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- 1. Synchronous Design Process1. Construct a state diagram and/or state/output table corresponding to the word description or specification2. Minimize the number of states3. Choose a set of state variables and assign state variable combinations to the named states4. Obtain the transition/output table5. Determine the number of flip-flops and select the type of flip-flop to be used (D is often the default)6. Construct the excitation table7. Derive excitation equations8. Derive output equations 1
- 2. Design a clocked synchronous state machine which detects a sequence of three or more consecutive 1’s in a string of bits coming through an input line.Mealy machine with D flip flopsMoore machine with D flip flopsMoore machine with JK flip flopsealy machine with D flip flops (change of encodingAssuming Mealy machine designLet the input be X and output be Z
- 3. Obtaining the state Diagram Assume initial condition to be Z = 0 Let the initial state be represented by state A If X = 0, then output Z = 0, same state AX/Z = 1, then output Z = 0, goes to state B 1/00/0 A B Mealy machine A 1 B 0 Moore machine 0 0
- 4. Obtaining the state Diagram Assume machine has moved to state B If X = 0, then output Z = 0, goes back to state A = 1, then output Z = 0, goes to state CX/Z 1/0 1/00/0 A B C Mealy machine 0/0 A 1 B 1 C 0 Moore machine 0 0 0 0
- 5. Obtaining the state Diagram Assume machine has moved to state C If X = 0, then output Z = 0, goes back to state A = 1, then output Z = 1, same state CX/Z 1/0 1/00/0 A B C 1/1 Mealy machine 0/0 0/0 A 1 B 1 C0 1 C1 0 1 0 0 0 1 0 Moore 0 0 machin
- 6. Obtaining the state/output table Mealy machine Moore machine State/output table State/output table State Input X State Input X Output S 0 1 S 0 1 Z A A,0 B,0 A A B 0 B A,0 C,0 B A C0 0 C A,0 C,1 C0 A C1 0 C1 A C1 1 Next State S*, Z Next State S*
- 7. Assigning state variable to obtain Mealy machinetransition/output table Moore machine Transition/output table Transition/output table State Input X State Input X Output Q1Q0 0 1 Q1Q0 0 1 Z 00 00,0 01,0 00 00 01 0 01 00,0 10,0 01 00 10 0 10 00,0 10,1 10 00 11 0 11 00 11 1 Next State Q1*Q0*, ZEncodingA = 00, B = Choosing D Next State Q1*Q0*01 type flip flop
- 8. Constructing the excitation table Mealy machine Moore machine Excitation/output table Excitation/output table State Input X State Input X Output Q1Q0 0 1 Q1Q0 0 1 Z 00 00,0 01,0 00 00 01 0 01 00,0 10,0 01 00 10 0 10 00,0 10,1 10 00 11 0 11 00 11 1 D1D0, Z D1D0
- 9. Transferring onto K-maps to derive excitationequations (Mealy Machine)Excitation/ State Input X State Input Xoutput table Q1Q0 0 1 Q1Q0 0 1 State Input X 00 0 0 00 0 1Q1Q0 0 1 01 0 1 01 0 0 00 00,0 01,0 11 X X 11 X X 01 00,0 10,0 10 0 1 10 0 0 10 00,0 10,1 D1 D0 D1D0, Z D1 = Q0 ⋅ X + Q1⋅ X D 0 = Q1 ⋅ Q 0 ⋅ X
- 10. Transferring onto K-maps to derive output equation (Mealy Machine)Excitation/output State Input Xtable Q1Q0 0 1 State Input X 00 0 0 Q1Q0 0 1 01 0 0 00 00,0 01,0 11 X X 01 00,0 10,0 10 0 1 10 00,0 10,1 Z D1D0, Z Z = Q1 ⋅ X
- 11. Circuit (logic) diagram Mealy machine D 0 = Q1 ⋅ Q 0 ⋅ X D1 = Q0 ⋅ X + Q1⋅ Xexcitation equations Z = Q1 ⋅ X output equation X Q0 Q0 Q1 Q1 Z D0 Q0 D Q Q D1 D Q Q1 Q Clk
