Sequential Circuit Design

Sequential Circuit
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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Combinational Circuit Design

Combinational Circuit Logic circuits for digital systems may be combinational or sequential. A combinational circuit consists of logic gates whose outputs at any time are determined by combining the values of the applied inputs using logic operations. A combinational circuit performs an operation that can be specified logically by a set of Boolean expression. In addition to using logic gates, sequential circuits employ elements that store bit values. Sequential circuit outputs are a function of inputs and the bit value in storage elements. These values, in turn, are a function of previously applied inputs and stored values. As a consequence, the outputs of a sequential circuit depend not only on the presently applied values of the inputs, but also on pas inputs, and the behavior of the circuit must be specified by a sequence in time of inputs and internal stored bit values. A combinational circuit consists of input variables, output variables, logic gates and interconnections. The interconnected logic gates accept signals from the inputs and generate signals at the output. The n input variables come from the environment of the circuit, and the m output variables are available for use by the environment. Each input and output variable exists physically as a binary signal that represents logic 1 or logic 0.

For n input variables, there are 2^n possible binary input combinations. For each binary combination of the input variables, there is one possible binary value on each output. Thus, a combinational circuit can be specified by a truth table that lists the output values for each combination of the input variables. A combinational circuit can also be described by m Boolean function, one for each output variable. Each such function is expressed as function of the n input variables.

Combinational Circuit Design

The design of combinational circuit starts from a specification of the problem and culminates in a logic diagram or set of Boolean equations from which the logic diagram can be obtained. The procedure involves the following steps:

1. From the specifications of the circuit, determine the required number of inputs and outputs, and assign a letter symbol to each.

2. Derive the truth table that defines the required relation ship between inputs and outputs.

3. Obtain the simplified Boolean functions of each outputs as function of the input variables.

4. Draw the logic diagram.

5. Verify the correctness of the design.

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