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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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chapter 10

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 types
State Machine Types
  • Moore Machine: A Finite State Machine (FSM) whose outputs are determined only by the Sequential Logic (FF) of the FSM.
  • Mealy Machine: An FSM whose outputs are determined by both the sequential logic and combinational logic of the FSM.
state machine basics
State Machine Basics
  • State Variable: The variable held in the SM (FF) that determines its present state.
  • A basic 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).
fsm design techniques
FSM Design Techniques
  • Classical Design: Makes use of state tables, FF excitation tables, and Karnaugh Mapping to find FF input control logic.
  • VHDL Design: Uses case statements or IF THEN ELSE statements to set the design and the logic synthesis tools to define equations.
classical design approach 1
Classical Design Approach – 1
  • 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.
classical design approach 2
Classical Design Approach – 2
  • 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.
fsm design example 1
FSM Design Example 1
  • Gray Code Counter that sequences {000, 001, 011, 010, 110, 111, 101, 100, 000}.
  • From this the state and excitation table is developed for D flip flops (see Table 10.2 in the textbook).
fsm design example 2
FSM Design Example 2
  • From the K-Maps for the inputs D0, D1, and D2, the following equations are developed:
  • Refer to Figure 10.6 in the textbook.
vhdl fsm design
  • Uses an enumerated type to declare state variables.
  • Enumerated Type: A user-defined type in which all possible values of a named identifier are listed in a type definition.
  • An FSM uses a CASE statement on the enumerated type state variable.
fsm vhdl example
FSM VHDL Example

-- gray_ct1.vhd

-- 3-bit Gray code counter

-- (state machine with decoded outputs)


USE ieee.std_logic_1164.ALL;

fsm vhdl entity

ENTITY gray_ct1 IS



q : OUT STD_LOGIC_VECTOR(2 downto 0));

END gray_ct1;

fsm vhdl architecture 1
FSM VHDL Architecture – 1


TYPE STATE_TYPE IS (s0,s1,s2,s3,s4,s5,s6,s7);





fsm vhdl architecture 2
FSM VHDL Architecture – 2

IF (clk’EVENT AND clk = ‘1’) THEN

CASE state IS

WHEN s0 => state <= s1;

WHEN s1 => state <= s2;

WHEN s2 => state <= s3;

WHEN s3 => state <= s4;

WHEN s4 => state <= s5;

fsm vhdl architecture 3
FSM VHDL Architecture – 3

WHEN s5 => state <= s6;

WHEN s6 => state <= s7;

WHEN s7 => state <= s0;




fsm vhdl architecture 4
FSM VHDL Architecture – 4


q <= “000” WHEN s0,

“001” WHEN s1,

“011” WHEN s2

“010” WHEN s3,

“110” WHEN s4,

“111” WHEN s5,

“101” WHEN s6,

“100” WHEN s7;

END a;

vhdl output assignment
VHDL Output Assignment
  • The output assignment for the following example could have also been in the CASE test statements (in the process).

WHEN s0 => state <= s1;

q <= “001”;

WHEN s1 => state <= s2;

q <= “011”;

fsm with control inputs
FSM with Control Inputs
  • 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 1
SM Diagram Notation – 1
  • Bubbles contain the state name and value (StateName/Value), such as Start/000.
  • Transitions between states are designated with arrows from one bubble to another.
  • Each transition has an ordered Input/Output, such as in1/out1.
sm diagram notation 2
SM Diagram Notation – 2
  • 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/out2,out1.
sm design 1
SM Design – 1
  • State Table for the State Diagram
sm design 2
SM Design – 2
  • The State Excitation Tables for the JK Inputs
sm design 3
SM Design – 3
  • The following equation represents the next state and output logic of the state machine.
sm design 4
SM Design – 4
  • The pulser SM has two outputs that are not always synchronized to clock.
  • The pulse out2 is always synched to a change in clock, but out1 could change if in1 changes.
  • The following slides show a VHDL implementation of the Pulser SM.
sm pulser architecture 1
SM Pulser Architecture – 1
  • Uses an enumerated type state listing of start and continue.