- 12. Transferring onto K-maps to derive excitationequation (Moore Machine)Excitation State Input X State Input Xtable Q1Q0 0 1 Q1Q0 0 1 State Input X 00 0 0 00 0 1Q1Q0 0 1 01 0 1 01 0 0 00 00 01 11 0 1 11 0 1 01 00 10 10 0 1 10 0 1 10 00 11 D1 D0 11 00 11 D1 = Q0 ⋅ X + Q1⋅ X D 0 = Q1 ⋅ X + Q 0 ⋅ X D1D0
- 13. Transferring onto K-maps to derive outputequation (Moore Machine)Excitation/outputtable State Input X Output Q1Q0 0 1 Z 00 00 01 0 01 00 10 0 Z = Q1⋅ Q0 10 00 11 0 11 00 11 1 D1D0
- 14. Circuit (logic) diagramMoore machineD 0 = Q1 ⋅ X + Q 0 ⋅ X D1 = Q0 ⋅ X + Q1⋅ Xexcitation equations Z = Q1⋅ Q0 output equation X Q0 Q0 Q1 Z D0 Q0 D Q Q D1 D Q Q1 QClk
- 15. Moore machine with JK flip flopsAssigning state variable to obtaintransition/output table Transition/output table Excitation table for State Input X Output JK flip flop Q1Q0 0 1 Z Q Q* J K 00 00 01 0 0 0 0 X 01 00 10 0 0 1 1 X 10 00 11 0 1 0 X 1 11 00 11 1 1 1 X 0 Next State Q1*Q0*
- 16. Constructing the excitation tableTransition/output table Excitation/output table State Input X Output State Input X Output Q1Q0 0 1 Z Q1Q0 0 1 Z 00 00 01 0 00 0X, 0X 0X, 1X 0 01 00 10 0 01 0X, X1 1X, X1 0 10 00 11 0 10 X1, 0X X0, 1X 0 11 00 11 1 11 X1, X1 X0, X0 1 Next State Q1*Q0* J1K1,J0K0
- 17. Transferring onto K-maps to derive excitationequationsExcitation State Input X State Input Xtable Q1Q0 0 1 Q1Q0 0 1State Input X 00 0 0 00 X XQ1Q0 0 1 01 0 1 01 X X 00 0X, 0X 0X, 1X 11 X X 11 1 0 01 0X, X1 1X, X1 10 X X 10 1 0 10 X1, 0X X0, 1X J1 K1 11 X1, X1 X0, X0 J 1 = Q0 ⋅ X K1 = X J1K1,J0K0
- 18. Transferring onto K-maps to derive excitationequationsExcitation State Input X State Input Xtable Q1Q0 0 1 Q1Q0 0 1State Input X 00 0 1 00 X XQ1Q0 0 1 01 X X 01 1 1 00 0X, 0X 0X, 1X 11 X X 11 1 0 01 0X, X1 1X, X1 10 0 1 10 X X 10 X1, 0X X0, 1X J0 K0 11 X1, X1 X0, X0 J0 = X K 0 = Q1 + X J1K1,J0K0
- 19. Transferring onto K-maps to derive outputequation Excitation/output table State Input X Output Q1Q0 0 1 Z 00 0X, 0X 0X, 1X 0 01 0X, X1 1X, X1 0 Z = Q1⋅ Q0 10 X1, 0X X0, 1X 0 11 X1, X1 X0, X0 1 J1K1,J0K0
- 20. Circuit (logic) diagramexcitation equations output equation J 1 = Q0 ⋅ X K1 = X Z = Q1⋅ Q0 J0 = X K 0 = Q1 + X X X Q0 Q1 Z J0 Q0 J Q K Q K0 J1 Q1 J Q K QClk K1
- 21. Assigning state variable to obtaintransition/output table machine Mealy Transition/output table State Input X Change Q1Q0 0 1 of 00 00,0 01,0 Encoding A = 00 01 00,0 11,0 B = 01 11 00,0 11,1 C = 11 Next State Q1*Q0*, Z Choosing D type flip flop
- 22. Constructing the excitation table M ealy machine Excitation/output table State Input X Q1Q0 0 1 00 00,0 01,0 01 00,0 11,0 11 00,0 11,1 D1D0, Z
- 23. Transferring onto K-maps to derive excitationequations (Mealy Machine)Excitation/ State Input X State Input Xoutput table Q1Q0 0 1 Q1Q0 0 1 State Input X 00 0 0 00 0 1Q1Q0 0 1 01 0 1 01 0 1 00 00,0 01,0 11 0 1 11 0 1 01 00,0 11,0 10 X X 10 X X 11 00,0 11,1 D1 D0 D1D0, Z D1 = Q 0 ⋅ X D0 = X
- 24. Transferring onto K-maps to derive output equation (Mealy Machine)Excitation/output State Input Xtable Q1Q0 0 1 State Input X 00 0 0 Q1Q0 0 1 01 0 0 00 00,0 01,0 11 0 1 01 00,0 11,0 10 X X 11 00,0 11,1 Z D1D0, Z Z = Q1 ⋅ X
- 25. Circuit (logic) diagram Mealy machine D0 = X D1 = Q0 ⋅ X excitation equations Z = Q1 ⋅ X output equation X Z D0 Q0 D Q Q D1 D Q Q1 Q Clk
