[aklug] Re: [OT] Re: random bits vs random Hex

On Tue, May 28, 2013 9:29 pm, Christopher Howard wrote:
> On 05/28/2013 06:54 PM, Szechuan Death wrote:
>>
>> Also, ultimately, keep in mind that your randomness tests are *only*
>> operating on binary digits; hex representation is only for
>> human-readable convenience. (The processor doan know from know hex, dude.)
>>
>
> I think this is the critical point: All you are changing is the label.
> The actual number of /allowed states/ does not change.
>
> I think the subject you are looking for is entropy and randomness. I
> don't quite grasp it myself yet, but the two critical components at
> least are the number of possible states, and the ability of the system
> to ensure that each of those possible states are equally likely to be
> chosen. In your scenario, neither has been changed.

That brings up an interesting point (which was not part of the original
post). What if you change to a base that doesn't match so well? For
example, take a random string of bits, group them into triplets, and
convert each one to a decimal digit.

001 011 000 110 111 010 010 101
..1 ..3 ..0 ..6 ..7 ..2 ..2 ..5

If the original string of bits is random, each new bit is equally likely
to take either of the possible states {0,1}. When converted to decimal,
though, each new digit is equally likely to be one of 0 through 7, but
it will never be 8 or 9. Whether that is useful information, of course,
depends on the application.

--
Bryan Medsker
bryanm@acsalaska.net
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