[STUDY] LOGIC STRIP & GRAPHIC MOD. [PT.2]

Here we go ! The second part of our study about logic strips. ūüėÄ

Like i have previously said, i will upgrade the system of “logic strip” (who plot the 8 bits data of each number processed on a vertical strip) with a “Not Gate” system who will plot inverting gate where it’s needed.

Let’s try with the number 4.

So the¬†software will plot the 0 to 64 numbers (on 8 bits), and , after that, it will invert bits for making the “4” number at each 0-64 numbers.

Example :

My list of number is 1 , 2, 5, 10 . After the work of the software my list will be : 4, 4, 4, 4.

If i set the reference number on 6 it will be 6, 6, 6, 6. There is absolutely no interest on a electronic way but i need a basic start.

ex1
Equivalent system.

Here is the plot (in blue = unchanged bits ; in purple = inverted bits) :

Not_4
[0 – 64] to 4
You’ve probably notice that it’s the same as the original count (0-64) but with a difference on the¬†third column .

If we change the plotting to Black = unchanged bit (Low) ; Red = Inverted bit (Low to High) ; Purple =  Inverted bit (High to Low) and Blue = unchanged bit [High) it does this :

Not_4_pEnum
[0-64] to 4 (differential)
We can clearly see that the third column : the “high” bit of 4 (00000100) , are different and with a clear pattern.

Quite logic because every number need to do 0000100. So when a bit is High it goes Low and the bit of the third column need to be High when Low and stay High when already High.

So the “Full Blue/Red” pattern is equal to :

Ex2.PNG

And it work for every similar cases :

Not_5_pEnum
[o – 64] to 5
We can observe other pattern on simple strips like [0-64] to [o-64] * 2 :

Not_jx2
[0 – 64] to [o-64] x 2
It’s more complicated but we can clearly see that the Red bits are High when the¬†previous column is High (and before processing). It’s of course triggered by the behavior of the “jx2″function (cf. previous study).

So those two pattern are identified and correct. But with some¬†systems, it’s way more complicated to resolve logic equations.

Even if some columns or local data are easily resolvable , the major strips is way too complicated for a quick analysis.

However , the “color – aspect” is useful for evaluating the amount of gate / component you need.

Finally , i can say that the “Logic Strips” method is a quick tool for pre-analysis of an logic equation. It’s the first step for building more complicated analysis and a good ally for the every day maker.

Please, be free to customize those techniques and tell me what you make with !

 

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