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# 16-FSM - Finite State Machines ECE2030 Introduction to...

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10/22/09 1 1 ECE2030 Introduction to Computer Engineering Lecture 16: Finite State Machines 2 Finite State Machines A finite state machine (FSM) consists of three sets I, O, and S and two functions f and g in which: I is a set of input combinations, O is a set of output combinations, S is a set of states f is the next state function f(I, S), and g is the output function f(S) [Moore model] or the output function f(I, S) [Mealy model]. The FSM is a fundamental mathematical model used for sequential circuits. State diagrams and state tables are two of many ways of representing FSMs. 3 State and State Diagram A state represents the machine snapshot at a given clock period A clock is typically used to synchronize the state transition A graph consists of a set of Circles: Each represents a state Use double circle to represent the initial state Directed arc: each represents a state transition Inputs/outputs Mealy machine: Label input/output along each arc Moore machine: Label input along each arc Label output inside the circle (i.e. state) 4 Mealy and Moore Machines Combinational circuits Inputs X(t) Outputs Z(t) Storage Element S(t) MEALY MACHINE Z(t) = λ {S(t), X(t)} Combinational circuits Inputs X(t) Outputs Z(t) Storage Element S(t) MOORE MACHINE Z(t) = λ {S(t)}

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10/22/09 2 5 State Diagrams Example: State: S(t) {S k , S j } Inputs: X(t) {a, b} Outputs: Z(t) {p, q}
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16-FSM - Finite State Machines ECE2030 Introduction to...

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