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Modulo-N Counters

Modulo-N Counters. According to how they handle input transitions Synchronous Asynchronous. General Modulo-N asynchronous Counter. Number of flip-flops? Number of states? Why the name “Modulo” Which state does the logic detect?. Asynchronous BCD counter. Which is the last stable output?.

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Modulo-N Counters

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  1. Modulo-N Counters • According to how they handle input transitions • Synchronous • Asynchronous

  2. General Modulo-N asynchronous Counter • Number of flip-flops? • Number of states? • Why the name “Modulo” • Which state does the logic detect?

  3. Asynchronous BCD counter • Which is the last stable output?

  4. Asynchronous BCD counter • State diagram • Counter passes through intermediate transient states (small circles) between the steady states (the large circles) • Which is the last unstable output and why?

  5. Constructing asynchronous Modulo-N counters from binary • Asynchronously resetting modulo-13 counter • What are the problems with asynchronous design?

  6. Synchronous Modulo-13 counter • Which state should the reset logic of a synchronous Modulo-N counter sense?

  7. Shift registers as counters • Number of storage elements (FFs)? • Number of states? • Bit patterns? • Where is a ring counter useful?

  8. Ring counter • Schematic • Transition diagram

  9. Ring counter equivalent • Can use a small counter plus a decoder • Why?

  10. Ring counter equivalent • Is the clear synchronous or asynchronous? • What is the drawback of this circuit?

  11. Twisted Ring counter • AKA Johnson Counter • How does it work? • Number of unique states? • State sequence? • Advantages over ring counter?

  12. Twisted Ring counter • Number of unique states? • 2n (n is # of flip-flops) • Advantages over ring counter? • Half the number of flip-flops

  13. Twisted Ring counter example

  14. Twisted Ring counter example • Desired timing diagram • Using ring counter – 2n states = 16; n =8 • Choose 8-bit shift register SN74164 and an inverter for the twist • Figure out the decoding logic for the functions

  15. Twisted Ring counter example

  16. Twisted Ring counter example • Logic diagram of the circuit

  17. Twisted Ring counter example • Timing diagram of the circuit

  18. Alternative implementations • 1) Using a ring counter • 2) Using a straight binary counter • What are advantages and disadvantages of each? • Twisted vs. non-twisted: • Half the Flip-Flops • Decode logic • Straight binary vs. ring • Exponentially fewer flip-flops for the straight counter • More logic

  19. Fractional rate multiplier • Clock drives an n-bit binary counter with outputs X1…Xn • Produce non-overlap pulse trains P1…Pn

  20. Fractional rate multiplier • The separation between the output pulses obtained by the fractional multiplier will vary • They are synchronized with the input clock

  21. Fractional rate multiplier • Why don’t Pi overlap? • What is the product Pi•Pj ? • How many pulses does each Pi generate per 2n clocks? • X1 is on ½ of the time • X2 is on ¼ of the time

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