1. 5 Chapter Synchronous Sequential Circuits 1

2. Logic Circuits- Review 2 Logic Circuits Sequential Circuits Combinational Circuits Consists of logic gates whose outputs are determined from the current combination of inputs. Performs an operation that can be specified by a set of Boolean functions. Employ storage elements in addition to logic gates. Outputs are a function of the inputs and the state of the storage elements. Output depend on present value of input + past input.

3. Overview  Storage Elements and Analysis  Introduction to sequential circuits  Types of sequential circuits  Storage elements  Latches  Flip-flops  Sequential circuit analysis  State tables  State diagrams 3

4. Introduction to Sequential Circuits  A Sequential circuit contains:  Storage elements: Latches or Flip-Flops  Combinatorial Logic:  Implements a multiple-output switching function  Inputs are signals from the outside.  Outputs are signals to the outside.  Other inputs, State or Present State, are signals from storage elements.  The remaining outputs, Next State are inputs to storage elements. 4 Combinational Logic Storage Elements Inputs Outputs State Next State

5. Introduction to Sequential Circuits  Sequential Logic  Output function Outputs = g(Inputs, State)  Next state function Next State = f(Inputs, State) 5 Combina- tional Logic Storage Elements Inputs Outputs State Next State

6. Types of Sequential Circuits  Depends on the times at which:  storage elements observe their inputs, and  storage elements change their state  Synchronous  Behavior defined from knowledge of its signals at discrete instances of time  Storage elements observe inputs and can change state only in relation to a timing signal (clock pulses from a clock)  Asynchronous  Behavior defined from knowledge of inputs at any instant of time and the order in continuous time in which inputs change  If clock just regarded as another input, all circuits are asynchronous! 6

7. 5.3 Storage Elements :Latches  Storage elements  Maintain a binary state (0 or 1) indefinitely as long as power is delivered to the circuit  Switch states (0  1 or 1  0) when directed by an input signal  Most basic storage element  Used mainly to construct Flip-Flops  Asynchronous storage circuit  Types of latches:  SR Latches  S`R` Latches  D Latches 7 X = X

8. Basic (NOR) S – R Latch  Cross-coupling two NOR gates gives the S – R Latch: 8 S (set) R (reset) Q Q Graphic Symbol R S Q Q

9. Basic (NOR) S – R Latch 9 Q’ t+1 Q t+1 QRS 1Q t+1 =Q =0000 01100 10010 10110 01001 01101 ؟ Undefined011 ؟ undefined111 Q t+1 RS Q t+1 =Q No change 00 Reset to 010 Set to 101 undefined11

10. Basic (NAND) Ś – Ŕ Latch  “Cross-Coupling” two NAND gates gives the Ś -Ŕ Latch: Q S (set) R (reset) Q 10 Graphic Symbol R Q Q S

11. Basic (NAND) Ś – Ŕ Latch 11 Q’ t+1 Q t+1 QRS ?? 000 ?? 100 01010 01110 10001 10101 10011 01111 RS Undefined00 Reset to 110 Set to 001 Q t+1 =Q No change 11

12. Clocked S - R Latch  Adding two NAND gates to the basic Ś - Ŕ NAND latch gives the clocked S – R latch:  Has a time sequence behavior similar to the basic S-R latch except that the S and R inputs are only observed when the line C is high.  C means “control” or “clock”. 12 S R Q C Q 1 1 S` R`

13. D Latch(Transparent Latch)  Adding an inverter to the S-R Latch, gives the D Latch:  Note that there are no “indeterminate” states! 13 C D Q Q D Q C Q

14. D Latch(Transparent Latch) 14 Q D Q(t+1) 0 0 0 0 1 1 1 0 0 1 1 1 Q t+1 D 00 11

15. Chapter 5: Sequential Circuits 5.4: Flip-Flops 15

16. Flip-Flops  The latch timing problem  Master-slave flip-flop  Edge-triggered flip-flop  Other flip-flops - JK flip-flop - T flip-flop 16

17. The Latch Timing Problem  In a sequential circuit, paths may exist through combinational logic:  From one storage element to another  From a storage element back to the same storage element  The combinational logic between a latch output and a latch input may be as simple as an interconnect  For a clocked D-latch, the output Q depends on the input D whenever the clock input C has value 1 17

18. The Latch Timing Problem (continued)  Consider the following circuit:  Suppose that initially Y = 0.  As long as C = 1, the value of Y continues to change!  The changes are based on the delay present on the loop through the connection from Y back to Y.  This behavior is clearly unacceptable.  Desired behavior: Y changes only once per clock pulse 18 Clock Y C D Q Q Y

19. The Latch Timing Problem (continued)  A solution to the latch timing problem is to break the closed path from Y to Y within the storage element  The commonly-used, path-breaking solutions replace the clocked D-latch with:  a master-slave flip-flop  an edge-triggered flip-flop 19

20. Master-Slave Flip-Flop  Consists of two clocked D latches in series with the clock on the second latch inverted  What happened when c=1?  The data from D input is transferred to the master.  The slave is disabled.  Any change in the input change the master output ( Y ) but can’t effect the slave output. 20 C D Q C C D Q D Master Slave Y

21.  What happened when C=0?  The master is disabled.  The slave is enable.  The value of ( Y ) is transferred to the slave as input.  The output ( Q ) is equal ( Y ). Conclusion: The output of the F.F. can change only during the transition of clock from 1 to 0 or at Trigger. 21 C D Q C C D Q D Master Slave Y

22. Timing 22

23.  A trigger: The state of a latch or flip-flop is switched by a change of the control input. 23 Timing

24. Graphic Symbols 24

25. Graphic Symbols 25

26. Other flip-flops 26 Other F-Fs can be built using D F-F There are four operation on a F-F - set to 1 - Reset to 0 - toggle ( complement ) of Q - nothing There are tow F-F - JK F-F - T F-F

27. JK Flip-Flops 27

28. JK Flip-Flops 28 D = JQ’ + K’Q Q t+1 KJ No change Q t+1 = Q 00 Reset to 010 Set to 101 Complement Q t+1= Q’ 11

29. T Flip-Flops 29 T Flip-Flops

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31. Characteristic Table 31

32. Characteristic Table 32

33. Characteristic Equations 33

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35. State Equation 35

36. State Equation 36

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39. Analysis  This circuit consist of :  2 D F-F A and B  Input x  Output Y  Q t+1 = D  A= D A  B = D B 39

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42. State Table 42

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44. State Diagram 44

45. 45 state Input / output

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48.  1 D F-F ( A )  2 Input X, Y  Q t+1 = D  D = A  X  y Analysis 48

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52.  2 JK F-F (A, B)  Input x  Q t+1 = JQ’ + K’Q 52 Analysis

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59.  2 T F-F ( A, B )  1 input X  1 output Y  Q t+1 = T  Q  The input equations are T_A = BX T_B = X  The out put equation is Y = AB  The characteristic equations are : A t+1 = T_A  A = BX  A = BX(A’) + (BX)’A = A’BX + AB’ + AX’ B t+1 = X  B 59 Analysis

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