Conversion of SR Flip-Flop to JK Flip-Flop

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What is SR Flip-Flop?

SR flip-flop is a simple 1-bit storage element which has two inputs namely S and R, and two outputs, i.e. Q and Q'. Where, S specifies Set input and R specifies Reset input. The output Q is the normal output and the Q' is the complemented or inverted output. In addition to SR inputs, the SR flip flop also has a clock input which is used for triggering the circuit.

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

The operation of the SR flip flop can be analyzed using its truth table, which is given below.

Here, Q_n+1 is the next state, and Qn is the present state of the output.

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

$$\mathrm{Q_{n+1} \: = \: S+R'Q_{n}}$$

What is 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-2 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,

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

After discussing about the basics of SR flip flop and JK flip flop. Let us now discuss the conversion of SR flip flop into JK 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 SR flip-flop into the JK flip-flop.

Conversion of SR Flip-Flop into JK Flip-Flop

As per the steps of conversion of flip-flops, the conversion process of SR flip-flop into JK flip-flop is described below.

Step 1 − The excitation table for the conversion of SR flip-flop into JK flip-flop is given below

Step 2 − Simplify the excitation for input expressions by using K-Map −

The K-Map simplification for S is,

S = JQ_n'

The K-map simplification for R is,

R = KQ_n

Step 3 − Finally, draw the logic diagram of JK flip flop by using SR flip flop, which is shown in figure-3 below.

In this way, we can convert the SR flip-flop into JK flip-flop.