Digital Electronics Lab (Pattern 2015)

Assignment No: 7 Group B

R C O T Dated
(2) (4) (2) (2) Sign

 Title: Flip-flop.

 Objective: Conversion of Flip-flop.

 Problem Statement: Conversion from one type of flip-flop to another type of flip-flop.
.
 Hardware & Software Requirement’s :

Digital Trainer Kit, IC 7476, IC 7474, IC 7408, IC 7432 & IC 7404.patch cords, +5V power
supply.

Theory:

A Flip – flop is an electronic device which is having two stable states and a feedback
path which is used to store 1 – bit of information by using the clock signal as input. Latches
are also used to do the same task except that they do not use a clock signal. Hence to say it
simply, “Flip – flops are clocked latches”. They are used to store only 1 – bit of information
and it can remain in the same state until the clock signal affects the state of the input.

There are four types of flip – flops

 SR flip – flop
 D flip – flop
 JK flip – flop
 T flip-flop

Generally, JK flip – flops and D flip – flops are the most widely used flip – flops. And so
their availability in the form of integrated circuits (IC’s) is abundant. Numerous varieties of
JK flip – flop and D flip – flop are available in the semiconductor market. The less popular
SR flip – flop and T flip – flop are not available in the market as integrated circuits (IC’s)
(even though a very few number of SR flip – flops are available as IC’s, they are not
frequently used).

There might be a situation where the less popular flip – flops are required in order to
implement a logic circuit. In order use the less popular flip – flops, we will convert one type
of flip – flop into another. Some of the most common flip – flop conversions are:-

1. SR Flip – flop to JK Flip – flop

2. SR Flip – flop to D Flip – flop
3. SR Flip – flop to T Flip – flop

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4. JK Flip – flop to SR Flip – flop

5. JK Flip – flop to D Flip – flop
6. JK Flip – flop to T Flip – flop
7. D Flip – flop to SR Flip – flop
8. D Flip – flop to JK Flip – flop
9. D Flip-flop to T Flip-flop

 General model used to convert one type of FF to other

In order to convert one flip – flop to other type of flip – flop, we should design a
combinational circuit that is connected to the actual flip – flop. Inputs to combinational
circuit are same as the inputs of the desired flip – flop. Outputs of combinational circuit are
same as the inputs of the available flip – flop. So the output of combinational circuit is
connected to the input of our available flip – flop. The pictorial representation of the same is
shown below.

1. SR Flip – flop to JK Flip – flop

Here we are required to convert the SR flip – flop to JK flip – flop. So first we design a
combinational circuit with J and K as its inputs and we connect its output to the input of our
available flip flop i.e. an SR flip – flop. So its outputs are same as that of JK flip – flop.

Let’s write a truth table for the two inputs, J and K. For two inputs along with the Q P, we get
8 possible combinations in truth table. Consider that when the two inputs are applied, Q P is
the present state and QN is the next state. For every combination of J, K , QP , we find the
corresponding QN state. Here QN will give the state values that to which the output of the JK
flip – flop will jump after the present state, on applying the inputs. Now we write all the
combinations of S and R in the truth table to get each QN value from corresponding QP. Hence
these are the values of S and R that are used to change the state of flip flop from Q P to QN.

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The conversion table:-

From SR flip – flop to JK flip – flop is shown below.

F/F PRESENT NEXT OUTPUTS

INPUTS STATE STATE

J K Qn Qn+1 S R

0 0 0 0 0 X

0 1 0 0 0 X

1 0 0 1 1 0

1 1 0 1 1 0

0 1 1 0 0 1

1 1 1 0 0 1

0 0 1 1 X 0

1 0 1 1 X 0

In order to deduce the Boolean equations of S and R in terms of J and K, we use Karnaugh
maps from the above table.

The K – map:-

The Boolean equation for S is S = JQP

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.K map :-

The Boolean equation for R is R = KQP.

The Boolean equations of S and R in terms of J, K and QP are: S = JQ’P and R = KQP

The logic diagram:-

JK flip – flop implemented from SR flip – flop is shown below. Here J and K are external
inputs to the circuit. S and R are the outputs of the designed combinational outputs.

2. SR Flip – flop to D Flip – flop

Converting the SR flip – flop to D flip – flop involves connecting the Data input (D) to the
SR flip – flop. Here the Data input is connected directly to the S input and the inverted D
input (using a NOT gate) is connected to R input. The same can be derived from truth table
and corresponding K – maps. S and R are the inputs of the flip – flop while QP and QP’ are the
present state and its complementary outputs of the flip – flop. We should design a
combinational circuit such that its input is D and outputs are S and R. Outputs from the
combinational circuit S and R are connected as inputs to the SR flip – flop.

