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Design Procedure

The design of sequential circuits follows the outline described in the preceding example. The behavior of the circuit is first formulated in a state diagram. The number of flip-flops needed for the circuit is determined from the number of bits listed within the circles of the state diagram. The number of inputs for the circuit is specified along the directed lines between the circles. We then assign letters to designate all flip-flops and input and output variables and proceed to obtain the state table.

For m flip-flops and n inputs, the state table will consist of m columns for the present state, n columns for the inputs, and m columns for the next state. The number of rows in the table will be up to 2' +" one row for each binary combination of present state and inputs. For each row we list the next state as specified by the state diagram. Next, the flip-flop type to be used in the circuit is chosen. The state table is then extended into an excitation table by including columns for each input of each flip-flop. The excitation table for the type of flip-flop in use can be found in Table 1-3. From the information available in this table and by inspecting present state-to-next state transitions in the state table, we obtain the information for the flop-flop input conditions in the excitation table.

Table 1-3

The truth table for the combinational circuit part of the sequential circuit is available in the excitation table. The present-state and input columns constitute the inputs in the truth table. The flip-flop input conditions constitute the outputs in the truth table. By means of map simplification we obtain a set of flip-flop input equations for the combinational circuit. Each flip-flop input equation specifies a logic diagram whose output must be connected to one of the flip-flop inputs. The combinational circuit so obtained, together with the flip-flops, constitutes the sequential circuit. The outputs of flip-flops are often considered to be part of the outputs of the sequential circuit. However, the combinational circuit may also contain external outputs. In such a case the Boolean functions for the external outputs are derived from the state table by combinational circuit design techniques. A set of flip-flop input equations specifies a sequential circuit in algebraic form. The procedure for obtaining the logic diagram from a set of flip-flop input equations is a straightforward process. First draw the flip-flops and label all their inputs and outputs. Then draw the combinational circuit from the Boolean expressions given by the flip-flop input equations. Finally, connect outputs of flip-flops to inputs in the combinational circuit and outputs of the combinational circuit to flip-flop inputs.

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