Difference between revisions of "CSC270 Exercises on FSM"

From dftwiki3
Jump to: navigation, search
(Created page with "--~~~~ ---- =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: ** t...")
 
(→‎Exercise #5)
 
(27 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
--[[User:Thiebaut|D. Thiebaut]] 15:24, 28 February 2011 (EST)
 
--[[User:Thiebaut|D. Thiebaut]] 15:24, 28 February 2011 (EST)
 
----
 
----
−
=Exercise #1=
+
==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:
Line 7: Line 7:
 
** 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.
−
* There is only one light on at a given time.
+
** There is only one light on at a given time.
 +
* What is the frequency of your clock signal?
 +
<br /><br />
 +
<br />
  
−
=Exercise #2=
+
<code><pre>
 +
 
 +
        +---------+              +--------
 +
        |        |       |
 +
  G -----+        +-------------------+
 +
                  +---------+
 +
                  |        |
 +
  Y ---------------+        +-----------------
 +
                            +---------+
 +
                            |        |
 +
  R -------------------------+        +-------
 +
 
 +
 
 +
</pre></code>
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
 
 +
<br />
 +
<br />
 +
 
 +
<br />
 +
 
 +
==Exercise #2==
  
 
* Same as Exercise 1, but this time the behavior is the following
 
* Same as Exercise 1, but this time the behavior is the following
Line 15: Line 54:
 
** 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.
 +
* What is the frequency of your clock signal?
 +
 +
<br />
 +
<center>[[Image:GYRSequencer2.png]]</center>
 +
<br />
 +
 +
==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==
 +
 +
 +
* Same question, but solve it with Python.
 +
* You may find the  [[CSC270 Python Operators for Simulation | Python Logic Operators Example Page]] useful for this exercise.
 +
 +
==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?
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<br />
 +
<onlydft>
 +
<code><pre>
 +
# flipflop.py
 +
# implements a simple sequencer
 +
#
 +
 +
def xor( a, b ):
 +
    if ( a==b ):
 +
        return 0
 +
    return 1
 +
 +
def main():
 +
    # assume we start in a state where all 3 flip-flops are outputing 0
 +
    D0 = 0
 +
    D1 = 0
 +
    D2 = 0
 +
 +
    for t in range( 20 ):
 +
        Q0 = D0
 +
        Q1 = D1
 +
        Q2 = D2
 +
 +
        if t==0:
 +
            print "%2s  %2s %2s %2s" % ( "t", "Q0", "Q1", "Q2" )
 +
            print "----|------------"
 +
 +
        print "%2d  %2d %2d %2d" % ( t, Q0, Q1, Q2 )
 +
       
 +
        D0 = 1 - Q0
 +
        D1 = xor( Q0, Q1 )
 +
        D2 = xor( Q1, Q2 )
 +
       
 +
 +
main()
 +
 +
 +
 +
;Output
 +
 +
 +
t  Q0 Q1 Q2
 +
----|------------
 +
0  0  0  0
 +
1  1  0  0
 +
2  0  1  0
 +
3  1  1  1
 +
4  0  0  0
 +
5  1  0  0
 +
6  0  1  0
 +
7  1  1  1
 +
8  0  0  0
 +
9  1  0  0
 +
10  0  1  0
 +
11  1  1  1
 +
12  0  0  0
 +
13  1  0  0
 +
14  0  1  0
 +
15  1  1  1
 +
16  0  0  0
 +
17  1  0  0
 +
18  0  1  0
 +
19  1  1  1
 +
 +
</pre></code>
 +
 +
</onlydft>
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
 +
<br />
 +
[[Category:CSC270]][[Category:Python]]

Latest revision as of 10:13, 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?




















...













Retrieved from "http://dominiquethiebaut.com/dftwiki3/index.php?title=CSC270_Exercises_on_FSM&oldid=13947"