The truth table for conversion of SR flip – flop to D flip – flop is shown below. The truth
table is drawn for the D input and QP output to find the corresponding QN output.

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Digital Electronics Lab (Pattern 2015)

The conversion table:-

F/F PRESENT NEXT OUTPUTS

INPUTS STATE STATE

D Qn Qn+1 S R

0 0 0 0 X

1 0 1 1 0

0 1 0 0 1

1 1 1 X 0

The K – map:-

The Boolean equation of S is S = D.

The K – map:-

The Boolean equation of R is R = D.

The Boolean equation for S and R in terms of D are: S = D and R = D. The logic diagram of
implementation of D flip – flop from SR flip – flop is shown below.

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The logic diagram:-

3. SR Flip – flop to T Flip – flop

The combinational circuit required in order to convert an SR flip – flop to T flip – flop can be
constructed from the truth table. The input to the combinational circuit is T (Toggle input)
and the outputs of the combinational circuit are S and R. Here S and R are the inputs of the
actual flip – flop. The output and the complement output of the flip – flop are QP and Q’P. The
truth table consists of combinations of T and QP in order to get QN where QN is the next state
output of the flip – flop. The combinations of S and R which results in QN are also tabulated
in the same table.

The conversion table:-

F/F PRESENT NEXT OUTPUT

STATE STATE
INPUT

T Qn Qn+1 S R

0 0 0 0 X

1 0 1 1 0

1 1 0 1 0

0 1 1 X 0

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The K – map:-

The Boolean equation of S is S = TQP.

The K – map:-

The Boolean equation for R is R = TQP.

The Boolean equations of S and R are: S = TQP and R = TQP. The logic circuit for the
implementation of T flip – flop from SR flip – flop is shown below.

The logic diagram:-

JK Flip – flop to other Flip – flops

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4. JK Flip – flop to SR Flip – flop

To convert the JK flip – flop into SR flip – flop, we design a combinational circuit with S and
R as its inputs and J and K as its outputs. Here J and K are the inputs of actual flip – flop. So
for making this conversion, we should obtain the J &amp, K values in terms of S, R and Q P.
Consider that when the two inputs S and R are applied, QP is the present state output and QN
is the next state output. For each combination of S, R and QP, we find the corresponding QN
state. Now, we prepare a truth table for the possible combination of the inputs S, R and Q P.
We can make 8 possible combinations for the two S and R inputs along with Q P. For each
combination of S and R inputs and QP we find the corresponding value of QN. Now we write
all the values of J and K in the truth table to get each Q N value from corresponding QP. In SR
flip – flop, when the 2 inputs are high i.e. S = 1 & R = 1,

The conversion table:-

F/F INPUTS PRESENT NEXT OUT PUT

STATE STATE

S R Qn Qn+1 J K

0 0 0 0 0 X

0 1 0 0 0 X

1 0 0 1 1 X

1 0 0 1 1 X

0 1 1 0 X 1

0 1 1 0 X 1

0 0 1 1 X 0

1 0 1 1 X 0

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The K – map:-

The Boolean equation for J is J = S.

The K – map:-

The Boolean equation for K is K = R.

The Boolean equations for J and K in terms of S and R are: J = S and K = R. Hence, there is
no requirement of any additional combinational circuit as S and R inputs are same as J and K
inputs. The logic circuit of implementing SR flip – flop from JK flip – flop is shown below.

The logic diagram:-

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5. JK Flip – flop to D Flip – flop

Converting the JK flip – flop to D flip – flop, involves in connecting the Data input (D) to the
JK flip – flop through a combinational circuit. Here the Data input is connected directly to the
J input and the inverted D input (using a NOT gate) is connected to K input.

The design of the combinational circuit should be in such a way that D is its input and J & K
are its outputs. The outputs of the combinational circuit J & K are connected as inputs to the
flip – flop. QP is the present state output of the flip – flop. Q’P is its complementary and QN
is the next state output. The truth table for converting JK flip – flop to D flip – flop is shown
below.

The conversion table:-

The K – maps in order to solve for J and K in terms of D and QP are shown below.

F/F PRESENT NEXT OUTPUTS

INPUTS STATE STATE

D Qn Qn+1 J K

0 0 0 X 0

1 0 1 X 1

0 1 0 0 X

1 1 1 1 X

K – Map:-

The Boolean equation for J is J = D.

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K – Map:-

The Boolean equation for K is K = D.

The Boolean equations for J and K are J = D and K = D’. The logic diagram that represents
the implementation of D flip – flop from JK flip – flop is shown below.

The logic diagram:-

6. JK Flip – flop to T Flip – flop

Converting the JK flip – flop to T flip flop, involves in connecting the Toggle input (T)
directly to the J and K inputs. So toggle (T) will be the external input to the combinational
circuit. Its output is connected to the Input of actual flip – flop (JK flip – flop).

