Question for Mathematicians/Engineers about using floating point with Grey encoding

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Reading about Genetic algorythms (articles.mql4.com/134) Genetic Algorythms: Mathematics:

I found the following statement:

Let us assume that the attribute values lie in the range of [0,1]. The range was split into 256 intervals for encoding. To encode their number, we will need 8 bit. The gene value is, for example, 00100101bG (the capital letter G means that it is the Gray code). First, using the Gray code, let us find the corresponding interval number: 25hG->36h->54d. Now, let's check what interval corresponds with it. By simple calculations, we obtain the interval of [0,20703125, 0,2109375]. I.e., the value of parameter will be (0,20703125+0,2109375)/2=0,208984375.

Question: What does the interval of [0,20703125,0,2109375] mean and where does it come from? Does this have to do with how floating point numbers are represented in storage?

Thanks in advance

gjrexach

 
Gray codes are integers. That part of article describes how the optimizer encodes floating point numbers to feed in to and out of the genetic algorithm, i.e. the internal workings of the optimizer.
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