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

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

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

SR flip flop

The excitation table of the 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 Q_n = 0, the next state becomes Q_n+1 = 0 for two input values S = 0, R = 0 and S = 0, R = 1. (It is shown in the first and third rows with yellow color)

From this we can say that, for the state transition from Q_n = 0 to Q_n+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 a don’t care condition(x).

Similarly, when you observe the truth table, to obtain the next state output Q_n+1 = 1 from the present state input Q_n = 0, the required SR inputs are S = 1 and R = 0(shown in the 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 the present state Qn = 1 to the next state Qn+1 = 0 happens only when the inputs are S = 0 and R = 1(observed from the 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 Q_n = 1 to Q_n+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 Q_n = 1, Q_n+1 = 1 and S = x, R = 0. Here x denotes the don’t care condition, as it has two values(0 and 1).

D flip flop

The excitation table of the D flip-flop is derived from its truth table. The excitation table is constructed in the same way as explained for the 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 Q_n = 0 to Q_n+1 = 0, the required excitation input is D = 0, regardless of Q_n value. For transition of states from Q_n = 0 to Q_n+1 = 1, the input required to excite is D = 1.

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

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

JK flip flop

For the 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 a don’t care condition(x).

Thus the state transition from Q_n = 0 to Q_n+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 Q_n = 0 to the next state Q_n+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 Q_n = 0, Q_n+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 Q_n = 1 to Q_n+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 the T flip flop, from which the excitation table is derived.

From the truth table, we can observe that, when the 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 Q_n = 0 to Q_n+1 = 0 and from Q_n = 1 to Q_n+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 is complimented. 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 third rows of the excitation table.