## Introduction

```
We have covered combinational design; that is the design of
circuits with no memory. This week we will start to look at
sequential design, which is the design of circuits with memory.
Sequential design will let us design much more complicated and
useful circuits like counters and even microprocessors.

```

## Definition of Sequential Circuits

```
Sequential circuits are circuits that have memory.
In other words, these are circuits where the output depends on
previous inputs.

In combinational circuits the output depends only on the current inputs.

```

## Flip Flops

Flip-Flops are basic storage/memory elements. A sequential circuit consists of a combinational circuit and storage elements (flip-flops) that together form a feedback system. We cannot continue with anymore theory until we look at the basic memory elements used in sequential design. Some of the basic flip-flops are listed below:

1. Set-Reset flip flop

The most basic flip flop is the S-R flip flop. (llustrate the operation of the F/F using the diagram below ).

2. Gated S-R flip flop

Quite often we only want the flip flop to be able to change states at certain times. For example one may have a flip-flop in an alarm system that is set by a window opening thus setting off the alarm. To prevent the alarm from going off when the alarm system is shut off we would like to disable the flip-flop when the alarm system is shut off. We can do this by adding some gates to a S-R F/F to make it a gated S-R F/F. (Illustrate the operation of the gated S-R F/F using the diagram below ).

3. CLOCKED FLIP-FLOPS

With the gated S-R F/F we only sampled the S and R inputs when the gate signal was high. There are flip flops that only sample data when the gate signal changes from a low to a high (positive going edge of the clock) or some sample when the gate signal goes from high to low (on the negative going edge of the clock). Illustrate this with the two fictional edge triggered F/Fs shown below.

In practice S-R F/Fs are not used that often. The most commonly used flip-flops are the D-flip flop and the JK flip-flop. We will look at each one in more details.

4. D flip flop

The D flip-flop(shown below) lets the input at D propogate through to Q on the positive going edge of the clock. The present state-next state chart illustrates the behavior of the D flip-flop. Basically Q(t+1) = D, which is the characteristic equation.

```
Characteristic Table		Excitation Table
====================            ===================
D  Q(t+1)  Operation            Q(t)  Q(t+1)   D
====================		===================
0    0     Reset                 0      0      0
--------------------            -------------------
1    1     Set                   0      1      1
====================            -------------------
1      0      0
-------------------
1      1      1
===================

```

5. JK flip-flop

The JK flip-flop(shown below) is very flexible and therefore allows simpler circuit designs. Most JK flip-flops allow the signal to change on the negative edge of the clock. The present state-next state chart(shown below ) illustrates the behavior of the flip-flop. The characteristic equation is Q(t+1) = JQ'(t) + K'Q(t).

```
Characteristic Table			Excitation Table
==========================            ===================
J  K  Q(t+1)  Operation               Q(t)  Q(t+1)  J  K
==========================	      ===================
0  0  Q(t)    No Change               0     0       0  x
--------------------------            -------------------
0  1  0       Reset                   0     1       1  x
--------------------------            -------------------
1  0  1       Set  		      1     0       x  1
--------------------------	      -------------------
1  1  Q'(t)   Complement	      1     1       x  0
==========================	      ===================

```

## Sequential Design Procedure

```
1. State the problem clearly

2. Determine inputs/outputs and assign letters to inputs/outputs

3. Draw a present state-next state diagram

4. For each input/output draw the karnaugh maps

5. Find the simplified the expressions for the inputs/outputs using
Karnaugh maps

6. Draw the logic diagram and implement the circuit
(a connection diagram will be needed if the circuit is to be hardwired)

```

## Sequential Design Examples

We have now covered the basic sequential circuit elements necessary to construct sequential designs.
We will learn how to interconnect JK flip-flops to make, for example, counter circuits.
The best way introduce you to sequential design is to look at a simple problem:

Trial and error may work for simple cases like this but for larger circuits it will not.
We will illustrate the method for larger problems as follows:

```
For each flip-flop we must establish what is to be connected
to the JK inputs to have that particular bit count properly.
We will look at each bit one at a time.

```

## Conclusion

```
Sequential circuits are circuits that have memory.
We examined the fundamental sequential circuits like S-R flip-flops
and JK flip-flops and explained the design steps necessary
to use these as building blocks for larger sequential circuits.

```