Spring 2002 ENGR 212 / CSCI 311 Homework 8

This assignment is due 3 April.

This is assignment is based on NCSU ECE 212 Homework 6. However, the numbers have been changed.

Problem 1

For the FSM (Finite State Machine) specified by the state table below, give the next-state and output equations (also show your K-maps), assuming D flip-flops. Use the following state assignment for Q1, Q2, and Q3: A = 000, B = 100, C = 010, and D = 001.

stateinput
01
AC/1D/0
BC/0A/0
CB/0C/1
DA/0B/1

Problem 2

Construct the equivalent state diagram for the FSM specified in problem 1.

Problem 3

Using the state table from problem #1, construct a state sequence chart for the input sequence x is 0 1 1 0 1 1 0 0 0 1. Assume the initial state is A. Note: A state sequence chart shows input, current state, next state, and output each cycle. For example, here is the first cycle done for you:

```   cycle           1 2 3 4 5 6 7 8 9 10
------------------------------------
x (input)       0 1 1 0 1 1 0 0 0 1
current state   A C
next state      C
z (output)      1
```

Problem 4

Design a Mealy state machine that will detect each of the following sequences. When the sequence is detected, a single output "z" is set to 1. Your design should include a state diagram and a state table for each machine.

1. Sequence = 10001. Overlapping sequences are allowed.
2. Sequence = 1001. Overlapping sequences are not allowed.