1. Introduction to Sequential Circuit By : Pn Siti Nor Diana Ismail CHAPTER 5

2. What is Sequential Circuit? Its behaviour is from : Inputs Outputs Present state Includes flip-flops with clock inputs Logic diagram may or may not include combinational gates.

3. Sequential Circuit Diagram

4. Important element in sequential circuit : i. Input equations ii. State table iii. State diagram

5. Diagram (A)

6. Diagram (B)

7. From previous diagrams (A and B) You should be able to identify, which part is : The inputs The outputs The combinational circuits The flip-flop

8. i.Input Equation Algebraic expression specifying logic diagram of a sequential circuit Imply the type of FF used Fully specify the combinational circuit that drives the

9. Try to analyze this circuit

10. What are the elements that you can identify? Type of flip-flop; Input; Output; The equations of the circuit.

11. INPUT Equations D A = D B = Y = STATES The element are: - Type FFs : D FFs - Input : X, State:A,B - Output : Y - Equation : 3 equations, D A, D B and Y

12. ii.State Table Shows functional relationship between inputs, outputs and FF states. State table consists of: -Present state -Input -Next state -Output

13. Example : State table

14. How many rows in state table? FF = m Inputs = n Number of rows = 2 m+n

15. How to fill in the state table? STEP 1 : List all possible binary combinations of present state and inputs. STEP 2 : Next state column is determined by logic diagram or input equations of FF (get the value for all FF inputs and then refer to FF truth table to get the next state value). STEP 3 : Output column is determined by logic diagram or input equations.

16. STEP 1 List down all binary numbers from 0 to (2 m+n – 1) in present state and input column. Let’s say you have 3 FF and 1 input, number of rows = 2 3+1 = 16 Binary numbers involved is 0 – 15

17. STEP 2 Determine the next column Substitute the values in every rows into the FF input equations that you have got earlier. You will get the input for each FF Trace down the value for the FF output

18. STEP 3 Determine the output Substitute the values in every rows into the input equations of output that you have got earlier. You will directly get the output value

19. Try to fill in this state table based on the given diagram

20. So, here is the answer

21. Types of sequential circuits Mealy model -Output depend on INPUTS and STATES Moore model -Output depend on STATES

22. Circuit Analysis :What type of this circuit?

23. Circuit Analyze Just take a look at the output equation Since Y involves both (A & B) states and (X) input, therefore it is a Mealy model.

24. Can you differentiate between the previous equation and this one? The output is Z. Only involves A (state).. So it is a Moore model

25. iii.State Diagram State – represented by a circle Transition between states – directed lines connecting the circles

26. Examples of State Diagram

27. Referring to State Diagram (a) Circuit diagram

28. State Table

29. Moore Model Circuit Diagram

30. Equation State Table

31. State Diagram (Mealy) Provide same info with state table Obtained from state table State (A B) Input (X) Output (Y)

32. State Diagram (Moore) Input X Input Y State Output

33. State Table

34. Exercise 1 A sequential circuit with two D flip-flops A and B, X input, and one output Y is specified by the following input equations : D A = XA D B = A+XB’ Y = XB Draw the logic diagram of the circuit Derive the state table State Diagram

35. Exercise 2 A sequential circuit with two D flip-flops A and B, two inputs X and Y, and one output Z is specified by the following input equations : D A = XA + XY D B = XA + XB Z = XB Draw the logic diagram of the circuit Derive the state table