Modulo-N Counters

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# Modulo-N Counters - PowerPoint PPT Presentation

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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Presentation Transcript
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?
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
• Asynchronously resetting modulo-13 counter
• What are the problems with asynchronous design?
Synchronous Modulo-13 counter
• Which state should the reset logic of a synchronous Modulo-N counter sense?
Shift registers as counters
• Number of storage elements (FFs)?
• Number of states?
• Bit patterns?
• Where is a ring counter useful?
Ring counter
• Schematic
• Transition diagram
Ring counter equivalent
• Can use a small counter plus a decoder
• Why?
Ring counter equivalent
• Is the clear synchronous or asynchronous?
• What is the drawback of this circuit?
Twisted Ring counter
• AKA Johnson Counter
• How does it work?
• Number of unique states?
• State sequence?
Twisted Ring counter
• Number of unique states?
• 2n (n is # of flip-flops)
• Half the number of flip-flops
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 example
• Logic diagram of the circuit
Twisted Ring counter example
• Timing diagram of the circuit
Alternative implementations
• 1) Using a ring counter
• 2) Using a straight binary counter
• 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
• Clock drives an n-bit binary counter with outputs X1…Xn
• Produce non-overlap pulse trains P1…Pn
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 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