Idea Transcript
CSE140 L Instructor: Thomas Y. P. Lee
February 15, 2006
Agenda z
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Lab3 Counters are FSM Finite State Machine Models to represent FSM – Mealy Machine and Moore Machine FSM Design Procedure State Diagram State Transition Table Next State Logic Functions Example One – Vending Machine Mealy Machine Implementation Moore Machine Implementation Quartus II Tutorial – Finite State Machine Implementation Improved Vending Machine z Moore Machine Implementation Mealy Machine Implementation
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Acknowledgement z z
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Materials in this lecture are courtesy of the following people Randy H. Katz (University of California, Berkeley, Department of Electrical Engineering &Computer Science) MIT Prof. Anantha Chandrakasan and Donald E. Troxel “Introduction to Digital System Design Lab” Professor C.K.Cheng, CSE140L John F. Wakerly, Digital Design, “Principles and Practices”, 3rd edition
Counters are FSM z
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Counters z proceed through well-defined sequence of states in response to enable Many types of counters: binary Up/Down, BCD, Gray-code,Divide-by3,… z 3-bit up-counter: 000, 001, 010, 011, 100, 101, 110, 111, 000, ... z 3-bit down-counter: 111, 110, 101, 100, 011, 010, 001, 000, 111, ... 001
000
010
011
100
3-bit up-counter
111
110
101
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Finite State Machine z
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Finite State Machines (FSMs) are a useful abstraction for sequential circuits with “states” of operation At each clock edge, combinational logic block computes outputs and next state as a function of inputs and present state
Two Types of FSM - Mealy and Moore
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Pipelined State Machine
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Often used in PLD-based state machines. Outputs taken directly from flip-flops, valid sooner after clock edge. But the “output logic” must determine output value one clock tick sooner (“pipelined”).
Comparison of Mealy and Moore Machine z
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Mealy machines tend to have less states z different outputs on arcs (n2) rather than states (n) Moore machines are safer to use z outputs change at clock edge (always one cycle later) z In Mealy machines, input change can cause output change as soon as logic is done – a big problem when two machines are interconnected – asynchronous feedback may occur if one isn’t careful Mealy machines react faster to inputs z react in same cycle – don't need to wait for clock z in Moore machines, more logic may be necessary to decode state into outputs – more gate delays after clock edge
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State Machine Analysis Steps z z z
Assumption: Starting point is a logic diagram. 1. Determine next-state function and output function 2. Construct state (transition) table For each state/input combination, determine the excitation value.Using the characteristic equation, determine the corresponding next-state values (trivial with DFF’s)
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3. Construct output table For each state/input combination, determine the output value (Can be combined with state table.)
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4. Draw state diagram
Example in Katz’s Book: Vending Machine z z z z
Release one item after 15 cents are deposited Single coin slot for dimes, nickels No change.-Æ not realistic The controller’s cause a single item to be released down a chute to the customer -> how to choose different items? Reset
N Coin Sensor
D
Vending Machine FSM
Open
Release Mechanism
Clock
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Vending Machine (Cont.) z
Suitable abstract representation typical input sequences: z z z z
Reset
3 nickels nickel, dime dime, nickel two dimes
