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CS402 Theory of Automata Assignment 4 Solution Fall 2012

Scenario: Consider the following sequential circuit:

X and Y are the two points showing state of above circuit. The presence and absence of current at the given points identify the following states:

q0(X=0, Y=0) = (0,0)
q1 (X=0, Y=1) = (0,1)
q2 (X=1, Y=0) = (1,0)
q3 (X=1, Y=1) = (1,1)

Questions:

a. Write down the expressions to find out new X, new Y and Output? [Marks 5]

b. Calculate all the values of the respective transition table for a mealy machine? [Marks 10]

 

Old States

Inputting 0

Inputting 1

State

Output

State

Output

q0 = (0, 0)

q0 = (0, 0)

1

q2 = (1, 0)

0

q1 = (0, 1)

q0 = (0, 0)

0

q2 = (1, 0)

1

q2 = (1, 0)

q1 = (0, 1)

1

q3 = (1, 1)

0

q3 = (1, 1)

q3 = (1, 1)

0

q1 = (0, 1)

1

c. Draw the resulting mealy machine from the transition table (calculated in step b)? [Marks 5]

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