This document discusses sequential circuits and flip-flop conversions. It begins by defining the characteristic equation of a flip-flop as the equation that expresses the next state (Qn+1) in terms of the present state (Qn) and inputs. It then provides the characteristic equations for SR, JK, T, and D flip-flops. Next, it introduces excitation tables, which indicate the inputs needed to transition between states. Excitation tables are derived for SR, JK, T, and D flip-flops from their characteristic tables. Finally, the document outlines the steps to convert between flip-flop types, including providing examples of converting an SR flip-flop to a JK flip-flop

1. Sequential Circuits
(Flip Flop Conversions)
Presented By:
Dr. Swati Singh
Assistant Professor
Department of Electronics and Communication Engineering
Chitkara University, Punjab, India

2. Characteristic Equation of Flip-Flop
• It is the equation expressing the next state
(Qn+1) of a flip-flop in terms of its present
state (Qn) and present excitations (i.e. inputs).
• Steps to obtain Characteristic equation of a
flip-flop:
i. Write the characteristic table of the flip flop
ii. Draw a K-map for the next state of the flip flop in terms of its present
state and inputs
iii. Simplify the K-map to obtain the characteristic equation.

3. Characteristic Equation of SR Flip-Flop
S R Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 X
1 1 1 X
Step 1: Characteristic Table of SR FF Step 2: K-Map
Step 3: Characteristic Equation
Qn+1 = S + R’ Qn
1
1 1 X X
S
RQn
00 11
01 10
0
1

4. Characteristic Equation of JK Flip-Flop
J K Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Step 1: Characteristic Table Step 2: K-Map
Step 3: Characteristic Equation
Qn+1 = Qn’ J + Qn K’
1
1 1 1
J 00 11
01 10
0
1
KQn

5. Characteristic Equation of T and D Flip-Flop
T Qn Qn+1
0 0 0
0 1 1
1 0 1
1 1 0
Step 1: Characteristic Table of T FF
Step 2: K-Map
Step 3: Characteristic
Equation
Qn+1 = Qn’ T + Qn T’
Step 1: Characteristic Table of D FF
D Qn Qn+1
0 0 0
0 1 0
1 0 1
1 1 1
Step 2: K-Map
Step 3: Characteristic
Equation
Qn+1 = D

6. Excitation Table of Flip-Flops
• Excitation table indicates the inputs required to be applied
to the flip-flop to take it from the present state to the next
state.
• It can be obtained from its characteristic table.
• Example: Excitation table of SR Flip Flop
• Find out the inputs required to go from present to next
state like from 0 to 0, 0 to 1, 1 to 0 and from 1 to 1.
Previous
State
Next State Required Inputs
Qn Qn+1 S R
0 0
0 1
1 0
1 1

7. Excitation Table of SR Flip-Flop
Characteristic Table of SR FF Excitation Table of SR FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 S R
0 0 0 X
0 1
1 0
1 1
Case 1: 0 → 0 Transition
S R Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 X
1 1 1 X

8. Excitation Table of SR Flip-Flop
Characteristic Table of SR FF
Excitation Table of SR FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 S R
0 0 0 X
0 1 1 0
1 0
1 1
Case 2: 0 → 1 Transition
S R Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 X
1 1 1 X

9. Excitation Table of SR Flip-Flop
Characteristic Table of SR FF
Excitation Table of SR FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 S R
0 0 0 X
0 1 1 0
1 0 0 1
1 1
Case 3: 1 → 0 Transition
S R Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 X
1 1 1 X

10. Excitation Table of SR Flip-Flop
Characteristic Table of SR FF Excitation Table of SR FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 S R
0 0 0 X
0 1 1 0
1 0 0 1
1 1 X 0
Case 4: 1 → 1 Transition
S R Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 X
1 1 1 X

11. Excitation Table of JK Flip-Flop
Characteristic Table of JK FF
Excitation Table of JK FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 J K
0 0 0 X
0 1
1 0
1 1
J K Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

12. Excitation Table of JK Flip-Flop
Characteristic Table of JK FF Excitation Table of JK FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 J K
0 0 0 X
0 1 1 X
1 0
1 1
J K Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

13. Excitation Table of JK Flip-Flop
Characteristic Table of JK FF Excitation Table of JK FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 J K
0 0 0 X
0 1 1 X
1 0 X 1
1 1
J K Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

14. Excitation Table of JK Flip-Flop
Characteristic Table of JK FF Excitation Table of JK FF
Previous
State
Next
State
Required Inputs
Qn Qn+1 J K
0 0 0 X
0 1 1 X
1 0 X 1
1 1 X 0
J K Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

15. Excitation Table of T and D Flip-Flop
Characteristic Table of T FF Excitation Table of T FF
Previous
State
Next
State
Required
Input
Qn Qn+1 T
0 0 0
0 1 1
1 0 1
1 1 0
T Qn Qn+1
0 0 0
0 1 1
1 0 1
1 1 0
Characteristic Table of D FF Excitation Table of D FF
D Qn Qn+1
0 0 0
0 1 0
1 0 1
1 1 1
Previous
State
Next
State
Required
Input
Qn Qn+1 D
0 0 0
0 1 1
1 0 0
1 1 1

16. Conversion of
Flip Flops

17. Steps for conversion of Flip-Flops
• Step 1: Identify actual and required flip-flop
• Step 2: Make characteristic table for required flip-flop
• Step 3: Make excitation table for actual flip-flop
• Step 4: Using K-maps, find out the expression for the
inputs of required flip-flop
• Step 5: Draw the circuit diagram

18. SR to JK flip flop Conversion
• Step 1: Identify actual and required flip
flop
JK - Required flip-flop
SR - Actual flip flop

19. SR to JK flip flop Conversion
• Step 1: Identify actual and required flip flop
JK - Required flip-flop
SR - Actual flip flop
• Step 2: Draw characteristic table of required flip
flop and excitation table of actual flip-flop
Previous
State
Next
State
Required Inputs
Qn Qn+1 S R
0 0 0 X
0 1 1 0
1 0 0 1
1 1 X 0
Characteristic Table of JK FF Excitation Table of SR FF
J K Qn Qn+1
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0

20. SR to JK flip flop Conversion
• Step 4: Combine both the truth table into
one conversion table.
External Inputs Present
State
Next
State
Flip – Flop Inputs
J K Qn Qn+1 S R
0 0 0 0 0 X
0 0 1 1 X 0
0 1 0 0 0 X
0 1 1 0 0 1
1 0 0 1 1 0
1 0 1 1 X 0
1 1 0 1 1 0
1 1 1 0 0 1

21. SR to JK flip flop Conversion
• Step 3: Find out the Boolean expressions for S and R using K-maps.
S = J Qn’ R = K Qn
■ Step 4: Draw the circuit diagram.

22. D to SR flip flop Conversion
• SR – Required – Characteristic Table
• D – Actual – Excitation table
External Inputs Present
State
Next
State
Flip – Flop
Inputs
S R Qn Qn+1 D
0 0 0 0 0
0 0 1 1 1
0 1 0 0 0
0 1 1 0 0
1 0 0 1 1
1 0 1 1 1

23. • K-map
• Circuit Diagram

24. Conversions For Practice
• SR to JK
• SR to D
• SR to T
• JK to SR
• JK to D
• JK to T
■ D to SR
■ D to JK
■ D to T
■ T to SR
■ T to JK
■ T to D

25. Thank You!!