S0 N
draw state diagram: z z
S1
inputs: N, D, reset output: open chute
N
assumptions: z
z
D
S3
assume N and D asserted for one cycle each state has a self loop for N = D = 0 (no coin)
N S7 [open]
S2 D
N
S4 [open]
S5 [open]
D S6 [open]
D S8 [open]
Initial vending-machine state diagram
Minimized Vending Machine’s States Minimize number of states - reuse states whenever possible S4,S5….,S8 have identical behavior=> combine into a single state present state 0¢
Reset
0¢ N 5¢ N D
5¢ D
10¢
10¢ N+D 15¢ [open]
15¢
inputs D N 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 X X
next state 0¢ 5¢ 10¢ X 5¢ 10¢ 15¢ X 10¢ 15¢ 15¢ X 15¢
output open 0 0 0 X 0 0 0 X 0 0 0 X 1
Minimized symbolic state transition table
Minimized vending-machine state diagram
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Vending Machine Encoded State Transition Table z
Uniquely encode states present state inputs Q1 Q0 D N 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1
next state D1 D0 0 0 0 1 1 0 X X 0 1 1 0 1 1 X X 1 0 1 1 1 1 X X 1 1 1 1 1 1 X X
output open 0 0 0 X 0 0 0 X 0 0 0 X 1 1 1 X
Moore Implementation of Vending Machine z
Mapping to Truth Table Q1
D1
0 1 1 1 D
X X X X
Q1
D0
0 0 1 1
Q1 Open 0 0 1 0
0 1 1 0 1 0 1 1
N D
0 0 1 0
N
X X X X
D
N
X X X X
1 1 1 1
0 1 1 1
0 0 1 0
Q0
Q0
Q0
D1 = Q1 + D + Q0 N D0 = Q0’ N + Q0 N’ + Q1 N + Q1 D OPEN = Q1 Q0
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Encoding in State Machine • State Machine Encoding Style: Binary, One-hot, Two-hot, Gray code, Johnson Code
Binary encoding Requires the least number of FFs. With n FFs, 2n states can be encoded. Disadvantages: require more logic, slower.
One-hotencoding one FF per state, with n FFs, n states can be encoded. Require the least amount of extra logic and fastest
Two- hot encoding Presents two bits active per state. With n FFs, n(n-1)/2 states can be encoded.
Gray code encoding Adjacent Gray codes are different in only one bit. n bits Gray code needs n FFs and can represent 2n states.
Johnson code encoding Use the output pattern of Johnson counter to encode the states. n bits Johnson code needs n FFs and can represent 2n states.
Different State Encodings Different state encodings leads to different circuit implementation, and thus different hardware cost and performance of state machines State encoding provides another dimension of optimizations Encoding Style
STATE
BINARY
TWOHOT
State0
000
State1
ONEHOT (8 bits)
Johnson Code (4 bits)
Gray Code (3 bits)
00011
00000001
0000
000
001
00101
00000010
0001
001
State2
010
01001
00000100
0011
011
State3
011
10001
00001000
0111
010
State4
100
00110
00010000
1111
110
State5
101
01010
00100000
1110
111
State6
110
10010
01000000
1100
101
State7
111
01100
10000000
1000
100
Number of FFs required
3
5
8
4
3
In Lab3: We use Binary Code, One-Hot State Encoding
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Vending Machine (Cont.) One-hot encoding
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present state Q3 Q2 Q1 Q0 0 0 0 1
0 0
1
0 1
0
1 0
0
0
0
0
inputs D N 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 - -
next state output D3 D2 D1 D0 open 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 - - - 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 - - - 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 - - - 1 0 0 0 1
D0 = Q0 D’ N’ D1 = Q0 N + Q1 D’ N’ D2 = Q0 D + Q1 N + Q2 D’ N’ D3 = Q1 D + Q2 D + Q2 N + Q3 OPEN = Q3
Equivalent Mealy and Moore State Diagrams z
Moore machine z
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outputs associated with state
N’ D’ + Reset
Reset
0¢ [0]
Mealy machine z
outputs associated with transitions
0¢
N’ D’
5¢ [0]
N’ D’
D/0
10¢ [0]
N’ D’
N’ D’/0
D/1
10¢
N’ D’/0
15¢
Reset’/1
N+D/1
N+D 15¢ [1]
5¢ N/0
N D
N’ D’/0
N/0
N D
(N’ D’ + Reset)/0
Reset/0
Reset’
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Mealy Implementation of Vending Machine Reset/0
Reset/0
0¢
present state inputs Q1 Q0 D N 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 – –
N’ D’/0
N/0 D/0
5¢
N’ D’/0
