L5 – Sequential Circuit Design. Sequential Circuit Design Mealy and Moore Characteristic...

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L5 – Sequential Circuit Design

Transcript of L5 – Sequential Circuit Design. Sequential Circuit Design Mealy and Moore Characteristic...

Page 1: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

L5 – Sequential Circuit Design

Page 2: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Sequential Circuit Design Mealy and Moore Characteristic Equations Design Procedure Example Sequential Problem – from

specification to implementation

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Page 3: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Types of State Machines Mealy Machine

Characterized by – Outputs are a function of both inputs and current state.

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NextStateLogic

OutputLogic

StateMemory

(F/F)

CLOCK

Inputs Excitation

CurrentState

Outputs

Page 4: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Types of State Machines Moore Machine

Characterized by – Outputs are a function of the current state only.

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NextStateLogic

OutputLogic

StateMemory

(F/F)

CLOCK

Inputs Excitation

CurrentState

Outputs

Page 5: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Notes on Mealy and Moore Both Mealy and Moore machine

implementation can be implemented with any sequential element.

Why choose one elements over another? Efficiency – The next state logic may differ

significantly when using different F/F types. Efficiency of implementation is also drastically

affected by choice of state assignment.

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Page 6: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

The characteristic equation The Characteristic Equation formally

specifies the flip-flop’s next state as a function of its current state and inputs

Q* means the next state value for the Q output of the F/F

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Page 7: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Characteristic equations for F/Fs

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S-R Latch D Latch D F/F D F/F with Enable J-K F/F T F/F

Q* = S + R’ Q Q* = D Q* = D Q* = EN D + EN’ Q Q* = J Q’ + K’ Q Q* = Q’

when T = 1

Page 8: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Summary of the Design Procedure 1. Given the problem statement, determine the relationship

between input and output. Understand the specification and or problem statement. Resolve any questions. Then generate a state graph and/or state table.

2. Reduce the state table to the minimum number of states. 3. From the number of state determine the number of flip-

flops (m states n flip-flops where m <= 2n) 4. Generate a transition table (current state – next state) 5. Use K-maps to derive flip-flop input equations. 6. Derive output functions and implement.

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Page 9: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Example – problem statement Sequential Code Converter (16.2 example) Word description: Design a sequential circuit to

convert BCD to excess 3 code. The inputs arrive sequentially, lsb first, i.e. serial input stream. After 4 inputs the circuit resets to the initial state ready for another group of 4 inputs. The excess 3 code is output serially at the same time.

First question – is it possible to generate the output serially without delay?

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Page 10: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Input – output table Input BCD – Output excess 3

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Page 11: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Construct a state Graph Walk through the sequences

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Page 12: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Build a state table From the State Graph can build the state table Note the relationship between the two

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Page 13: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Then reduce the state table And just how is that done – (the coming

attraction) How many flip-flops are needed?

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Page 14: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

What next? Choose state assignment Pick flip-flop of implementation – here D

F/Fs

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Page 15: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Next state logic Logic to generate the next state is generated Use K-maps

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Page 16: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

From there: implement the design D flip-flop implementation

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Page 17: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Implementation with other F/Fs? Use the characteristic equation for generation

of the transition table. Say T flip-flops – example for T1

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T1 = Q1' Q2' + Q1 Q2

Page 18: L5 – Sequential Circuit Design. Sequential Circuit Design  Mealy and Moore  Characteristic Equations  Design Procedure  Example Sequential Problem.

Assignment See course web page

Spring 2014 – implement BCD to Excess 3 converter in a FPGA. HW2 – submit to dropbox.

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