Sequential Systems Design: Logic Basics and Analysis

1. W’05 CS M51A/EE M16 Winter’05 Section 1 Logic Design of Digital SystemsLecture 13 March 2 Yutao He yutao@cs.ucla.edu 4532B Boelter Hall http://courseweb.seas.ucla.edu/classView.php?term=05W&srs=187154200

2. Outline • Administrative Matters • Basic sequential devices - Recap • Design of sequential systems w/ FFs • Analysis of sequential systems • Timing Analysis • Functional analysis

3. Administrative Matters • Quiz #3 • Given on Friday • Closed-book/Closed-note • You’ll be given FF Excitation Tables if they’re used • Project #3 • Is posted and due at 2pm March 11 (Friday), 2005 • Midterm Solution • Is posted

4. D Q CLK positiveedge-triggeredflip-flop D Q G CLK Level-sensitivegated latch Latch and FF • Loop feedback introduces “memory” capability D CLK QFF Qlatch behavior is the same unless input changes while the clock is high

5. Edged-Trigged Flip-Flops • Development of D-FF • Level-sensitive used in custom integrated circuits • Edge-triggered used in programmable logic devices • Good choice for data storage register • Historically J-K FF was popular but now never used • Similar to R-S but with 1-1 being used to toggle output • Good in days of TTL/SSI (more complex input function): D = JQ' + K'Q • Not a good choice for PALs/PLAs as it requires 2 inputs • Can always be implemented using D-FF • Asynchronous preset and clear inputs are highly desirable on FFs • Used at start-up or to reset system to a known clean state

6. Excitation Functions of Flip-Flops SR Flip-Flop D Flip-Flop JK Flip-Flop T Flip-Flop

7. Roadmap of Implementation w/ FFs Start with State Table Select FF Types Fill in Truth Table of FF inputs Simplify with K-Map Write up Switching Expressions Draw Networks (FFs+Gates)

8. Ex. 8.8 - Modulo-5 Counter • Use T flip-flops to design a modulo-5 counter

9. 5, 6, and 7 are don’t cares! Ex. 8.8 - Modulo-5 Counter (Cont’d) • State Assignment • State Transition Table

10. x To Be Designed y2 T T T Q Q Q CLK CLK CLK y1 Q Q Q y0 Ex. 8.8 - Modulo-5 Counter (Cont’d) • Truth Tables for T0,T1,T2

11. Ex. 8.8 - Modulo-5 Counter (Cont’d) • K-Maps • Switching Expressions

12. Ex. 8.8 - Modulo-5 Counter (Cont’d)

13. Example 8.9

14. Example 8.9 (Cont’d)

15. Example 8.9 (Cont’d)

16. 00 01 10 11 Example 8.9 (Cont’d)

17. Example 8.9 (Cont’d)

18. State Assignment Revisit • Basic goal: • Encode each “symbolic” state with a binary number • Basic fact: • With n state bits for m states, there are 2n! / (2n – m)! • Basic approaches of state assignment: • One-FF-per-bit • Binary code: just number states as they appear in the state table • Other codes, etc. Gray Code • Random: pick random codes • One-FF-per-state (One-hot) • State encoding with fewer bits has fewer equations • However, each may be more complex • State encoding with more bits has simpler equations

19. Determined by inputs One-FF-Per-State(One-Hot) Approach • Each flip-flop implements each state • There is only single 1 in state encoding • State functions are simple • Design directly from the state diagram

20. x D D D D Q Q Q Q D Q Q’ Q’ Q’ Q’ S1 S0 S2 Q’ S3 S4 CLK Example: Modulo-5 Counter

21. Compare M-5 Counter Implementations

22. Analysis of Sequential Systems • Goal: • Decide the timing and functional behavior from the implementation of a sequential system composed of FFs and logic gates • Types: • Timing analysis • Functional analysis

23. Clock Revisit • A regular periodic signal • Period T • Time between two consecutive ticks • Frequency f • f = 1/T • Duty-cycle d • Time clock is high between ticks • Usually expressed as % of period duty cycle (in this case, 50%) CLK period

24. Ideal Reality Level-sensitive Edge-triggered Clock Signal • Questions to ask: • When inputs are sampled? • When the next state is computed? • When outputs are asserted? (i.e. the value is 1)