- 26. Example 1: State Diagram• Design the FSM for the given state diagram – Graphical version of states, inputs, transitions and outputs W Z State X Y assignmentGiven state diagram Assigned state diagram 26
- 27. Example 1: State Table • For each current-state, specify next-state(s) as a function of the present inputs • For each current-state, specify the output(s) as a function of the present inputsState VariablesWe often use Q0, Q1,Q2, etc. to acknowledgethat state variables areF-F outputs 27
- 28. Example 1: Alternate State Table • State table, alternate format emphasizing state transitions • Notation: A → Q(t) and A+ → Q(t+1), used to indicate the change in state variable needed for the desired transition Q1(t) Q0(t) →Q1(t+1) Q0(t+1) ( ) a more descriptive notation 28
- 29. Example 1: Flip-Flop Excitation Tables• Use these tables to “move” Q to next state• Used to design the memory control CL circuit We will use the D F-F 29
- 30. Example 1: Flip-Flop Excitation Tables• Why are we are interested in the D Flip-Flop for this design? Q(t) Q(t+1) D Operation 0 0 0 Reset 0 1 1 Set 1 0 0 Reset 1 1 1 Set We select D Flip-Flops because the D input is simply the value of Q(t+1) that we desire 30
- 31. Example 1: Block Diagram• We need to use two D flip-flops x y (output)• The sequential circuit would look as shown (next state) Q1 D1• We will design the CL for a 3-input, 3-output Q2 D2 circuit – CL for Output (y) – CL for Next State controls (D1 and D2) inputs = x, Q1, Q2 outputs = y, D1, D2 31
- 32. Example 1: Truth Table• The truth table for this 3-input, 3-output circuit can be generated from the original state table• We will need to minimize each output function using Karnaugh maps, mindful of overlap 0 1 2 3minterms 4 5 6 7 32
- 33. Example 1: Karnaugh Maps • Minimizing each of the three outputs:A+ B+ 1 1 1 1 1 A+ = x ∙ Q1 + x ∙ Q2 B+ = x ∙ Q1y A = Q1 and B = Q2 1 1 1 y = x ∙ Q1 + x ∙ Q2 33
- 34. Example 1: Circuit Diagram• The circuit that results from these equations is shown below: y = x ∙ Q1 + x ∙ Q2 y = x ∙ (Q1 + Q2) A+ = x ∙ Q1 + x ∙ Q2 A+ = x ∙ (Q1 + Q2) B+ = x ∙ Q1 34
- 35. Design: Example 2• Given the state diagram as follows, design the sequential circuit using JK Flip-Flops D A C B state assignment A = 01 B = 10 C = 11 D = 00 35
- 36. Design: Example 2• Note that this is a state diagram for a Mealy machine inputs outputs 36
- 37. Design: Example 2• Block diagram, signal identification Input, x Sequential Logic 1-bit Circuit CP We need to determinewhat goes in here? 37
- 38. Design: Example 2• From state table, get input flip-flop function KB = Ax + A’x’ KB = Ax + A’x’ 38
- 39. Design: Example 2• Input flip-flop function JA Input, x A B KA x JB• Logic Diagram 1-bit KB CP x x′ B A x x B 39
- 40. CLKQAQDQCQB 0 1 2 3 4 8 9 10 11 12 0 101 overlap M oore machine 1 1 A 1 B 0 C0 1 C1 0 0 0 0 1 0 0
- 41. CLKQDQCQBQALD 5 6 7 8 9 10 11 12 13 14 5 Initial Counting Reloading Loading starts
- 42. 1110 Moore machine 1 0 1 A 1 B 1 C 1 D 0 E 0 0 0 0 0 0 1 0 0
- 43. 43
- 44. State Input X Output S 0 1 Z A A B 0 B A C0 0 C A C1 0 D A C1 1 Next State S* 44
- 45. X Q0 Q1 X Q0 D0 Q0 D Q Q D1 D Q Q1 Q D2 D Q Q2 ZClk Q
- 46. State Input X Output S 0 1 Z A A B 0 B A C0 0C0 A C1 0C1 A C1 1 Next State S* 46

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