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- Conversion of Flip-Flops
- D Flip-Flops
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Digital Electronics - Conversion of Flip-Flops
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.
| Present State | Next State | SR Flip-Flop Inputs | D flip-flop input | JK Flip-Flop Inputs | T Flip-Flop Input | ||
|---|---|---|---|---|---|---|---|
| Q(t) | Q(t+1) | S | R | D | J | K | T |
| 0 | 0 | 0 | x | 0 | 0 | x | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 | x | 1 |
| 1 | 0 | 0 | 1 | 0 | x | 1 | 1 |
| 1 | 1 | x | 0 | 1 | x | 0 | 0 |
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
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 Input | Present State | Next State |
|---|---|---|
| D | Q(t) | Q(t + 1) |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
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 Input | Present State | Next State | SR Flip-Flop Inputs | |
|---|---|---|---|---|
| D | Q(t) | Q(t + 1) | S | R |
| 0 | 0 | 0 | 0 | x |
| 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 1 | x | 0 |
From the above table, we can write the Boolean functions for each input as below.
$$\mathrm{S \: = \: m_{2} \: + \: d_{3}}$$
$$\mathrm{R \: = \: m_{1} \: + \: d_{0}}$$
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
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 Input | Present State | Next State |
|---|---|---|
| T | Q(t) | Q(t + 1) |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
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 Input | Present State | Next State | D Flip-Flop Input |
|---|---|---|---|
| T | Q(t) | Q(t + 1) | D |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
From the above table, we can directly write the Boolean function of D as below.
$$\mathrm{D \: = \: T \: \oplus \: Q \: \left ( t \: \right )}$$
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
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 Input | Present State | Next State |
|---|---|---|
| T | Q(t) | Q(t + 1) |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
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 Input | Present State | Next State | JK Flip-Flop Inputs | |
|---|---|---|---|---|
| T | Q(t) | Q(t + 1) | J | K |
| 0 | 0 | 0 | 0 | x |
| 0 | 1 | 1 | x | 0 |
| 1 | 0 | 1 | 1 | x |
| 1 | 1 | 0 | x | 1 |
From the above table, we can write the Boolean functions for each input as below.
$$\mathrm{J \: = \: m_{2} \: + \: d_{1} \: + \: d_{3}}$$
$$\mathrm{K \: = \: m_{3} \: + \: d_{0} \: + \: d_{2}}$$
We can use 2 variable K-Maps for getting simplified expressions for these two inputs. The k-Maps for J & K are shown below.
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 doesnt 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
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 Input | Present State | Next State | T Flip-Flop Input | |
|---|---|---|---|---|
| D | Q(t) | Q(t + 1) | T | |
| 0 | 0 | 0 | 0 | |
| 0 | 1 | 0 | 1 | |
| 1 | 0 | 1 | 1 | |
| 1 | 1 | 1 | 0 | |
From the above table, we can directly write the Boolean function of T as below.
$$\mathrm{T \: = \: D \: \oplus \: Q \left ( t \right )}$$
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.