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?

Answer Key

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).

Figure 1: Sequence Detector State Diagram
Sequence detector state diagram

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.

Figure 2: J-K Flip-Flop 2
J-K flip-flop 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:

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