D position: Nmod2>=1 means D is 1.
C position: Nmod4>=2 means C is 1.
B position: Nmod8>=4 means B is 1.
A position: Nmod16>=8 means A is 1.
For D, we obviously have the names of Even/Odd assigned to numbers. But I do not know if there are names for the groups of numbers categorized by the value in certain place in their binary representation, bar the least significant one (even/odd).
And thanks to you asking this question and helping me think on this issue, I came up with this (although someone probably has better) function to convert numbers into binary:
Code: Select all
^0::
Loop, 25
list.=A_Index ":`t" ConvertToBinaryStringRedux(A_Index) "`n"
MsgBox %list%
return
ConvertToBinaryStringRedux(number){
If number is not integer
return
Loop
string:=((Mod(number,x:=(2**A_Index))>=x/2)?1:0) string
Until x>number
return string
}
Edit, here's a bit of a roundabout way to show the numbers with this property using the function above:
Code: Select all
^0::
Loop, 25
list.=ConvertToBinaryStringRedux(A_Index) "`n"
MsgBox %list%
StringSplit, array, list, `n
Loop % array0
btruelist.=x:=SubStr(000 . array%A_Index%,-2,1)?A_Index ":`t" array%A_Index% "`n":""
MsgBox % btruelist
return
The -2 there in the second parameter of the SubStr() pulls the third to last digit (in your table in the original post, this would be the B column). If it's a 1, then it's part of this group whose binary has a 1 in the B column, so it's added to the list "btruelist". It also keeps track of the decimal values added to the list so you can see the pattern emerging. The pattern is that you have 2^(k-1) consecutive numbers when you look at the kth digit from the right in the binary representation. That is, when k=1, we're looking in column D and find that the longest streak of consecutive numbers is 1. 2^(1-1) = 2^0 = 1. When you look in column C, the longest streak of consecutive numbers is 2. 2^(2-1) = 2^1 = 2. When you look in column B, the streak is 4. Column A, the streak is 8. In fact, that's exactly the value of the column itself - the right most is 1, the second right most is 2, the third right most is 4, the fourth right most is 8.
I deleted my post after about a 1 min. because I thought about it some more and eventually, I think, understood what you meant.
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