14. Flip Flop Conversions.pptx

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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 (Q n+1 ) of a flip-flop in terms of its present state ( Q n ) and present excitations (i.e. inputs). Steps to obtain Characteristic equation of a flip-flop: Write the characteristic table of the flip flop Draw a K-map for the next state of the flip flop in terms of its present state and inputs Simplify the K-map to obtain the characteristic equation.

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

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

5. Characteristic Equation of T and D Flip-Flop T Qn Qn+1 1 1 1 1 1 1 Step 1 : Characteristic Table of T FF Step 2 : K-Map Step 3: Characteristic Equation Q n+1 = Q n ’ T + Q n T’ Step 1 : Characteristic Table of D FF D Qn Qn+1 1 1 1 1 1 1 Step 2 : K-Map Step 3: Characteristic Equation Q n+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 1 1 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 X 1 1 1 1 Case 1: 0 → 0 Transition S R Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 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 X 1 1 1 1 1 Case 2: 0 → 1 Transition S R Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 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 X 1 1 1 1 1 1 Case 3: 1 → 0 Transition S R Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 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 X 1 1 1 1 1 1 X Case 4: 1 → 1 Transition S R Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 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 X 1 1 1 1 J K Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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 X 1 1 X 1 1 1 J K Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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 X 1 1 X 1 X 1 1 1 J K Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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 X 1 1 X 1 X 1 1 1 X J K Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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 1 1 1 1 1 1 T Qn Qn+1 1 1 1 1 1 1 Characteristic Table of D FF Excitation Table of D FF D Qn Qn+1 1 1 1 1 1 1 Previous State Next State Required Input Qn Qn+1 D 1 1 1 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 X 1 1 1 1 1 1 X Characteristic Table of JK FF Excitation Table of SR FF J K Qn Qn+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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 X 1 1 X 1 X 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1

21. SR to JK flip flop Conversion Step 3: Find out the Boolean expressions for S and R using K-maps. S = J Q n ’ R = K Q n 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 1 1 1 1 1 1 1 1 1 1 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!!