Experiment 7
蔡政翰, Jeng-Han Tsai
jhtsai@ntnu.edu.tw
Department of Applied Electronic Technology
Finite State Machines
Two Types of FSMs
Moore FSM
Inputs
X 0 ,X1,...Xn
Comb.
Logic
Next
State
n
D Flip-flop Q
S+
Comb.
Logic
Outputs
Yk = Fk (S)
clk
n
Present state S
Mealy FSM
Direct combinational path!
Outputs
Inputs
X 0 ,X1,...Xn
Comb.
Logic
n
Comb.
Logic
D Flip-flop Q
S+
clk
n
2
Yk = Fk (S,X 0 ...Xn )
Moore FSM
A sequential circuit
(inputs, current state)  (output, next state)
State Diagram
State Table
3
Moore FSM
D=JQ'+K'Q
A(t  1)  JA  K A
B(t  1)  JB  K B
State equation for A and B:
A(t  1)  BA  ( Bx) A  AB  AB  Ax
B(t  1)  xB  ( A  x)B  Bx  ABx  ABx
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Moore FSM
//Moore model FSM (See Fig.5.19)
module Moore_Model_Fig_5_19 (
output [1:0] y_out,
input
x_in, clock, reset);
reg [1:0]
state;
parameter S0 = 2’b00, S1 = 2’b01,
S2 = 2’b10, S3 = 2’b11;
always @ (posedge clk, negedge reset)
if (reset == 0) state <= S0; // Initialize to state S0
else case (state)
S0: if(~x_in) state <= S1; else state <= S0;
S1: if(x_in) state <= S2; else state <= S3;
S2: if(~x_in) state <= S3; else state <= S2;
S3: if(~x_in) state <= S0; else state <= S3;
endcase
assign y_out = state; // Output of flip-flops
endmodule
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Mealy FSM
A sequential circuit
(inputs, current state)  (output, next state)
State Diagram
State Table
6
Mealy FSM
State equations
A(t+1) = A(t)x(t) + B(t)x(t)
B(t+1) = A'(t)x(t)
The output equation
y(t) = (A(t)+B(t))x'(t)
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Mealy FSM
//Mealy FSM zero detector (See Fig.5.16)
module Mealy_Zero_Detector(
output reg y_out,
input
x_in, clock, reset);
reg [1:0] state, next_state;
parameter S0 = 2’b00, S1 = 2’b01,
S2 = 2’b10, S3 = 2’b11;
always @ (posedge clk, negedge reset)
if (reset == 0) state <= S0;
else
state <= next_state;
always @ (state, x_in) // Form the next state
case (state)
S0: if(x_in) next_state = S1; else next_state = S0;
S1: if(x_in) next_state = S3; else next_state = S0;
S2: if(~x_in) next_state = S0; else next_state = S2;
S3: if(x_in) next_state = S2; else next_state = S0;
endcase
always @ (state, x_in) // Form the output
case (state)
S0:
y_out = 0;
S1, S2, S3: y_out = ~x_in;
endcase
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endmodule
Example
Level-to-Pulse
A level-to-pulse converter produces a single-cycle pulse each time its input goes high
it’s a synchronous rising edge detector
L
Whenever input L
goes from low to high
Level to
pulse
converter
P
… output P produces a single
pulse, one clock period wide
clk
State Transition Diagrams
is a useful FSM representation and design aid
“if L=1 at the clock edge,
then jump to state 01”
L=1
L=0
00
Low input,
Waiting for rise
P=0
L=1
01
Edge detected
P=1
L=0
“if L=0 at the clock edge,
then stay in state 00”
L=0
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Binary values states
11
11
High input,
Waiting for fall
P=0
P=0
L=1
This is the output that results
from this state.
(Moore or Mealy)
Example
Logic Derivation for a Moore FSM
converted to a state transition table
L=1
00
Low input,
Waiting for rise
P=0
L=0
L=1
01
Edge detected
P=1
L=0
11
High input,
Waiting for fall
P=0
L=1
L=0
Current
state
S0
S1
0
0
0
0
1
0
1
0
1
1
1
1
Combinational logic may be derived by Karnaugh maps
S1 S 0
L
0
1
S1 S 0
L
0
1
S1
for S 1
00 01 11 10
0 0 0 X
0 1 1 X
for
S 0
00 01 11 10
0 0 0 X
1 1 1 X
L
Next
n
State
D Flip-flop Q
S
Comb.
Logic
0
L
0
1
0
1
0
1
fo r
Present state S
P
10
P
S0
0
0
1
0
X
1
1
0
Comb.
Logic
cl
k
S1  LS0
S + L
n
Next
state
S 0
S1
0
0
1
0
0
0
1
1
0
0
1
1
In
P  S1S0
P
Out
P
0
0
1
1
0
0
Example
Moore Level-to-Pulse Converter
S1  LS0
S0  L
L
P  S 1S 0
S0
D
clk

1
Q
S0
Q
D
Q
S
Q
11
S1
P
Mealy Level-to-Pulse Converter
Since outputs are determined by state and inputs, Mealy FSMs may need fewer
states than Moore FSM implementations
When L = 1 and S = 0, output P is
asserted immediately and until the
state transition occurs (or L changes)
Output transitions
immediately.
State transitions at the
clock edge.
1
L
2
P
Clock
State
L=1/ P=1
0
Input is low
L=0/P=0
1
Input is high
After the transition to S = 1 and as long
as L remains at 1, output P is asserted
L=1/ P=0
L=0/ P=0
Pres. State
In
Next State
Out
S
L
S
P
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
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Mealy Level-to-Pulse Converter
Mealy FSM circuit implementation
P
S
L
CLK
D
Q
Q
S
FSM’s state simply remembers the previous value of L
Circuit benefits from the Mealy FSM’s implicit single-cycle assertion of outputs during state
transitions
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Trade-Offs between Moore/Mealy
Differences
Moore outputs are based on state only
Mealy outputs are based on state and input
Mealy outputs generally occur one cycle earlier than a Moore
L
L
P
P
Clock
Clock
State[0]
State
Compared to a Moore FSM, a Mealy FSM might...
Be more difficult to conceptualize and design
Have fewer states
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Practice
Department of Applied Electronic Technology
Practice 1
Please think about level-to-pulse converter, and give a reason why the number of the states
cannot be reduced to two states in Moore FSM. (回答於實驗報告內)
請完成Page11與Page13兩種型態的Verilog語法，不限撰寫層次；
並以波形模擬、DE2實驗板驗證
DE2 Board Pin:
Input: L (SW0)
Output: P (LEDR0) , State (HEX0)
參考投影片中的準位脈衝轉換電路，試設計另一形態之脈衝轉換電路，波形如下：
Moore或Mealy FSM擇一。
波形模擬、DE2實驗板驗證。
DE2 Board Pin:
Input: L (SW0)
Output: P (LEDR0) , State (HEX0)
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The END
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