TYPE PULSER IS (start, continue);

SIGNAL sequence : PULSER;




sm pulser architecture 2
SM Pulser Architecture – 2
  • A portion of the case statement:

IF(clk’EVENT AND clk = ‘1’) THEN

CASE sequence IS

WHEN start =>

IF in1 = ‘1’ THEN

sequence <= start;

out1 <= ‘0’;

out2 <= ‘0’;

sm pulser architecture 3
SM Pulser Architecture – 3
  • In the VHDL case statement, an IF conditional test statement was used to check the Input Signal (in1) for State = Start.
  • IF in1 = 1, stay at State = Start; IF in1 = 0, then move to State = Continue (next clk).
  • If the present state was continue, the next state is always start, so an IF statement is not required.
switch debouncer
Switch Debouncer
  • A digital circuit that is used to remove the mechanical “bounce” from a switch contact.
  • When a switch is closed, the contacts bounce from open to closed to cause false transitions.
  • A simple debouncer is a cross-coupled NAND Latch.
shift register debouncer 1
Shift Register Debouncer – 1
  • An SR can be used to delay the glitches (bounces) with a slow clock (T = 2.6 ms).
  • The input of the SR is from the switch, and it is clocked through a 4-bit register.
  • The output of the SR is compared to the input, and if it is equal, the SR is still loaded.
shift register debouncer 2
Shift Register Debouncer – 2
  • When the switch bounces, the SR input and output are not equal, so the register stops loading to allow the delay to be added.
  • The comparison is done by an XNOR gate to control the SR Load.
shift register debouncer 3
Shift Register Debouncer – 3
  • 4-bit LPM SR clocked every 2.6 ms
  • If pb_in pb_out for 10.4 ms, the output changes.
  • If not, then the output remains the same.
  • Change on the input must be stable for 4 clock cycles before the output changes.
sr debounce entity
SR Debounce Entity
  • Uses an in from SW (pb_in) and a debounced output (pb_out).

ENTITY debouncer IS


pb_in, clock : IN STD_LOGIC;

pb_out : OUT STD_LOGIC);

END debouncer;

sr debounce architecture 1
SR Debounce Architecture – 1

ARCHITECTURE debounce OF debouncer IS

SIGNAL ctr_q :STD_LOGIC_VECTOR (15 downto 0);

SIGNAL srg_parallel_in :STD_LOGIC_VECTOR (3 downto 0);

SIGNAL srg_serial_in :STD_LOGIC;

SIGNAL srg_serila_out :STD_LOGIC;


sr debounce architecture 2
SR Debounce Architecture – 2


clock_divider : lpm_counter


PORT MAP (clock => clock, q => ctr_q);

sr debounce architecture 3
SR Debounce Architecture – 3

-- shift register clocked by MSB of counter 216

delay_ element : lpm_shiftreg


PORT MAP (clock => ctr_q (15),

load => srg_load,

data => srg_parallel_in,

shiftin => srg_serial_in,

shiftout => srg_serial_out);

sr debounce architecture 4
SR Debounce Architecture – 4

srg_load <= (not pb_in) xnor srg_serial_out;

srg_parallel_in (3) <= srg_serial_out;

srg_parallel_in (2) <= srg_serial_out;

srg_parallel_in (1) <= srg_serial_out;

srg_parallel_in (0) <= srg_serial_out;

srg_serial_in <= not pb_in;

pb_out <= srg_serial_out;

END debounce;

unused states 1
Unused States – 1
  • 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 2
Unused States – 2
  • 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.
unused states example slide 1
Unused States Example Slide – 1
  • A five-variable state diagram is shown in the previous slide, with unused states assigned to the initial state = Start.
  • The normal state sequence is StartWait1  Wait2  Pulse1  Pulse2 and then back to Start.
  • Any other states cause a transition back to Start.
unused states example slide 2
Unused States Example Slide – 2
  • The Input (in1) Sequence of 101 causes the machine to advance from StartWait1  Wait2. Then it does two unconditional transitions to Pulse1 and Pulse2.
  • The Pulse1 and Pulse2 States generate two pulses on the Outputs (out1 and out2).
unused states example slide 3
Unused States Example Slide – 3
  • Any unused states are given the value of Start (000) for its next state.
  • For the FSM 3-Bit Register (FF), this generates the equations shown on the next slide.
traffic light fsm 1
Traffic Light FSM – 1
  • The FSM controls are for a North-South Road and an East-West road (see Figure 10.38 in textbook).
  • This generates 3 Outputs for each road (nsr, nsy, nsg, and ewr, ewy, ewg) for the Red, Yellow, and Green Lights (Low = ON).
traffic light fsm 2
Traffic Light FSM – 2
  • An Input called TIMER controls the length of a light cycle (TIMER = 1 causes a S0 to S1 or a S2 to S3 transition).
  • When one light is green (S0(EW) or S2(NS)), the other is red.
traffic light fsm 3
Traffic Light FSM – 3
  • There is an unconditional timed transfer from yellow to red or red to green.
  • A normal cycle is 4 clocks GREEN, 1 clock YELLOW, 5 clocks RED.
  • Solution is left as an example problem.