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Counters: One Step Down From And An Integral Part of Computers

Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

In the first meeting of my Computer Systems Organization lecture class for the twelfth week of the third term, I talked about counters, which are one natural application of state diagrams and state tables that I had taught them in the previous meeting.

Of course I started with sequential counters, that, again for n-bits required are implemented with n flip-flops, and therefore have two raised to n minus 1 total states.

We used a 3-bit counter for our first example. I gave the state diagram first, and from there we went to the state table where the various present states and various next states were shown.

From there we had to determine based on the type of flip-flop that we used (T or J-K) what the inputs have to be to be able to result in the next state.

For the J-K flip-flop, we were able to limit the possible inputs by connecting both inputs to one line, and therefore used only a state table of four instead of eight, eliminating those where the inputs had different values.

From there, the next part was how to manipulate the present states to be able to get the desired new inputs, sometimes using gates.

The last part was constructing the circuit for the counter, again having the output of the flip flops return and be used as input again, or gated before being placed in the input again.

For the first time also, the students were able to see one input consistently connected to a value or 1 or high or 5V, since it means the next state is always the complement or the inverse of its present state, which for the T flip-flop means the input has to be a 1.

For the non-sequential counters, we could have don’t care fields and therefore make the input connections easier, sometime not even having to use gates at all.

And I gave them a seatwork where they were supposed to complete the state table after being given a non-sequential state diagram.

Session 1057 is non-sequential. Class dismissed.


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