Read Kleitz, Chp. 12 (and review Chp. 13). You may want to review chp.10.
1. Create a divide-by-ten counter out of flip-flops (you may use J/K, S/R, D, and/or T flip-flops) and any basic logic gates (AND, OR, NAND, NOR, NOT, XOR, XNOR) that you need). Draw the schematic and briefly describe how it works. I recommend using MultiSim or a similar program to draw the schematics (that’s how I draw many of the ones in the lectures and labs), but hand-drawn schematics are fine if you prefer to do that.
You’re welcome to use MultiSim in the Electronics lab,
when the room is available.
2. One of the most important concepts in electronics – especially in digital electronics – is modularity. Once a circuit has been designed to do a particular function (like the divide-by-ten circuit above), it can be kept as part of a circuit library, and reused – without having to re-invent it each time.
Using three divide-by-ten “black boxes,” each with a clock input and four outputs (Q3, Q2, Q1, Q0), design a divide-by-1,000 counter. (You don’t need to redraw the schematic from #1 above; just assume that it works and use a “black box” for each instance of it, with the inputs and outputs labeled.
3. How many (legal) states does your design from #2 above have? Why?
4. Since each flip-flop might power up in either the Set or Reset state,
a counter which uses N flip-flops might power up in any of 2^N possible states. How many total (legal and illegal) states does your design from #2 above have?
5. (extra credit, since this is tricky) How many possible states could your design from #2 above be in, after it is powered up in an unknown state and fifty (50) clock cycles have been input? (Hint: after that many cycles, you know the ones’ place counter will be in a legal state. What about the others? What states could they be in?)
Explain your reasoning for full credit.
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