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Excitation table

The excitation table of a sequential circuit is an extension of the state table. This extension consists of a list of flip-flop input excitations that will cause the required state transitions. The flip-flop input conditions are a function of the type of flip-flop used. If we employ JK flip-flops, we need columns for the j and K inputs of each flip-flop. We denote the inputs of flip-flop A by JA and KA, and those of flip-flop B by jB and KB.

The excitation table for the JK flip-flop specified in Table 1-3 is now u~ed to derive the excitation table of the sequential circuit. For example, in the first row of Table 1-5, we have a transition for flip-flop A from 0 in the present state to 0 in the next state. In Table 1-3 we find that a transition of states from Q(t) = 0 to Q(t + 1) = 0 in a JK flip-flop requires that input J= 0 and input K = X. So 0 and x are copied in the first row under JA and KA, respectively. Since the first row also shows a transition for flip-flop B from 0 in the present state to 0 in the next state, 0 and x are copied in the first row under JB and KB. The second row of Table 1-5 shows a transition for flip-flop B from 0 in the present state to 1 in the next state. From Table 1-3 we find that a transition from Q(t) = 0 to Q(t + 1) = 1 requires that input j= 1 and input K = X. So 1 and x are copied in the second row under JB and KB, respectively. This process is continued for each row of the table and for each flip-flop, with the input conditions as specified in Table 1-3 being copied into the proper row of the particular flip-flop being considered.

Table 1-3

Table 1-5

Let us now consider the information available in an excitation table such as Table 1-5. We know that a sequential circuit consists of a number of flip-flops and a combinational circuit. From the block diagram of Fig. 1-24, we note that the outputs of the combinational circuit must go to the four flip-flop inputs J,,, KA, JB, and KB. The inputs to the combinational circuit are the external input x and the present-state values of flip-flops A and B. Moreover, the Boolean functions that specify a combinational circuit are derived from a truth table that shows the input-output relationship of the circuit. The entries that list the combinational circuit inputs are specified under the "present state" and "input" columns in the excitation table. The combinational circuit outputs are specified under the "flip-flop inputs" columns. Thus an excitation table transforms a state diagram to a truth table needed for the design of the combinational circuit part of the sequential circuit.

Figure 1-24

Figure 1-28

The simplified Boolean functions for the combinational circuit can now be derived. The inputs are the variables A, B, and x. The outputs are the variables JA, KA, JB, and KB. The information from the excitation table is transferred into the maps of Fig. 1-28, where the four simplified flip-flop input equations are derived:

JA = BX K,q = BX

JB=x KB =x

The logic diagram is drawn in Fig. 1-29 and consists of two JK flip-flops and an AND gate. Note that inputs j and K determine the next state of the counter when a clock signal occurs. If both j and K are eoualto Q, a clocks signal will have no effect; that is, the state of the flip-flops will not change. Thus when x = 0, all four inputs of the flip-flops are equal to 0 and the state of the flip-flops remains unchanged even though clock pulses are applied continuously.