inputs Outputs next_state present_state clock Combinational Output Logic
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11 Finite State Machines I 3/22/2010 © Copyright Kenneth Short 2003, 2006 5 3/22/2010 © Copyright Kenneth Short 2003, 2006 9 Mealy State Diagram ± A Mealy FSM state diagram has each directed arc labeled with
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LEC-11 - 11 Finite State Machines I 3/22/2010 Finite State...

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