Difference between revisions of "CSC270 Exercises on FSM"

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--[[User:Thiebaut|D. Thiebaut]] 15:24, 28 February 2011 (EST)
 
--[[User:Thiebaut|D. Thiebaut]] 15:24, 28 February 2011 (EST)
 
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=Exercise #1=
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==Exercise #1==
  
 
* Implement a sequencer (FSM) which activates 3 Lights: a green light, a yellow light, and a red light.  The behavior of the FSM is the following:
 
* Implement a sequencer (FSM) which activates 3 Lights: a green light, a yellow light, and a red light.  The behavior of the FSM is the following:
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** the yellow light comes on and stays on for 30 seconds, then
 
** the yellow light comes on and stays on for 30 seconds, then
 
** the red light comes on and stays on for 30 seconds, then we repeat the pattern.
 
** the red light comes on and stays on for 30 seconds, then we repeat the pattern.
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* There is only one light on at a given time.
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** There is only one light on at a given time.
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* What is the frequency of your clock signal?
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<code><pre>
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        +---------+              +--------
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        |        |       |
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  G -----+        +-------------------+
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                  +---------+
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                  |        |
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  Y ---------------+        +-----------------
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                            +---------+
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                            |        |
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  R -------------------------+        +-------
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</pre></code>
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==Exercise #2==
 
==Exercise #2==
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** the yellow light comes on and stays on for the next for 15 seconds,
 
** the yellow light comes on and stays on for the next for 15 seconds,
 
** the red light comes on after the yellow light for 30 seconds.
 
** the red light comes on after the yellow light for 30 seconds.
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* What is the frequency of your clock signal?
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<br />
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<center>[[Image:GYRSequencer2.png]]</center>
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<br />
  
 
==Exercise #3==
 
==Exercise #3==
  
 
* Create a "true" frequency divider that divides by 4.
 
* Create a "true" frequency divider that divides by 4.
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==Exercise #4==
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* What is the state diagram of the 3-flip-flop circuit with the following equations:
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      D0 = Q0'
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      D1 = Q0 XOR Q1
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      D2 = Q1 XOR Q2
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==Exercise #5==
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* Same question, but solve it with Python.
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* You may find the  [[CSC270 Python Operators for Simulation | Python Logic Operators Example Page]] useful for this exercise.
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==Exercise #6==
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* What is the state diagram of this FSM?
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** D1= Q0
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** D0 = ( Q0 ^ Q1 )'
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* What happens when the flip-flops start in the state where Q0 and Q1 are both 1?
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<onlydft>
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<code><pre>
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# flipflop.py
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# implements a simple sequencer
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#
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def xor( a, b ):
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    if ( a==b ):
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        return 0
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    return 1
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def main():
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    # assume we start in a state where all 3 flip-flops are outputing 0
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    D0 = 0
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    D1 = 0
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    D2 = 0
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    for t in range( 20 ):
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        Q0 = D0
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        Q1 = D1
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        Q2 = D2
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        if t==0:
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            print "%2s  %2s %2s %2s" % ( "t", "Q0", "Q1", "Q2" )
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            print "----|------------"
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        print "%2d  %2d %2d %2d" % ( t, Q0, Q1, Q2 )
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        D0 = 1 - Q0
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        D1 = xor( Q0, Q1 )
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        D2 = xor( Q1, Q2 )
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main()
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;Output
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t  Q0 Q1 Q2
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----|------------
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0  0  0  0
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1  1  0  0
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2  0  1  0
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3  1  1  1
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4  0  0  0
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5  1  0  0
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6  0  1  0
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7  1  1  1
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8  0  0  0
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9  1  0  0
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10  0  1  0
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11  1  1  1
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12  0  0  0
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13  1  0  0
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14  0  1  0
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15  1  1  1
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16  0  0  0
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17  1  0  0
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18  0  1  0
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19  1  1  1
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</pre></code>
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[[Category:CSC270]][[Category:Python]]

Latest revision as of 11:13, 2 March 2012

--D. Thiebaut 15:24, 28 February 2011 (EST)

Exercise #1

  • Implement a sequencer (FSM) which activates 3 Lights: a green light, a yellow light, and a red light. The behavior of the FSM is the following:
    • the green light stays on for 30 seconds, then
    • the yellow light comes on and stays on for 30 seconds, then
    • the red light comes on and stays on for 30 seconds, then we repeat the pattern.
    • There is only one light on at a given time.
  • What is the frequency of your clock signal?





         +---------+  	      	       +--------
         |         |		       |
  G -----+         +-------------------+
                   +---------+
                   |         |
  Y ---------------+         +-----------------
                             +---------+
                             |         |
  R -------------------------+         +-------












Exercise #2

  • Same as Exercise 1, but this time the behavior is the following
    • the green light comes on after the red light and stays on for 30 seconds,
    • the yellow light comes on and stays on for the next for 15 seconds,
    • the red light comes on after the yellow light for 30 seconds.
  • What is the frequency of your clock signal?


GYRSequencer2.png


Exercise #3

  • Create a "true" frequency divider that divides by 4.

Exercise #4

  • What is the state diagram of the 3-flip-flop circuit with the following equations:
     D0 = Q0'
     D1 = Q0 XOR Q1
     D2 = Q1 XOR Q2

Exercise #5

Exercise #6

  • What is the state diagram of this FSM?
    • D1= Q0
    • D0 = ( Q0 ^ Q1 )'
  • What happens when the flip-flops start in the state where Q0 and Q1 are both 1?




















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