Conversion of JK Flip-Flop to T Flip-Flop

---

---

What is a JK Flip-Flop?

JK flip flop is also a 1-bit storage device having two inputs similar to SR flip flop, but it has inputs denoted by J and K instead of S and R. It has two outputs viz. Q (normal output) and Q' (inverted output). The clock signal is used for synchronization of the circuit.

The block diagram of the JK flip flop is shown in Figure-1 below.

The operation of the JK flip flop can be understood with the help of its truth table which is given below

The characteristic equation of the JK flip flop is given by,

$$\mathrm{Q_{n+1}\:=\:JQ_{n}^{'}+K'Q_{n}}$$

What is a T Flip-Flop?

T flip-flop, also called toggle flip flop, is a type of digital flip flop which has a single input specified by the letter T. It has two outputs namely Q and Q', where Q is the normal output and Q' is the complemented output.

The block diagram of T flip flop is shown in Figure-2.

The truth table of the T flip flop is depicted below.

From the truth table of the T flip flop, it is clear that when the input T is equal to 0, there is no change in the output of the flip flop. When T is equal to 1, the output of the T flip flop toggles.

The characteristics equation of the T flip flop is given by,

$$\mathrm{Q_{n+1}\:=\:T'Q_{n}+TQ_{n}^{'}}$$

After discussing the basics of JK flip flop and T flip flop, let us now discuss the conversion of JK flip flop into T flip flop.

Conversion of Flip-Flop

We can convert a one type of flip-flop into another type of flip-flop. The conversion process of flip-flops involves the following steps

Step 1 − Write the excitation table of the flip flops.

Step 2 − Simplify the excitation table with the help of Karnaugh Map (K-map).

Step 3 − Draw the required logic circuit diagram.

Now, let us convert the JK flip-flop into the T flip-flop.

Conversion of JK Flip-Flop into T Flip-Flop

The conversion of JK flip-flop into T flip-flop is done as per the following steps

Step 1 − The excitation table for the conversion of JK flip flop to T flip flop is given below.

Step 2 − The excitation table is simplified by using K-Map technique to obtain the expression of inputs as follows −

The K-map simplification for the input J is,

J = T

The K-map simplification for the input K is,

K = T

Step 3 − The logic diagram of the T flip-flop using JK flip flop is shown in Figure-3 below.

In this way, we can convert JK flip flop into T flip flop.