25. D Q CLK CLK Timing Parameters of A Basic Cell • Setup time (tsu): minimum time before the clock triggering edge by which the input must be stable • Hold time (th): minimum time after the clock triggering edge until which the input must remain stable • Propagation delay (tp): time interval between input transition and output transition it causes tsu th Don’t care Don’t care Input D tp Output Q Unknown

26. CLK Timing Behavior of Sequential Network Output input CLK • All storage cells are controlled by the same clock edge • The Com. Logic blocks: • Inputs are updated at each clock tick • All outputs MUST be stable before the next clock tick • Network setup time, hold time, propagation delay • Minimal clock cycle (maximal clock frequency) • is a function of the critical path

27. Clock Skew

28. Dealing with Asyn. Inputs • Clocked synchronous circuits • Inputs, state, and outputs sampled or changed in relation to acommon reference signal (called the clock) • E.g., master/slave, edge-triggered • Asynchronous circuits • Inputs, state, and outputs sampled or changed independently of a common reference signal (hazards a major concern) • E.g., gated latch • Asynchronous inputs to synchronous circuits • Inputs can change at any time, will not meet setup/hold times • Dangerous, synchronous inputs are greatly preferred • Cannot be avoided (e.g., reset signal, memory wait, user input)

29. Clocked Synchronizer Synchronous System Q0 D Q D Q D Q Async Q0 Async Input Input Clock Clock D Q D Q Q1 Q1 Clock Clock Dealing with Asyn. Inputs • Never allow asynchronous inputs to fan-out to more than one flip-flop • Synchronize as soon as possible and then treat as synchronous signal

30. Functional Analysis • Major goal: • Obtain specification (high-level or binary level) of a sequential system from its implementation • Basic approach: • Break the loop at inputs of FFs • Use characteristic equations of FFs • Basic steps: • Step 1. Obtain switching expressions of output and next state functions • Step 2. Remove inputs of FFs from the expressions • Step 3. Write transition table or draw state diagram • Step 4. Select suitable encoding scheme and figure out high-level function

31. Characteristic Equation of FFs

32. State Transition: Output: Example 8.4

33. Input Output State Encoding Scheme State Transition Table Example 8.4 (Cont’d)

34. Example 8.4 (Cont’d) High-Level Specification

35. Example 8.4 (Cont’d) State Diagram Time-behavior Specification

36. Example 8.7

37. JAKA, JBKB 10,01 01,01 10,10 01,10 00,00 01,00 10,10 11,10 Example 8.7 (Cont’d)

38. Example 8.7 (Cont’d)

39. Example 8.7 (Cont’d)

40. Creativity Good designs Mediocre designs Bad designs About Design

41. Dependability Performance Cost Design Requirements

42. Performance • Concern • How well it can perform? • Criteria • Short delay • Low power dissipation • Rich Functionalities • Goal • High-Performance

43. List price Average selling price Direct Cost Gross Margin Average Discount Component Cost Cost • Which part of cost you can control? • How to obtain a good design in a cost-effective way? • Chip area • number of gates • number of inputs • design time

44. Dependability • Concern: What if • design is not perfect, or • operational environments cause a fault in the system, or • a malicious fault committed by human being? • High Confidence • Techniques: • Fault -Avoidance: Testing, Verification • Zero-defect is impossible for complex systems • Fault-Tolerance: • Design the system such that it will perform well as expected in spite of presence of faults • Error detection/correction Codes • One area of my research interests

45. Rules-of-thumb of a Good Design • Divide-and-conquer Principle • Partition a complex problem into a set of simple problems • Start from a simple problem step-by-step • Formulate a final solution by combining the solutions to all simple problems • KISS Principle • Keep It Simple, Stupid! • The simplest solution is the correct one • Keep it simple and make it work first

46. Rules-of-thumb of a Good Design (Cont’d) • Murphy’s Law • Things DO break at the last minute! • Plan ahead, start earlier, and make continuous progress. • Forrest Gump’s Law • Never give up! • It does not fail until you give up • Working hard is never an excuse for failure

47. Summary • Design of sequential systems with FFs • State assignment • one-FF-per-bit • one-FF-per-state • Implementation • Use excitation function of FFs • Analysis of sequential systems with FFs • Timing analysis • Functional analysis • Use characteristic equations of FFs

48. Next Lecture • Chapter 9