Your assignment is to implement this finite state machine using J-K flip
flops. Assume that the state assignments are 000 for S_{0},
001 for S_{1}, 010 S_{2}, 011 for S_{3},
100 for S_{4}, and 101 for S_{5}.

- In the truth table below, let A, B and C be
the current states and A', B' and C' be the next states stored in
the J-K flip flops. (E.g., S
_{4}is assigned A=1, B=0 and C=0.) We also use D for the 1 bit input. Fill in the rest of the truth table using the excitation table for J-K flip flops. For example, in row 9, flip-flop A is currently storing 1 and must store 0 in the next state. To achieve this, we look at the 10 entry of the excitation table and note that the J input to flip-flop A (call it JA) can be set to anything, but the K input, KA, must be set to 1.

- Use the Karnaugh maps provided to simplify the Boolean
formulas for the J and K inputs to each J-K flip flop and for the
output value z.

- Implement the resulting circuit in DigSim.

A | B | C | D | A' | B' | C' | z | JA | KA | JB | KB | JC | KC | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||

1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | ||||||

2 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | ||||||

3 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||||||

4 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | ||||||

5 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | ||||||

6 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | ||||||

7 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | ||||||

8 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | ||||||

9 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | d |
1 | ||||

10 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | ||||||

11 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | ||||||

12 | 1 | 1 | 0 | 0 | d |
d |
d |
d |
d |
d |
d |
d |
d |
d |

13 | 1 | 1 | 0 | 1 | d |
d |
d |
d |
d |
d |
d |
d |
d |
d |

14 | 1 | 1 | 1 | 0 | d |
d |
d |
d |
d |
d |
d |
d |
d |
d |

15 | 1 | 1 | 1 | 1 | d |
d |
d |
d |
d |
d |
d |
d |
d |
d |

Q | Q' | J | K |

0 | 0 | 0 | d |

0 | 1 | 1 | d |

1 | 0 | d |
1 |

1 | 1 | d |
0 |

Karnaugh maps are available in PDF.

- Consider the layout of your circuit with some care before you start DigSim. You will have 6 wires for the 3 J-K flip-flops going from one side of the circuit to another. Be sure to leave room for this.
- Be sure to check your work carefully.
- Test your circuit and compare the transitions against the original transition diagram.

For this assignment you will turn in your work both on paper and online. In class on Tuesday May14, turn in the truth table, the Karnaugh maps and the resulting Boolean formulas on paper.

Save your circuit as you did in DigSim Assignment 1.
Submit the circuit file and the README file using the Unix submit
command as in previous assignments. The submission name for this
assignment is: `digsim3`.

Last Modified: 2 Dec 2002 11:57:02 EST by Richard Chang to Spring 2002 CMSC 313 Section Homepage