Conversion of Flip-Flops | Digital Logic - Computer Science Engineering (CSE) PDF Download

In previous chapter, we discussed the four flip-flops, namely SR flip-flop, D flip-flop, JK flip-flop & T flip-flop. We can convert one flip-flop into the remaining three flip-flops by including some additional logic. So, there will be total of twelve flip-flop conversions.
Follow these steps for converting one flip-flop to the other.

• Consider the characteristic table of desired flip-flop.
• Fill the excitation values inputs of given flip-flop for each combination of present state and next state. The excitation table for all flip-flops is shown below.
  
• Get the simplified expressions for each excitation input. If necessary, use Kmaps for simplifying.
• Draw the circuit diagram of desired flip-flop according to the simplified expressions using given flip-flop and necessary logic gates.

Now, let us convert few flip-flops into other. Follow the same process for remaining flipflop conversions.

SR Flip-Flop to other Flip-Flop Conversions

• SR flip-flop to D flip-flop
• SR flip-flop to JK flip-flop
• SR flip-flop to T flip-flop

SR flip-flop to D flip-flop conversion
Here, the given flip-flop is SR flip-flop and the desired flip-flop is D flip-flop. Therefore, consider the following characteristic table of D flip-flop.

We know that SR flip-flop has two inputs S & R. So, write down the excitation values of SR flip-flop for each combination of present state and next state values. The following table shows the characteristic table of D flip-flop along with the excitation inputs of SR flip-flop.

From the above table, we can write the Boolean functions for each input as below.

S = m₂ + d₃
R = m₁ + d₀

We can use 2 variable K-Maps for getting simplified expressions for these inputs. The k-Maps for S & R are shown below.

So, we got S = D & R = D' after simplifying. The circuit diagram of D flip-flop is shown in the following figure.

This circuit consists of SR flip-flop and an inverter. This inverter produces an output, which is complement of input, D. So, the overall circuit has single input, D and two outputs Q t & Q t'. Hence, it is a D flip-flop. Similarly, you can do other two conversions.

D Flip-Flop to other Flip-Flop Conversions

• D flip-flop to T flip-flop
• D flip-flop to SR flip-flop
• D flip-flop to JK flip-flop

D flip-flop to T flip-flop conversion
Here, the given flip-flop is D flip-flop and the desired flip-flop is T flip-flop. Therefore, consider the following characteristic table of T flip-flop.

We know that D flip-flop has single input D. So, write down the excitation values of D flip-flop for each combination of present state and next state values. The following table shows the characteristic table of T flip-flop along with the excitation input of D flip-flop.

From the above table, we can directly write the Boolean function of D as below.

D = T ⊕ Q(t)

So, we require a two input Exclusive-OR gate along with D flip-flop. The circuit diagram of T flip-flop is shown in the following figure.

This circuit consists of D flip-flop and an Exclusive-OR gate. This Exclusive-OR gate produces an output, which is Ex-OR of T and Q t. So, the overall circuit has single input, T and two outputs Q t & Q t’. Hence, it is a T flip-flop. Similarly, you can do other two conversions.

JK Flip-Flop to other Flip-Flop Conversions

• JK flip-flop to T flip-flop
• JK flip-flop to D flip-flop
• JK flip-flop to SR flip-flop

JK flip-flop to T flip-flop conversion
Here, the given flip-flop is JK flip-flop and the desired flip-flop is T flip-flop. Therefore, consider the following characteristic table of T flip-flop.

We know that JK flip-flop has two inputs J & K. So, write down the excitation values of JK flip-flop for each combination of present state and next state values. The following table shows the characteristic table of T flip-flop along with the excitation inputs of JK flipflop.

From the above table, we can write the Boolean functions for each input as below.

J = m₂ + d₁ + d₃
K = m₃ + d₀ + d₂

We can use 2 variable K-Maps for getting simplified expressions for these two inputs. The k-Maps for J & K are shown below.

So, we got, J = T & K = T after simplifying. The circuit diagram of T flip-flop is shown in the following figure.

This circuit consists of JK flip-flop only. It doesn’t require any other gates. Just connect the same input T to both J & K. So, the overall circuit has single input, T and two outputs Q t & Q t’. Hence, it is a T flip-flop. Similarly, you can do other two conversions.

T Flip-Flop to other Flip-Flop Conversions

• T flip-flop to D flip-flop
• T flip-flop to SR flip-flop
• T flip-flop to JK flip-flop

T flip-flop to D flip-flop conversion
Here, the given flip-flop is T flip-flop and the desired flip-flop is D flip-flop. Therefore, consider the characteristic table of D flip-flop and write down the excitation values of T flip-flop for each combination of present state and next state values. The following table shows the characteristic table of D flip-flop along with the excitation input of T flip-flop.

From the above table, we can directly write the Boolean function of T as below.

T = D⊕Q(t)

So, we require a two input Exclusive-OR gate along with T flip-flop. The circuit diagram of D flip-flop is shown in the following figure.
This circuit consists of T flip-flop and an Exclusive-OR gate. This Exclusive-OR gate produces an output, which is Ex-OR of D and Q t. So, the overall circuit has single input, D and two outputs Q t & Q t’. Hence, it is a D flip-flop. Similarly, you can do other two conversions.