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Digital Circuits - Conversion of Flip-Flops

 

Digital Circuits - Conversion of Flip-Flops


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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  of given flip-flop for each combination of present state and next state. The excitation table for all flip-flops is shown below.

Present StateNext StateSR flip-flop inputsD flip-flop inputJK flip-flop inputsT flip-flop input
QQ+1SRDJKT
000x00x0
011011x1
10010x11
11x01x00
  • 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.

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SR Flip-Flop to other Flip-Flop Conversions

Following are the three possible conversions of SR flip-flop to other flip-flops.

  • 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.

D flip-flop inputPresent StateNext State
DQQ+1
000
010
101
111

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.

D flip-flop inputPresent StateNext StateSR flip-flop inputs
DQQ+1SR
0000x
01001
10110
111x0

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

=2+3

=1+0

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

Conversion of Flip-Flop

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

Circuit Diagram of D Flip-Flop

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 & Q'. Hence, it is a D flip-flop. Similarly, you can do other two conversions.

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D Flip-Flop to other Flip-Flop Conversions

Following are the three possible conversions of D flip-flop to other flip-flops.

  • 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.

T flip-flop inputPresent StateNext State
TQQ+1
000
011
101
110

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.

T flip-flop inputPresent StateNext StateD flip-flop input
TQQ+1D
0000
0111
1011
1100

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

=()

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.

Circuit Diagram of T Flip-Flop

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. So, the overall circuit has single input, T and two outputs Q & Q’. Hence, it is a T flip-flop. Similarly, you can do other two conversions.

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JK Flip-Flop to other Flip-Flop Conversions

Following are the three possible conversions of JK flip-flop to other flip-flops.

  • 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.

T flip-flop inputPresent StateNext State
TQQ+1
000
011
101
110

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.

T flip-flop inputPresent StateNext StateJK flip-flop inputs
TQQ+1JK
0000x
011x0
1011x
110x1

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

=2+1+3

=3+0+2

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

K Map for J and K

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

Circuit Diagram of T Flip-Flop with JK Flip-Flop

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 & Q’. Hence, it is a T flip-flop. Similarly, you can do other two conversions.

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T Flip-Flop to other Flip-Flop Conversions

Following are the three possible conversions of T flip-flop to other flip-flops.

  • 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.

D flip-flop inputPresent StateNext StateT flip-flop input
DQQ+1T
0000
0101
1011
1110

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

=()

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.

T Flip-Flop circuit Diagram

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. So, the overall circuit has single input, D and two outputs Q & Q’. Hence, it is a D flip-flop. Similarly, you can do other two conversions

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