Modulo n counters
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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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Modulo n counters

Modulo-N Counters

  • According to how they handle input transitions

    • Synchronous

    • Asynchronous


General modulo n asynchronous counter

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

    Asynchronous BCD counter

    • Which is the last stable output?


    Asynchronous bcd counter1

    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?


    Constructing asynchronous modulo n counters from binary

    Constructing asynchronous Modulo-N counters from binary

    • Asynchronously resetting modulo-13 counter

    • What are the problems with asynchronous design?


    Synchronous modulo 13 counter

    Synchronous Modulo-13 counter

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


    Shift registers as counters

    Shift registers as counters

    • Number of storage elements (FFs)?

    • Number of states?

    • Bit patterns?

    • Where is a ring counter useful?


    Ring counter

    Ring counter

    • Schematic

    • Transition diagram


    Ring counter equivalent

    Ring counter equivalent

    • Can use a small counter plus a decoder

    • Why?


    Ring counter equivalent1

    Ring counter equivalent

    • Is the clear synchronous or asynchronous?

    • What is the drawback of this circuit?


    Twisted ring counter

    Twisted Ring counter

    • AKA Johnson Counter

    • How does it work?

    • Number of unique states?

    • State sequence?

    • Advantages over ring counter?


    Twisted ring counter1

    Twisted Ring counter

    • Number of unique states?

      • 2n (n is # of flip-flops)

    • Advantages over ring counter?

      • Half the number of flip-flops


    Twisted ring counter example

    Twisted Ring counter example


    Twisted ring counter example1

    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


    Twisted ring counter example2

    Twisted Ring counter example


    Twisted ring counter example3

    Twisted Ring counter example

    • Logic diagram of the circuit


    Twisted ring counter example4

    Twisted Ring counter example

    • Timing diagram of the circuit


    Alternative implementations

    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


    Fractional rate multiplier

    Fractional rate multiplier

    • Clock drives an n-bit binary counter with outputs X1…Xn

    • Produce non-overlap pulse trains P1…Pn


    Fractional rate multiplier1

    Fractional rate multiplier

    • The separation between the output pulses obtained by the fractional multiplier will vary

    • They are synchronized with the input clock


    Fractional rate multiplier2

    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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