We prepare a truth table by considering 4 possible combinations of the Toggle input (T)
along with QP. QP and QP’ are the present state output and its complement output of the flip –
flop. QN is the next state output. The truth table is drawn for the T input and QP output to find
the corresponding QN output. The truth table is shown below.

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The conversion table:-

F/F PRESENT NEXT OUTPUT

STATE STATE
INPUT

T Qn Qn+1 J K

0 0 0 0 X

1 0 1 1 X

1 1 0 X 1

0 1 1 X 0

The K – map:-

The Boolean equation for J is J = T.

The K – map:-

The Boolean equation for K is K = T.

The logic circuit for converting JK flip – flop to T flip – flop is shown below.

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The logic diagram:-

D Flip – flop to other Flip – flops

I). D Flip – flop to SR Flip – flop

To convert the D flip – flop into SR flip – flop, a combinational circuit should be constructed
where its inputs are S and R and its output is D. Here Data (D) is the input of actual flip –
flop. The truth table is drawn with the 8 possible combinations of the two inputs S & R and
QP. QP and QP’ are the present state and its complement outputs of the flip – flop.

When the two inputs of SR flip – flop are high i.e. S = 1 and R = 1, then the QP value is
invalid and hence the Data (D) inputs for the corresponding Q P’s are considered as ‘Don’t
cares’.
The truth table for S, R and QP in order to get QN is shown below. It also consists of D inputs
in order to get the same QN.

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The Conversion Tabel:-

F/F INPUT PRESENT NEXT OUT

STATE STATE PUT

S R Qn Qn+1 D

0 0 0 0 0

0 1 0 0 0

1 0 0 1 1

0 1 1 0 0

0 0 1 1 1

1 0 1 1 1

The K – map for solving the equation of D in terms of S, R and Q P.

K MAP:-

The Boolean equation of D is D = S + RQP.

The logic diagram using this equation to implement an SR flip – flop from D flip – flop is
shown below.

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The logic diagram:-

II). D Flip – flop to JK Flip – flop

When we need to convert the D flip – flop into JK flip – flop, J and K are the inputs of the
combinational circuit with D as its output. Here Data (D) is the input of actual flip – flop. The
truth table is drawn with the 8 possible combinations of the two inputs J & K along with Q P.
QP and QP’ are the present state and its complement outputs of the flip – flop.

The truth table consists of combinations of J, K and QP in order to get QN. Here QN is the next
state output of the flip – flop. The truth table also consists of D inputs that lead to Q N output.

The conversion table:-

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F/F INPUT PRESENT NEXT OUT

STATE STATE PUT

J K Qn Qn+1 D

0 0 0 0 0

0 1 0 0 0

1 0 0 1 1

1 1 0 1 1

0 1 1 0 0

1 1 1 0 0

0 0 1 1 1

1 0 1 1 1

The K – map:-

D = JQ’P + K’QP.

The Boolean equation of D deduced from the above K – map is the logical representation of
implementing JK flip – flop from D flip – flop is shown below.

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The logic diagram:-

III). D Flip – flop to T Flip – flop

When we need to convert the D flip – flop into T flip – flop, T (Toggle input) is the input of
the combinational circuit with D as its output. Here Data (D) is the input of actual flip – flop.
The truth table is drawn with the 4 possible combinations of the input T along with Q P. QP
and QP’ are the present state and its complement outputs of the flip – flop.

The truth table consists of combinations of T and QP in order to get QN. Here QN is the next
state output of the flip – flop. The truth table also consists of D inputs that lead to Q N output.

The conversion table is shown below.

The Conversion Table:-

F/F PRESENT NEXT OUTPUT

STATE STATE
INPUT

T Qn Qn+1 D

0 0 0 0

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1 0 1 1

1 1 0 0

0 1 1 1

The K – map:-

D = TQP + TQP.

The Boolean equation of D in terms of T and QP is The logic circuit for implementing T flip –
flop with D flip – flop is shown below.

The logic diagram:-

Application of Flip-flop:
1. Elimination of keyboard de-bounce.
2. As a memory element.
3. In a various types of Registers.
4. In counters/timers.
5. As a delay element.

Outcomes: Successfully implement the conversion of flip-flop.

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Digital Electronics Lab (Pattern 2015)

University Asked Conversions:

1. SR Flip – flop to JK Flip – flop

2. SR Flip – flop to D Flip – flop
3. SR Flip – flop to T Flip – flop
4. JK Flip – flop to SR Flip – flop
5. JK Flip – flop to D Flip – flop
6. JK Flip – flop to T Flip – flop

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