# Spring 2003 ENGR 212 Homework 6

This homework is due 9 April, 4:30 PM.

## Problem 1

For the FSM (Finite State Machine) specified by the state table below, derive the minimized next-state (Q1Q2*) and output (z) equations. (Show your K-maps.) Use the following state assignment for Q1 Q2: A = 00, B = 10, C = 11, and D = 01.

state x
0 1
A B/1 C/0
B D/1 C/1
C B/1 A/0
D B/0 C/1

## Problem 2

For each of the following state tables, construct the state diagram.

### Problem 2A

Use state table from Problem 1.

### Problem 2B

state x1 x2 z1 z2
00 01 10 11
A A C A B 0 1
B A C B C 0 0
C D D C D 1 0
D A B A B 1 0

## Problem 3

For the FSM in Problem 2B above, derive the minimized next-state (Q1Q2*) and output (z1 z2) equations. Use the following state assignment for Q1 Q2: A = 00, B = 10, C = 11, and D = 01.

## Problem 4

Using the state table from Problem 1, construct a state sequence chart for the input sequence x = 0 1 1 0 1 1 0 0 0 1. 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 0 1 1 0 1 1 0 0 0 1 current state A B next state B z 1

## Problem 5

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.

• 11000
• 10110