[aclug-L] IP address question

[Jonathan Hall <jonhall@xxxxxxxxxxxx>]

Well, I got a few replies in responce to my question, "How many _routeable_
IP addresses have exactly 12 digits?"  I think one was correct (I can't find
it right now).  That person doesn't live in Kansas any more, though, so I
guess that relieves us from furnishing a prize?  :-)

Here's the answer as I've figured it... someone tell me if I'm wrong or
overlooking something:

573452724

This is how I figured it:

Normal 32-bit IP space contains 4294967296 IP addresses,
0.0.0.0 - 255.255.255.255.  This number can be found by taking 256^4; 256
possible numbers for each of 4 locations.

To get 12 digits in an IP address, each of the 4 numbers must have 3 digits. 
This means that there are only 155 possibilities for each number (100
through 255).  So, we can take 155^4 (155 possibilities in each of 4
locations) and come up with 577200625 possible IP addresses--that's only
13.4% of the original IP space.

Not all of these 570 million IP addresses are routeable, though.

There are three subnets that are deemed 'non-routable' and for use in
private networks only:

10.0.0.0/255.0.0.0
192.168.0.0/255.255.0.0
172.16.0.0/255.255.240.0

So, we need to remove these three subnets from our calculations.  Only one
of these (192.168.0.0) even needs to be considered, though, b/c theother two
have numbers with less than 3 digits.  In the 192.168.0.0 subnet, we have
155^2 or 24025 hosts with 12 digits, so we subtract that from 577200625 for
577176600.

Also, 127.0.0.0/255.0.0.0 is private and non-routable.  Here we have 155^3
or 3723875 12-digit IPs we must discount leaving us with 573452725.

Then, for my final answer I subtracted one more for 255.255.255.255, and
get... 573452724

So the answer is: 155^4 - 155^3 - 155^3 - 1 = 573452724

Did I miss anything?  :-)


--
"Yes, the president should resign. He has lied to the American people, time
and time again, and betrayed their trust. He is no longer an effective
leader.  Since he has admitted guilt, there is no reason to put the American
people through an impeachment. He will serve absolutely no purpose in
finishing out his term, the only possible solution is for the president to
save some dignity and resign."
      -- William Jefferson Clinton, 1974 on President Nixon.
--
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  Jonathan Hall  *  jonhall@xxxxxxxxxxxx  *  PGP public key available
 Systems Admin, Future Internet Services; Goessel, KS * (316) 367-2487
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