The Task - Create a logic circuit with the following functionality:

There should be two data inputs A, B (plus a Clock signal ?) + one output:  F = f( A, B)

If A=1 and B=1 then  F = A and B until A=0 and B=0
If A=0 and B=0 then  F = A  or  B  until A=1 and B=1

•  Documentation of a sequential circuit (State machine):
    The output depends not only on the inputs (as for the combinatorial circuit) but also on the former input values.

One way to document a sequential circuit could be a "horizontal truth table" which shows the output F as a function of time and the inputs (A,B)

Please note the need of showing the (internal) states: OR - AND

The waveform display can also be seen as a "real-life" presentation as this can be seen with a logic analyser.

•  State diagrams and State/output tables

The most popular graphical way to document a Sequential system called State Diagrams.

Each State should be given a name or number and the transitions between states shown with arrows and their input conditions.

Moore outputs depends only at the state.

Mealy outputs depends at both state and input.

A state table just another way to present states, conditions and transitions.

Compare the State diagram above with the Table.

•  The Coding of 2-states: (Kind of a joke:-)

In order to actually implement a Sequential circuit with logic must all states be converted into binary numbers.

The case with two states kind of easy, since it can be done with only one bit.

•  Asynchronous State Machines:

The design and implementation of Asynchronous feedback loops (in Async. State Machines) not a task for beginners and even profs will have a hard time doing it, hence the ISE-tools not meant for this.

This Ad-hoc Asynchronous design will work in practice as its kind of simple.

The state memory formed by a SR-Latch, which controls a multiplexer.

The Set-signal activated when A=1 and B=1.

The Reset-signal activated when A=0 and B=0 (a NOR function)

•  Synchronous State Machines:

Instead of watching the input signals (A, B) continually as for the Asynchronous circuit will it be easier to create a circuit which only "evaluates" the signal at certain times, controlled by a Clk signal.

Please note the state changes follows the Clk (Rising edges) where as the output signal F also depends on the input signals A, B

•  Synchronous State Machine with Mealy output

From the Coded state/Output (shown above this) can the "Next State equations" be found

The same is true for the "Output equations"

Try to derive the Equations yourself and check the State Machine shown here.

IMPORTANT NOTE:
In real-life systems must you avoid random (asynchronous) changes of input signals (A or B).

The Q output from the F/F's might go metastable and/or more likely will the state become undefined due to timing-hazard.

SOLUTION: Use a Synchronisation F/F for each input.

•  Synchronous State Machine with Moore output

The alternative to Mealy-outputs called Moore-outputs.

   (MOOre depends on State Output Only)

Study the State/Output table shown at the right and draw the equivalent State Diagram.

How come we now need four states instead of two?

•  The Coding of 4-states:

How many Flip/Flops needed for the coding of this state machine?

How many ways (combinations) do you have to choose among when coding the state machine?

Why seems this coding to be a better solution?

•  Test the circuit yourself: for the BASYS - Test_state_machines.bit - or  NEXYS_test_state_machines.bit

•  Get the project here:     Exer4_1_Statemachines1.zip