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ENGR 2720 Chapter 10. State Machine Design. State Machine Definitions. State Machine: A synchronous sequential circuit consisting of a sequential logic section and a combinational logic section.

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ENGR 2720 Chapter 10

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Engr 2720 chapter 10

ENGR 2720 Chapter 10

State Machine Design

State machine definitions

State Machine Definitions

  • State Machine: A synchronous sequential circuit consisting of a sequential logic section and a combinational logic section.

  • The outputs and internal flip flops (FF) progress through a predictable sequence of states in response to a clock and other control inputs.

State machine basics

State Machine Basics

  • State Variable: The variable held in the SM (FF) that determines its present state.

  • A basic Finite State Machine(FSM) has a memory section that holds the present state of the machine (stored in FF) and a control section that controls the next state of the machine (by clocks, inputs, and present state).

Moore machine a fsm whose outputs are determined only by the sequential logic ff of the fsm

Moore-Type State Machine

Moore Machine: A FSM whose outputs are determined only by the Sequential Logic (FF) of the FSM.

Mealy type state machine

Mealy-Type State Machine

Mealy Machine: An FSM whose outputs are determined by both the sequential logic and combinational logic of the FSM

Classical design approach moore type

Classical Design Approach(Moore-Type)

  • Define the actual problem.

  • Draw a state diagram (bubble) to implement the problem.

  • Make a state table. Define all present states and inputs in a binary sequence. Then define the next states and outputs from the state diagram.

  • Use FF excitation tables to determine in what states the FF inputs must be to cause a present state to next state transition.

  • Find the output values for each present state/input combination.

  • Simplify Boolean logic for each FF input and output equations and design logic.

Moore state machine example

Moore State Machine Example

  • Define the problem: Design a counter whose output progress is a 4-bit Gray code sequence. A Gray Code is a binary code that progresses such that only one bit changes between two successive codes.

How to build a 4 bit gray code table

How to build a 4-bit Gray Code Table

4 bit gray code table

4-bit Gray Code Table

State machine example

State Machine Example

2.Draw a State Diagram

State machine example1

State Machine Example

3. Make a State Table

State machine example2

State Machine Example

  • Use Flip-flop excitation tables to determine at what state the flip-flop synchronous input must be to make the circuit go from each state to its next state.

    • This is not necessary if we use “D flip-flops”,

      since output Q follows input D. The D inputs are the same as next state outputs.

    • For JK or T flip-flops, we would follow the same procedure as for a synchronous counters as outlined in Chapter 9

State machine example3

State Machine Example

5. Simply the Boolean expression for each synchronous input

State machine example4

State Machine Example

6. Draw the logic circuit for the state machine

Fsm with control inputs mealy type

FSM with Control Inputs(Mealy-Type)

  • Same design approach used for FSM such as counters.

  • Uses the control inputs and clock to control the sequencing from state to state.

  • Inputs can also cause output changes not just FF outputs.

Engr 2720 chapter 10

FSM with Control Inputs

Sm diagram notation

SM Diagram Notation

  • Bubbles contain the state name and value

    (State Name/Value), such as Start/0.

  • Transitions between states are designated with arrows from one bubble to another.

  • Each transition has an ordered Input/Output, such as in1/out1, out2.

Sm diagram notation1

SM Diagram Notation

  • For example, if SM is at State = Start and if in1 = 0,

    it then transitions to State = Continue and out1 = 1, out2 = 0.

  • The arrow is drawn from start bubble to continue bubble.

  • On the arrow the value 0/10 is given to represent the in1/out1,out2.

Analyzing the state diagram

Analyzing the State Diagram

  • There are two sates called start and continue.

  • The machine begins in the start state waits for a Low in1. As long as in1 is High, the machine waits and out1 and out2 are both Low.

  • When in1 goes Low, the machine makes a transition to continue in one clock pulse. Output out1 goes High.

  • On the next clock pulse, the machine goes back to start. Output out2 goes High and out1 goes back Low.

  • If in1 is High, the machine waits for a new Low on in1. Both outs are Low again. If in1 goes Low. The cycle repeats.

Sm design

SM Design

Sm design1

SM Design

Sm design2

SM Design

Sm design3

SM Design

Sm design4

SM Design

Sm design5

SM Design

Unused states

Unused States

  • Some modulus counters, such as MOD-10, have states that are not used in the counter sequence.

  • The MOD-10 Counter would have 6 unused states (1010, 1011….1111) based on 4-bits.

Unused states1

Unused States

  • An FSM can also have unused states, such as an SM, with only 5 bubbles in the state diagram (5-states). This FSM still requires 3 bits to represent these states so there will be 3 unused states.

  • These unused states can be treated as don’t cares (X) or assigned to a specific initial state.

Engr 2720 chapter 10

Unused States

State diagram

State Diagram

State table

State Table

State table1

State Table

State table2

State Table

State table3

State Table

State table4

State Table

State table5

State Table

State table6

State Table

State table7

State Table

State table8

State Table

State table9

State Table

State table10

State Table

State table11

State Table

State table12

State Table

State table13

State Table

K maps


Simplified equations

Simplified Equations

Engr 2720 chapter 10


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