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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 State Machine Design
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 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-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 Machine: An FSM whose outputs are determined by both the sequential logic and combinational logic of the FSM
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 • 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.
State Machine Example 2. Draw a State Diagram
State Machine Example 3. Make a State Table
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 Example 5. Simply the Boolean expression for each synchronous input
State Machine Example 6. Draw the logic circuit for the state machine
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.
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 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 • 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.
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 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.
