4 Sequential Logic Circuits, State Machines

The combinational circuits treated so far can be completely characterized by the actual values on their input parameters. This information alone is sufficient to determine all output parameter values. Circuits of this type do not contain any internal storage elements.

For such combinational circuits the following limitations are (implicitly) valid:

• The combinational circuits are implemented without any feedbacks.
• At any input of a circuit a signal change is only allowed after all signal variations inside the circuit have stopped. This guarantees that inside the circuit only signals exist that originate from the same source.
  

In order to abolish these limitations feedbacks will now be introduced, so that circuits of the following type will be possible:

Figure 4.1: Switching Circuit with Feedback.

Circuits of this kind can be described in the known way, e.g. using truth tables, but the internal states v_i and z_i must now be taken into consideration. These internal states affect the outputs y_i. Therefore another differentiation has to be done in stable and unstable states:

Thus circuit inputs as well as circuit outputs form two classes, respectively:

• Switching Circuit Inputs:
  free external inputs that can for instance be connected with the outputs of other circuits;
  feedback inputs that are interconnected with signals from the circuit itself (feedback loops).
  
• Switching Circuit Outputs:
  external outputs that send information to other circuits;
  internal outputs that represent the feedbacks and that can also transmit - like the external outputs - information to other circuits.
  

The distinctive feature are the feedback signals that trigger the following sequence of events in the circuit:
In the stable state of the system a change of an input signal may occur. When this causes a change of the feedback output v_i, then the circuit input z_i will also change.

For the subsequent process two cases can be distinguished:

1. With the new value z_i none of the feedback outputs v_i change. The circuit remains in a stable state.
2. With the new value z_i a value of the feedback outputs v_i changes, the sequence is repeated.

It has to be observed at this point that the signal changes can occur at the feedback inputs at a time when not all internal signal changes have reached the circuit outputs.

Thus the second limitation defined above has been removed, too. Also those signals have now to be considered that change at the circuit inputs at different times. Thus very complicated processes can occur in the switching circuits that are determined by the gate propagation delay times.

The circuits with feedback shown here are called sequential logical circuit (in contrast to the simple combinational circuits).The signals can cycle through those sequential logical circuits several times until finally a stable state is reached.

The term "state" plays a central role at this point. It is used in its colloquial form, describing the current state of the sequential circuit. It is the logical consequence of all the previous states and the current external inputs of the sequential circuit. Consequently it represents for the subsequent state the entire previous status (history) of the circuit .