CSC270 Exercises on FSM

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

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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:
  • 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.

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.

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