10/2/0810/2/2008 ECE 561 -ECE 561 - Lecture 5 1

State Machine Implementation

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Lecture Overview

• Another Example – a counting machine• Another Example – Tail light controller

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Counting Machine

• “Design a clocked synchronous state machine with two inputs, X and Y, and one output Z. The output should be 1 inputs on X and Y since reset is a multiple of 4, and 0 otherwise.

• There are 4 states

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Construct a state table

• From word description construct a state table for the problem.

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X Y

Meaning S 00 01 11 10 Z

Have zero 1's mod 4 S0 S0 S1 S2 S1 1Have one 1 mod 4 S1 S1 S2 S3 S2 0Have two 1's mod 4 S2 S2 S3 S0 S3 0Have three 1's mod 4 S3 S3 S0 S1 S0 0

S*

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Do a state assignment

• Having state table pick a state assignment• From here we can generate the excitation equations

X Y

Q1 Q2 S 00 01 11 10 Z

00 S0 00 01 11 01 101 S1 01 11 10 11 011 S2 11 10 00 10 010 S3 10 00 01 00 0

Q1* Q2*

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Excitation Equations

• D1 = Q2 X’ Y + Q1’ X Y + Q1 X’ Y’ + Q2 X Y’

• Z = Q1’ Q2’

• D2 = Q1’ X’ Y + Q1’ X Y’ + Q2 X’ Y’ + Q2 X Y

0 0 1 0

0 1 1 1

1 1 0 1

1 0 0 0

X Y

00 01 11 10

00

01

11

10

D1 Map

0 1 1 1

1 1 0 1

1 0 0 0

0 0 1 0

X Y

00 01 11 10

00

01

11

10

D2 Map

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Another Example

• Design a clocked synchronous state machine with one input X and two outputs, UNLK and HINT. The UNLK output should be 1 if and only if X is 0 and the sequence of inputs received on X the preceding seven clock ticks was 0110111. The HINT output should be 1 if and only if the current value of X is the correct one to move the machine close to being in the “unlocked” state (with UNLK = 1).

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Create State Table

• Create a state table from the word description X

Meaning S 0 1

Got Zip A B,01 A,00Have 0 B B,00 C,01 Have 01 C B,00 D,01Have 011 D E,01 A,00Have 0110 E B,00 F,01Have 01101 F B,00 G,01Have 011011 G E,00 H,01Have 0110111 H B,11 A,00

S*,UNLK,HINT

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Choose a state assignment

• To get transition/excitation tableX

Q1 Q2 Q3 0 1

Q1*Q2*Q3*,UNLK HINT

000001010011100101110111

001,01001,00001,00100,01001,00001,00100,00001,11

000,00010,01000,00100,01101,01110,01111,01000,00

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Can use Karnaugh Map to get excitation equations

• D1 = Q1 Q2’ X + Q1’ Q2 Q3 X’ . + Q1 Q2 Q3’

• D2 = Q2’ Q3 X + Q2 Q3’ X• D3 = Q1 Q2’ Q3’ + Q1 Q3 X’ + Q2’ X’ .

. + Q3’ Q1’ X’ + Q2 Q3’ X• UNLK = Q1 Q2 Q3 X’• HINT = Q1’ Q2’ Q3’ X’ + Q1 Q2’ X .

+ Q2’ Q3 X + Q2 Q3 X’ + Q2 Q3’ X

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For both examples

• Having the excitation and output equation can do the implementation in discrete logic or perform a schematic capture for FPGA tools such as XILINX or Altera.

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Another example

• This is a example of a “real” deisgn• The T-Bird Tail Light Problem

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The Transistion Table

• Can again get the transition table

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The State Diagram

• Can also draw a state diagram

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Final steps

• Choose F/F type• Choose a state assignment• Develop the transition/excitation table for

that state assignment• Generate the equations

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Assignment 3

• Carry through the remaining steps to get implementation and output equations and the circuit diagram for an implementation for the following state table.

Next State

Present State w = 0 w=1 Z

A B C 1 B A F 1 C F C 0 F C A 0