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# What is the excitation table? How it is derived for SR, D, JK and T Flip flops?

by | Last updated Feb 27, 2021 | Sequential Circuits

The excitation table has the minimum inputs, which will excite or trigger the flip flop to go from its present state to the next state. It is derived from the truth table.

Generally, the operation of each flip flop is explained with the help of the truth table. The truth table has all the input combinations, for which the flip flop reacts to produce the next state output.

The excitation table consists of two columns for present state(Qn) and next state(Qn+1) and one or two column for each inputs. The input columns depend on the type of the flip flop.

Now, let us look at the excitation table for each flip flops.

Page Contents

## SR flip flop

The excitation table of SR flip flop can be constructed from the information available in the truth table. In the diagram shown below, the first table shows the truth table, from which the excitation table is derived.

From the truth table, you can observe that when the present state is Qn = 0, the next state becomes Qn+1 = 0 for two input values S = 0, R = 0 and S = 0, R = 1. (It is shown in first and third rows with yellow color)

From this we can say that, for the state transition from Qn = 0 to Qn+1 = 0, the excitation inputs required are S = 0 and R = 0 or 1. It is filled in the first row(Yellow color) of the excitation table. Since R has two values(0 and 1), it is denoted as don’t care condition(x).

Similarly, when you observe the truth table, to obtain the next state output Qn+1 = 1 from the present state input Qn = 0, the required SR inputs are S = 1 and R = 0(shown in 5th row as pink color). Thus for state transition from 0 to 1, the excitation inputs require are S = 1 and R = 0. It is filled in the second row of the excitation table.

The state transition from present state Qn = 1 to the next state Qn+1 = 0 happens only when the inputs are S = 0 and R = 1(observed from 4th row in light green color). It is filled in the third-row of the excitation table.

In the same way, the state transition from Qn = 1 to Qn+1 = 1 happens at S = 0, R = 0 and S = 1, R = 0(shown in second and sixth row of the truth table). It is filled in the fourth row of the excitation table as Qn = 1, Qn+1 = 1 and S = x, R = 0. Here x denotes the don’t care conition, as it has two values(0 and 1).

## D flip flop

The excitation table of D flip flop is derived from its truth table. The excitation table is constructed in the same way as explained for SR flip flop.

Here, when you observe from the truth table shown below, the next state output is equal to the D input. So it is very simple to construct the excitation table.

For the state transition from Qn = 0 to Qn+1 = 0, the required excitation input is D = 0, regardless of Qn value. For transition of states from Qn = 0 to Qn+1 = 1, the input required to excite is D = 1.

The state transit from Qn = 1 to Qn+1 = 0 for the input D = 0. For the input D = 1, the state transition takes place from Qn = 1 to Qn+1 = 1.

All the above-mentioned state transitions for D flip flop from the present state(Qn) to the next state(Qn+1) for the corresponding excitation inputs are filled in the table to get the excitation table.

## JK flip flop

For JK flip flop, the excitation table is derived in the same way. From the truth table, for the present state and next state values Qn = 0 and Qn+1 = 0(indicated in the first and third row with yellow color), the inputs are J = 0 and K = 0 or 1. Since K input has two values, it is considered as don’t care condition(x).

Thus the state transition from Qn = 0 to Qn+1 = 0 takes place when J = 0, K = x. It is filled in the first row of the excitation table.

The state transition from present state Qn = 0 to the next state Qn+1 = 1 occur, when the inputs are either J = 1, K = 0 or J = 1, K = 1(indicated in the fifth and seventh row with pink color). Thus the excitation table is filled with datas Qn = 0, Qn+1 = 1, J = 1 and K = x.

Similarly, for the transition of the state from 1 to 0, the inputs are J = 0, K = 1 or J = 1, K = 1(indicated in the fourth and eighth row with ash color). So for this transition, the required inputs are J = x and K =1, as the value of J can be either 0 or 1.

For the state transition from Qn = 1 to Qn+1 = 1, the J input can be 0 or 1 but the K input remains at o(indicated in the second and sixth row with violet color). For this transition to occur, the excitation inputs are J = x and K = 0.

## T flip flop

The following figure shows the truth table of T flip flop, from which the excitation table is derived.

From the truth table, we can observe that, when T input is 0, there is no change in the state. So for the state transition from the present state to the next state, i.e., from Qn = 0 to Qn+1 = 0 and from Qn = 1 to Qn+1 = 1, the excitation input require is T = 0. It is filled in the first and the fourth row in the excitation table.

Similarly, from the truth table, we can also observe, when T = 1, the state of the flip flop toggles or complemented. Thus, for the transition of the state from either 0 to 1 or from 1 to 0, the excitation input is T = 1. It is filled in the second and the third row of the excitation table.

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