10¢
N’ D’/0
15¢
Reset’/1
N/0 D/1 N+D/1
Q1 Open 0 0 1 0 0 0 1 1 D
N
X X 1 X 0 1 1 1
D0 D1 OPEN
next state D1 D0 0 0 0 1 1 0 – – 0 1 1 0 1 1 – – 1 0 1 1 1 1 – – 1 1
output open 0 0 0 – 0 0 1 – 0 1 1 – 1
= Q0’N + Q0N’ + Q1N + Q1D = Q1 + D + Q0N = Q1Q0 + Q1N + Q1D + Q0D
Q0
Mealy Implementation of Vending Machine (Cont.) D0 = Q0’N + Q0N’ + Q1N + Q1D D1 = Q1 + D + Q0N OPEN = Q1Q0 + Q1N + Q1D + Q0D
make sure OPEN is 0 when reset – by adding AND gate
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Vending machine: Moore to Synch. Mealy OPEN = Q1Q0 creates a combinational delay after Q1 and Q0 change in Moore implementation This can be corrected by retiming, i.e., move flip-flops and logic through each other to improve delay OPEN.d = (Q1 + D + Q0N)(Q0'N + Q0N' + Q1N + Q1D) = Q1Q0N' + Q1N + Q1D + Q0'ND + Q0N'D Implementation now looks like a synchronous Mealy machine z it is common for programmable devices to have FF at end of logic
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Vending Machine: Mealy to Synch. Mealy z z
OPEN.d = Q1Q0 + Q1N + Q1D + Q0D OPEN.d = (Q1 + D + Q0N)(Q0'N + Q0N' + Q1N + Q1D) = Q1Q0N' + Q1N + Q1D + Q0'ND + Q0N'D Q1 Open.d 0 0 1 0 0 0 1 1 D
Q1 Open.d 0 0 1 0 0 0 1 1
N
1 0 1 1 0 1 1 1 Q0
D
N
X X 1 X 0 1 1 1 Q0
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Hardware Description Languages (HDL) and Finite State Machine Input
Output Combinational Logic
pr_state
nx_state
Sequential Logic
Clock Reset
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FSM approach => tasks constitute a well-structured list so that All states can be easily enumerated
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VHDL coding z
ARCHITECTURE => user defined enumerated data type, containing a list of all possible system states
Finite State Machine – VHDL (Cont.) LIBRARY ieee; USE ieee.std_logic_1164.all; --------------------------------------------------------------------ENTITY IS PORT ( input: IN ; reset, clock: IN STD_LOGIC; output: OUT ); END ; --------------------------------------------------------------------ARCHITECTURE of IS TYPE state IS (state0, state1, state2, state3,…); SIGNAL pr_state, nx_state: state: BEGIN ------------- lower section (sequential logic)---------------PROCESS (reset, clock) BEGIN IF (reset = ‘1’) THEN pr_state Start Compilation, fix all compilation error until successful message window appears
Examine the compilation reports (on the left of figure), check (1) (2) (3) (4) (5)
Flow Summary: contain part number, the number of pins used,…etc Resource Usage Summary (fitter->resource section-> resource usage summary) Input/Output Pins (fitter->resource section-> Input pins, fitter-> resource section->output pins), these two reports show the I/O pin assignments Floorplan View (fitter->Floorplan View), shows layout of the logic cells, which logic cells were used and how, etc. Analysis and Synthesis Equations (Analysis and Synthesis ->Analysis and Synthesis Equations)
QuartusII - Simulation
Open Waveform Editor, Select File-> New->Other File -> Vector Waveform File
In order to define the size of waveform, Edit -> End Time ( select 500ns, for example) Edit -> Grid Size ( select Period = 50ns, duty cycle = 50%) Select View -> Fit in Window Note: change default, go to Tools->Options->Waveform Editor->general 4. Add the input and output signals to the waveform window. Click the right mouse button inside the white area under Name. Select Insert Node or Bus. In the next box, select Node Finder. Make sure that Filter is set to Pins: all. Click on Start, then on >>, and finally OK. The waveforms window contains all all signals in VHDL/Verilog code. 5. Set the values of the input signals. (clk, rst,d,….) To set up the clock signal, select the entire clk line. A setup box will be displayed, choose period = 100 ns 6. For rst, select only the first portion (from 0 to 25 ns), which will cause change from 0 to 1. 7. Save the waveform file as *.vwf 8. The system is now ready for simulation. Select Processing -> Start Simulation 1. 2. 3.
