# Problem set 12 for CSCI 255 -- Spring 2000

• Due: Monday, 1 May, 3:15 pm

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## The problem

Start with a finite state machine which three states, A, B, and C, and a single input and output described using the following state table:

 Old state Input New State Output A 0 A 0 A 1 B 0 B 0 A 0 B 1 C 1 C 0 B 1 C 1 C 1

Do a state assignment, using two Boolean values, for the three states of the finite state machine. Write your answers in the column labeled "Two bit assignment".

 State Two bit assignment A B C

Now write a state table using your Boolean state assignments. Furthermore assume that you are going to implement this state machine using two JK flipflops. Use the excitation table for the JK flipflop to determine the flipflop inputs.

 Old state Input New State Output flipflop inputs

Your sequential circuit can now be described by five Boolean functions, one for the output and four for the JK flipflop inputs. Write the Boolean equations for those five functions.