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 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
Qt$�$	Qt+1$�+1$	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.

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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 input	Present State	Next State
D	Qt$�$	Qt+1$�+1$
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	Qt$�$	Qt+1$�+1$	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.

S=m2+d3$$�={�}_2+{�}_3$$

R=m1+d0$$�={�}_1+{�}_0$$

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

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 Qt$�$ & Qt$�$'. 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 input	Present State	Next State
T	Qt$�$	Qt+1$�+1$
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	Qt$�$	Qt+1$�+1$	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.

D=T⊕Q(t)$$�=�\oplus �\left(�\right)$$

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 Qt$�$. So, the overall circuit has single input, T and two outputs Qt$�$ & Qt$�$’. 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 input	Present State	Next State
T	Qt$�$	Qt+1$�+1$
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	Qt$�$	Qt+1$�+1$	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.

J=m2+d1+d3$$�={�}_2+{�}_1+{�}_3$$

K=m3+d0+d2$$�={�}_3+{�}_0+{�}_2$$

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

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 Qt$�$ & Qt$�$’. 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 input	Present State	Next State	T flip-flop input
D	Qt$�$	Qt+1$�+1$	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.

T=D⊕Q(t)$$�=�\oplus �\left(�\right)$$

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