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Modulo-N Counters

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- According to how they handle input transitions
- Synchronous
- Asynchronous

- Number of flip-flops?
- Number of states?
- Why the name “Modulo”

- Which is the last stable output?

- 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?

- Asynchronously resetting modulo-13 counter
- What are the problems with asynchronous design?

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

- Number of storage elements (FFs)?
- Number of states?
- Bit patterns?
- Where is a ring counter useful?

- Schematic
- Transition diagram

- Can use a small counter plus a decoder
- Why?

- Is the clear synchronous or asynchronous?
- What is the drawback of this circuit?

- AKA Johnson Counter
- How does it work?
- Number of unique states?
- State sequence?
- Advantages over ring counter?

- Number of unique states?
- 2n (n is # of flip-flops)

- Advantages over ring counter?
- Half the number of flip-flops

- 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

- Logic diagram of the circuit

- Timing diagram of the circuit

- 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

- Twisted vs. non-twisted:

- Clock drives an n-bit binary counter with outputs X1…Xn
- Produce non-overlap pulse trains P1…Pn

- The separation between the output pulses obtained by the fractional multiplier will vary
- They are synchronized with the input clock

- 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