1. Sequential Circuits1 DIGITAL LOGIC DESIGN by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN

2. Sequential Circuits2 Note  Most of the figures are from your course book

3. Sequential Circuits3  Combinational  The outputs depend only on the current input values  It uses only logic gates  Sequential  The outputs depend on the current and past input values  It uses logic gates and storage elements  Example Vending machine Vending machine  They are referred as finite state machines since they have a finite number of states

4. Sequential Circuits4 Block Diagram  Memory elements can store binary information  This information at any given time determines the state of the circuit at that time

5. Sequential Circuits5 Sequential Circuit Types  Synchronous  The circuit behavior is determined by the signals at discrete instants of time  The memory elements are affected only at discrete instants of time  A clock is used for synchronization Memory elements are affected only with the arrival of a clock pulse Memory elements are affected only with the arrival of a clock pulse If memory elements use clock pulses in their inputs, the circuit is called If memory elements use clock pulses in their inputs, the circuit is called  Clocked sequential circuit

6. Sequential Circuits6 Sequential Circuit Types  ASynchronous  The circuit behavior is determined by the signals at any instant of time  It is also affected by the order the inputs change

7. Sequential Circuits7 Clock  It emits a series of pulses with a precise pulse width and precise interval between consecutive pulses  Timing interval between the corresponding edges of two consecutive pulses is known as the clock cycle time, or period

8. Sequential Circuits8 Flip-Flops  They are memory elements  They can store binary information

9. Sequential Circuits9 Flip-Flops  Can keep a binary state until an input signal to switch the state is received  There are different types of flip-flops depending on the number of inputs and how the inputs affect the binary state

10. Sequential Circuits10 Latches  The most basic flip-flops  They operate with signal levels  The flip-flops are constructed from latches  They are not useful for synchronous sequential circuits  They are useful for asynchronous sequential circuits

11. Sequential Circuits11 SR Latch with NOR

12. Sequential Circuits12 SR Latch with NOR

13. Sequential Circuits13 SR Latch with NAND

14. Sequential Circuits14 SR Latch with NAND

15. Sequential Circuits15 SR Latch with Control Input

16. Sequential Circuits16 D Latch

17. Sequential Circuits17 Symbols for Latches

18. Sequential Circuits18 Note  The control input changes the state of a latch or flip-flop  The momentary change is called a trigger  Example: D Latch  It is triggered every time the pulse goes to the logic level 1  As long as the pulse remains at the logic level 1, the change in the data (D) directly affects the output (Q)  THIS MAY BE A BIG PROBLEM since the state of the latch may keep changing depending on the input (may be coming from a combinational logic network)

19. Sequential Circuits19 How to Solve?  Trigger the flip-flop only during a signal transition

20. Sequential Circuits20 Edge-Triggered D Flip-Flop

21. Sequential Circuits21 Characteristics of D Flip- Flop

22. Sequential Circuits22 Edge-Triggered J-K Flip-Flop How???????

23. Sequential Circuits23 Excitation Table

24. Sequential Circuits24 Edge-Triggered T Flip-Flop

25. Sequential Circuits25 Excitation Table

26. Sequential Circuits26 Direct Inputs  You can use asynchronous inputs to put a flip-flop to a specific state regardless of the clock  You can clear the content of a flip-flop  The content is changed to zero (0)  This is called clear or direct reset  This is particularly useful when the power is off The state of the flip-flop is set to unknown The state of the flip-flop is set to unknown

27. Sequential Circuits27 D Flip-Flop with Asynchronous Reset

28. Sequential Circuits28 State Equations A state equation shows the next state as a function of the current state and inputs

29. Sequential Circuits29 State Table

30. Sequential Circuits30 State Diagram

31. Sequential Circuits31 Analysis with D Flip-Flops

32. Sequential Circuits32 State Reduction  Reduce the number of states but keep the input-output requirements  Reducing the number of states may reduce the number of flip-flops  If there are n flip-flops, there are 2^n states  If you have two circuits that produce the same output sequence for any given input sequence, the two circuits are equivalent  They may replace each other

33. Sequential Circuits33 State Reduction Example Find the states for which the next states and outputs are the same

34. Sequential Circuits34 Example (Cont.) In the next state, g is replaced with e In the next state, f is replaced with d

35. Sequential Circuits35 Example (Cont.)

36. Sequential Circuits36 State Assignment  You need to assign binary values for each state so that they can be implemented  You need to use enough number of bits to cover all the states

37. Sequential Circuits37 State Assignments

38. Sequential Circuits38 Design Procedure  Derive a state diagram  Reduce the number of states  Assign binary values to the states  Obtain binary coded state table  Choose the type of flip-flop to be used  Derive simplified flip-flop input equations and output equations  Draw the logic diagram

39. Sequential Circuits39 Example  Design a circuit (with D flip-flops) that detects three or more consecutive 1’s in a string of bits coming through an input line

40. Sequential Circuits40 Example (Cont.)

41. Sequential Circuits41 Example (Cont.)

42. Sequential Circuits42 Example (Cont.)

43. Sequential Circuits43 Example  Design a circuit (with JK flip-flops) that detects three or more consecutive 1’s in a string of bits coming through an input line

44. Sequential Circuits44 Example (Cont.)

45. Sequential Circuits45 Example (Cont.)

46. Sequential Circuits46 Example (Cont.)

47. Sequential Circuits47 Study Problems  Course Book Chapter – 5 Problems  5 – 3  5 – 5  5 – 6  5 – 7  5 – 10  5 – 12  5 – 13  5 – 19

48. Sequential Circuits48 Questions