CSC270 Exercises on FSM

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--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?




GYRSequencer1.png













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

  • Same question, but solve it with Python.



















# 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