Synchronous Sequential Circuit

Analysis and Synthesis of Synchronous Sequential Circuit

The analysis of a synchronous sequential circuit is the process of determining the functional relation that exists between its outputs, and its internal states. The contents of all the flip flops in the circuit combined determine the internal state of the circuit. Thus, if the circuit contains n flip flops. It can be in one of the 2ⁿ states. Knowing the present state of the circuit and the input values at any time t, We should be able to derive its next state (i.e.. the state at time t+1) and the output produced by the circuit at t.

A sequential circuit can be described completely by a state table . That is very similar to the ones shown for flip flops

For a circuit can be 2ⁿ rows in the state table. If there are m inputs to the circuit, there will be 2ⁿ column in the state table. At the intersection of each row and column, the next stable and the output information are recorded. A state diagram is a graphical representation of the state table in which each state is represented by a circle and the state transitions are represented by arrows between the circles. The input combination that brings about the transition and the corresponding output information are shown on the arrow.

Analysing a sequential circuit thus corresponds to generating the state table and the state diagram for the circuit. The state table or state diagram can be used to determine to output sequence generated by the circuit for a given input sequence if the initial state it known. It is important to note that for proper operation, a sequential circuit must be in its initial state before the inputs to it can be applied. Usually the power up circuits are used to initialize the circuit to the appropriate state when the never is turned on.

Sequential circuit analysis (a) circuit (b) next state and output tables (c) transition table (d) state diagram

Design of synchronous sequential circuit

The design of a sequential circuit is the process of deriving a logic diagram from the specification of the circuits required behaviour. The circuit behaviour is often expressed in words. The first step in the design is then to derive an exact specification of the required behaviour in terms of either state diagram or a state table. This is probably the most difficult step in the design, since no definite rules can be established to derive the state diagram or a state table.  The designer intuition and experience are the only guides.

Once the description is converted into the state diagram or a state table, the remaining steps become mechanical. We will examine the classical design procedure through the examples in this section. It is not always necessary to follow this classical procedure, as some designs lend themselves to more direct and intuitive design methods. The classical design procedure consist of the following steps:

1.   Deriving the state diagram (and state table) for the circuit from the problem statement.

2.   Deriving the number of flip flops (p) needed for the design from the number of states in the state diagram, by the formula 

3.   Deciding on the types of flip flops to be used. (this often simply depends on the type of flip flops available for the particular design)

4.   Assigning a unique p bit pattern (state vector) to each state.

5.   Deriving the state transition table and the output table.

6.   Separating the transition table into p tables, one for each flip flop.

7.   Deriving an input using the excitation tables.

8.   Deriving input equations for each flip flop input and the circuit output equations.

9.   Drawing the circuit diagram.