# Practical Application for Computer Architecture: Sequential Circuits

Instructor: Martin Gibbs

Martin has 16 years experience in Human Resources Information Systems and has a PhD in Information Technology Management. He is an adjunct professor of computer science and computer programming.

In this practical lesson, you will design and build a sequential circuit. The circuit is a 11011 sequence detector, and it will use J-K flip-flops. You will simulate the circuit in Logisim.

## Lesson Overview & Knowledge Required

In order to complete this practical lesson, you should have an understanding of sequential circuits, how they use memory, and flip-flops. You should also be able to create and simulate circuit designs using Logisim.

## Sequential Circuit

Recall that a sequential circuit needs to remember its past inputs as well as keep track of the current input values. The storage component is the flip-flop; the state of the flip-flop is part of the previous input into the sequential circuit.

A sequence detector is a sequential circuit that has an output of 1 if a specific pattern of bits arrives as input. A sequence detector can be overlap or non-overlap. In a detector that allows overlap, the last bits of a given sequence can start another sequence. For non-overlap detectors, this is not allowed.

## Designing a Sequential Circuit

Now it is your turn to design a sequence detector. The design can accept overlap. The input sequence will be 11011. There are 5 bits in each sequence so there are five states (A-E). In order to complete this assignment, complete the following steps:

1. Draw the state diagram
2. Create the state table
3. Using the J-K flip-flop, transform the state table into P tables for each flip-flop
4. Simplify the input equations using a Quinn-McCloskey method (you can search for an online tool or reduce them manually)
5. Build the circuit in Logisim and simulate the design

## Follow-Up Questions

1. If you designed a circuit that does not allow overlap, what would happen to our values when 11011 is detected?
2. How many states would we have for an input of 110?
3. A circuit must do what with the inputs from previous cycles?

Below are the solutions to the sequential circuit design and the follow-up questions.

### Sequential Circuit Design

The detector will input 11011 sequence using JK flip-flops and allow overlap. The table below shows the states and what values it is waiting for.

State Value Waiting For
A null 11011
B 1 1011
C 11 011
D 110 11
E 1101 1

#### State Diagram

Each state has two lines for each bit (1 or 0). Following from A to E we follow the expected path (11011). Since this allows overlap, we can go to C because the next valid input would be a 1.

We also have the 0-bit lines, for example, if state E receives a 0, the last bits were 11010, and this isn't part of the sequence. Therefore, we go back to A (start over).

#### State Table

Current State Next State Output
X = 0 X = 1
A A / 0 B / 0
B A / 0 C / 0
C D / 0 C / 0
D A / 0 E / 0
E A / 0 C / 1

In this sequential circuit, there are 3 flip-flops.

#### J-K Flip-Flop

Figures 2 to 4 below show the J-K flip-flops with d/c for the don't-care state. This actually goes in order from 3rd flip-flop to the first. Therefore the order is from flip-flop 2 to flip-flop 0.

The first flip-flop is Y2 as shown in Figure 2.

First we look at the X = 0 columns followed by the X = 1 columns. Then we try to combine the two.

When generating the table, start with all 0 -> 0 transitions, then work on 0 -> 1. When matching up the patterns, the following rules are in place:

To unlock this lesson you must be a Study.com Member.

### Register to view this lesson

Are you a student or a teacher?

### Unlock Your Education

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.