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Step 2 - Create a Generic Base-2 Counter
Common Lines Shared by All Stages
The first thing to do, after finding out the number of required flip flops, is to connect the "clocks" of the flip flops together to make a synchronous counter because the shortcut method was designed to deal with this type of counting configuration. Next, the "reset" inputs should be tied together by default if there is no information regarding how the flip flops are to be configured during each reset condition. Now that those small, yet important, items have been dealt with, we move onto the problem of what we are to do with the Q's and T's.
Linking Stages Together
Linking individual stages to one another requires nothing more than the following basic procedure: The T input of each stage requires that all the Qs of the previous stages be ANDed together. Simple huh?
As to the reason as to why we do such a thing, the answer is simple to understand as well as long as one knows how to count in binary. You do know how to count in binary right? Analyze the following counting example and see if you can find what it takes for one bit to flip in relation to all the other bits before it.
| Number | MSB ... LSB |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
From the counting example given above, you may be able to tell that in order for a bit to change, all the bits before it must be a '1'. This can be readily seen by comparing numbers such as 3 against 4 or 7 against 8 in binary. Note that although there does not appear to be a '1' before the least significant bit, LSB, it can be assumed that it will always flip as shown when comparing any row of the table against its previous or proceeded row.
EXAMPLE:
Connect the following 4 flip flops together so that they form a generic mod-16 counter.
The first thing to do is connect all the "clock" pins to one another since this shortcut method is for creating a synchronous counter. The "reset" pins will be connected together as well by default because no information has been given concerning them.
Next, we are to AND the previous Q's of each stage we are dealing with and feed the result into the the T input of the current stage.
- First Stage: Since there are no previous Q's and we want the first stage to always toggle, we can connect the first T input to logic '1'.
- Second Stage: Since the only Q output that is before the second stage is the one coming from the first flip flop, we can directly connect the Q from first stage to the T of the second stage.
- Third Stage: Since the third stage needs the first and second stage's Q's to be a '1' before being able to toggle, we need to AND both of them and feed the result to the T input of the third stage.
- Fourth Stage: Since the fourth stage, the last one, needs all of the previous stage's Q's to be a '1' to toggle correctly, we need to AND all three of them and feed the result into the T input of the fourth stage. Note that we can save ourselves from having to use a three input AND gate by taking the output of the first AND gate and ANDing that with the output of the third flip flop because this is essentially the same as ANDing all three Q's together.
Although there are plenty of steps after this to complete the shortcut method, we can stop here because stepping though the logic (You can do it by yourself =p ) yields the correct counting scheme that we desire. This is true for any Mod-2^n counter that we are to make because the automatic rollover from 2^n - 1 to 0 is an inherent property of these base-2 counters.
EXAMPLE:
Make a mod-32 counter.
Since we are not given the number of flip flops required to make the counter, we will need to find out by using either one of the two equations on the previous page. Using the last equation on the third page, the one that deals directly with a given mod-N value, we find that we need at least 5 T flip flops. Laying them out and hooking up the "Clock" and "Reset" signals yields the following:
Like the previous example, we AND the all the previous Q's, if available, of a particular stage and then feed the result to the T input of that stage. Notice that with this example, I went ahead and labeled the LSB and MSB stages because knowing where they are will be very important for the next step.
Being that this counter is a mod-2^n type, we are able to stop here and declare that this is our final answer.
Creating Counters that are Not Mod-2n
Although we are able to arrive at our the final solution for counters that are mod-2^n rather quickly, there will often be times that we will need to design ones that are not of this particular special mod number and thus we need to go through the entire shortcut instead of having the luxury of terminating early. For such a scenario, we are able to proceed by connecting our flip flops together as if we are creating a mod-2^n counter where 'n' is the number of minimum flip flops needed.
EXAMPLE (Well, a fourth of an example):
Make a mod-10 counter
We begin by figuring out how many stages we need to be able to construct the required counter; which, in this case, comes to being 4 flip flops. Laying out all four flip flops and connecting them as if we are creating a mod-2^n counter yields the following result:
Though we are not finished with this example, we will continue using it as we cover more steps.
