Sequential Circuit Design

The digital circuits considered thus far have been combinational. Although every digital system is likely to include a combinational circuit, most systems encountered in practice also include storage elements, requiring that the systems be described as sequential circuits.

A combinational circuit and storage elements are interconnected to form a sequential circuit. The storage elements are circuits that are capable of storing binary information. The binary information stored in these elements at any given time defines the state of the sequential circuit at that time. The sequential circuit receives binary information from its environment via inputs. These inputs together with the present state of the storage elements, determine the binary value of the outputs. They also determine the values used to specify the next state of the storage elements. The next state of the storage elements is also a function of the inputs and present state. Thus, a sequential circuit is specified by a time sequence of inputs, internal states, and outputs.

Sequential Circuit Design

The design of clocked sequential circuits starts from a set of specification and culminates in a logic diagram or a list of Boolean functions from which the logic diagram can be obtained. In contrast to a combinational circuit, which is fully specified by a truth table, a sequential circuit requires a state table for its specification. Thus, the first step in the design of a sequential circuit is to obtain a state table or an equivalent representation such as state diagram.

A synchronous sequential circuit is made up of flip-flops and combinational gates. The design of the circuit consists of choosing the flip-flops and finding a combinational circuit structure which, together with the flip flops, produces a circuit that fulfills the stated specifications. The number of flip-flops is determined from the number of states in the circuit; n flip-flops can represent up to 2^n binary states. The combinational circuit is derived from the state table by evaluating the flip-flop input equations and output equations. In fact, once the type and number of flip-flops are determined, the design process involves a transformation from a sequential circuit problem into a combinational circuit problem. In this way, the techniques of combinational circuit design can be applied.

Design Procedure

This following is a procedure for the design of sequential circuits

1. Obtain either the state diagram or the state table from the statement of the problem.

2. If only a state diagram is available from step 1, obtain the state table.

3. Assign binary codes to the states.

4. Derive the flip-flops input equations from the next-state entries in the encoded state table.

5. Derive output equations from the output entries in the state table.

6. Simplify the flip-flops input equations and output equation.

7. Draw the logic diagram with D flip-flops and combinational gates, as specified by the flip-flop input equation and output equation.

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