1. Sequential Circuits

2. Combinational Circuits + Storage element output depends both on previous state and input Fig. 5-1

3. Fig. 5-2 (a): a buffer t G the delay the information enters the buffer at t and output at t+ t G the stored information only retained in buffer by t G longer storage time is necessary in most applications

4. Fig. 5-3 Use flip-flop

5. A storage element can maintain a binary state indefinitely, until directed by an input signal to switch states. The most basic storage elements are latches.

6. Fig. 5-5

8. Fig. 5-7

9. Fig. 5-8

10.  A change in value on the control input allows the state of a latch in a flip-flop to switch.  This change is called a trigger  The trigger enable (trigger) the flip-flops  See Fig. 5-3 for sequential circuits  A present (original) and next (new) state occur in flip-flop before and after the trigger, respectively  The most important element in sequential circuits  Can be derived from latch

11. Fig. 5-9

12. Fig. 5-10 Pulse trigger Pulse in the inputs SR will results wrong output Initially unknown Unknown due to R=1 S=1 Pulse input results wrong output

13. Fig. 5-11

15. Fig. 5-13

16. Fig. 5-14

17. 17 5-4 Sequential Circuit Analysis  The output and the next state are a function of the inputs and the present state.  An example Fig. 5-15 input equations output equation

18. State table

19. Two-dimensional state table

20. Mealy model/Moore model  Mealy model circuits  Sequential circuits in which the outputs depend on the input, as well as on the states  The circuits in Fig. 5-15  Moore model circuits  Sequential circuits in which the outputs depend only on the states  The circuits in Fig. 5-16

21. A Moore model circuit (Fig. 5-16)

22. State diagram (a): for Fig. 5-15 (b): for Fig. 5-16

23. Example 5-1 States reduction  equivalent

24. Example 5-1 States reduction 

25. equivalent

26. Example 5-1 States reduction  Reduce from 4 states, 2 flip-flops to 2 states, 1 flip-flop may or may not result in reduced cost

27. Sequential Circuit Simulation  A simulator for the input/output of a designed circuit  Functional simulation  Timing simulation