The T flip-Flop has one input. When the input is 1 then its output toggles. Let’s say the present state of the flip-flop is Qn. So, with T = 1, if Qn = 0 then in the next state, the output of the flip-flop Qn+1 will become 0. And similarly currently if Qn is 1 then in the next state, the output will become 0.

With T = 1 input, since the output of the flip-flop toggles at every clock pulse, so it is known as T flip-flop. When T = 0, then the flip-flop will remain in the same state. The symbol and the truth table of the T flip-flop is shown below.

The symbol which is shown above is the symbol of the positive edge triggered flip-flop. The triangle in the symbol indicates that, the flip-flop responds to the input only at the rising edge of the clock. Similarly, the symbol of the negative edge triggered ?T flip-flop is shown below.

Characteristic Equation of T Flip-Flop

The characteristic equation of the flip-flop is the algebraic representation of the next state of the Flip-Flop (Q_n+1) in terms of the present state (Q_n) and the current input (T).

That means, here the input variables are Q_n and T, while the output is Q_{n+1 .}

From the truth table, as you can see, the output Q _n+1 is 1 for two different input combination of Q_n and T.

Let’s write down these two input combinations in the K-map, and let’s try to simplify the Boolean expression.

From the K-map, the two minterms are T Q_n ‘ and T ‘ Q_n . That means the characteristic equation of the T flip-flop is

Excitation Table of T Flip-Flop

The excitation table of the flip-flop shows the required excitation to the flip-flop, or the required input to the flip-flop, to go from the given state to the next particular state. For the T input, when T = 0 then the flip-flop remains in the same state and when T = 1 then the output of the flip-flop toggles at every clock pulse. The excitation table of the T flip-flop is shown below.

Circuit Diagram of T Flip-Flop

With the little modification, the JK flip-flop can be used as a T flip-flop. The truth table of the T flip-flop is shown below.

As you can see form the truth table, when both inputs of JK flip-flop are 0 then it hold the current state. And when its both inputs are 1, then the output of the flip-flop toggles. That means by connecting both inputs of the JK flip-flop together, it can be used as a T flip-flop.

That means with the little modification in the circuit of the JK flip-flop, it can be used as a T flip-flop. The circuit of the T flip-flop is shown below.

For more information, check this video on T flip-Flop.

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