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Introduction to Sequential Logic Design

Introduction to Sequential Logic Design. Finite State-Machine Analysis. Prev…. Flip Flops D FFs T FFs J-K FFs. Clocked Synchronous State-Machine. State machine : generic name for sequential circuits; (Finite State Machine: FSM ) Clocked : the storage elements (FFs) use a clock input;

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Introduction to Sequential Logic Design

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  1. Introduction to Sequential Logic Design Finite State-Machine Analysis

  2. Prev… • Flip Flops • D FFs • T FFs • J-K FFs

  3. Clocked Synchronous State-Machine • State machine: generic name for sequential circuits; (Finite State Machine: FSM) • Clocked: the storage elements (FFs) use a clock input; • Synchronous: all of the FFs in a circuit use the same clock signal. Such a FSM changes states only when a triggering edge (rising or falling) on the clock signal.

  4. State Machine Structure • State memory: n FFs to store current states. All FFs are connected to a common clock signal. • Next-state logic: determine the next state when state changes occur; • Output logic: determines the output as a function of current state and input • Mealy machine vs. Moore machine

  5. Mealy Machine Next state= F (current state, input) Output= G (current state, input)

  6. Moore Machine Next state= F (current state, input) Output= G (current state)

  7. Characteristic Equations • A Characteristic equation specifies the FF’s (or latch’s) next state as a function of its current state and inputs.

  8. Analysis of FSM with D FFs Next state= F (current state, input) Output= G (current state, input) Step 1: Determine the next-state and output functions F, G Step 2: Use F, G to construct a state/output table that completely specifies the next state and output of the circuit for every possible combination of current state and input. Step 3: (optional) Draw a state diagram which is a graphical form of the state/output table.

  9. Example: clocked synchronous FSM using positive-edge triggered D FFs

  10. Transition, state, state/output tables Excitation equations Transition Equations (next-state equations) Output equations

  11. State Diagram

  12. Summary: how to analyze a clocked synchronous state machine? • Determine the excitation equations for the FF control inputs; • Substitute the excitation equations into the FF characteristic equations to obtain transition equations; • Use the transition equations to construct a transition table; • Determine the output equations; • Add output values to the transition table for each state (Moore) or state/input combination (Mealy) to create a transition/output table; • Name the states and substitute state names for state-variable combinations in the transition/output table to obtain state/output table; • Draw a sate diagram corresponding to the state/output table.

  13. Another Example Excitation Eq Tran. Eq Tran.Table Output Eq Tran/out Table State/out Table State Dagram

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