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QuartusII – State Machine Viewer
The State Machine Viewer provides a high-level graphical representation of the states and state transitions, as well as a state transition table
After running Analysis & Synthesis, you can also view encoding information for the state transitions in the State Machine Viewer.
To view state machine nodes, transitions, and encoding in the State Machine Viewer: Open Project,.On the Tools menu, click State Machine Viewer. Or, In the RTL Viewer, in the hierarchy list, expand the design element that contains the state machine you want to view, and then expand the State Machines category to select the specific state machine and view it in the State Machine Viewer. Turn on the Highlight Fan-In and Highlight Fan-Out commands (View menu) to highlight node fan-in and fan-out, respectively. To view the transitions for a state machine, select the state machine in the schematic view and then click the Transitions tab.
To view the encoding for a state machine: Perform Analysis & Synthesis first, Select the state machine in the schematic view and then click the Encoding tab.
Vending Machine – How to Improve? Lab assistants demand a new soda machine for school. You need to design the FSM controller. All selections are $0.30 The machine makes changes! (Dimes and nickels only.) Inputs: limit 1 per clock Q - quarter inserted D - dime inserted N - nickel inserted Outputs: limit 1 per clock DC - dispense can DD - dispense dime DN - dispense nickel But, machine still has problem! Can machine select drinks? No !
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FSM States Encoding
Moore Machine Implementation State Transition DiagramNot minimized yet
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State Reduction (remove duplication)
Moore State Machine Implementation in Verilog Code of Vendor Machine
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Moore State Machine Implementation in Verilog Code of Vendor Machine (cont.)
Moore State Machine Simulation Result
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Combine Next-State and Output Logic
Mealy Machine Implementation
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Verilog Code for Mealy Machine Implementation
Verilog Code for Mealy Machine Implementation
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Simulation Result of Mealy Machine Implementation
State Encoding in Verilog Code Binary (Decimal) encoding parameter IDLE = 0; parameter GOT_5c = 1; parameter GOT_10c = 2; parameter GOT_15c = 3; parameter GOT_20c = 4; parameter GOT_25c = 5; parameter GOT_30c = 6; parameter GOT_35c = 7; parameter GOT_40c = 8; parameter GOT_45c = 9; parameter GOT_50c = 10; parameter RETURN_20c = 11; parameter RETURN_15c = 12; parameter RETURN_10c = 13; parameter RETURN_5c = 14;
One-hot Encoding parameter IDLE = 16’b0000000000000001; parameter GOT_5c =16’b0000000000000010; parameter GOT_10c=16’b0000000000000100; parameter GOT_15c= ….; parameter GOT_20c= …; parameter GOT_25c= ..; parameter GOT_30c= … ; parameter GOT_35c= …; parameter GOT_40c= ..; parameter GOT_45c= …; parameter GOT_50c= ..; parameter RETURN_20c = ……..; parameter RETURN_15c = ……..; parameter RETURN_10c = ……..; parameter RETURN_5c = ………;
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Lab 3 Assignment Two types of Finite State Machines Moore – Outputs are a function of current state only Mealy – Outputs a function of both the current state and input function Lab 3 assignment – please fix the problem in lecture! we need to have capability to select different drinks, and depense the selected drink and changes We will cover how to fix Glitching in FSM? Timing Requirement in FSM, “String Pattern Recognizer” next week. Final Exam – Tuesday, March 21, 2006, 9:00AM- 10:30AM, HSS1330 March 15- Oral exam by TA on Lab 4
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