network cisco ccna gns3 certification arteq

network cisco ccna gns3 certification arteq
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Wednesday, December 26, 2012

repost minus 256...

this has eclipsed all others for amount of hits, and rightly so...  i wrote and posted this on the internet back in 2004...


comfort with binary to decimal conversion

comfort with exponents of 2, ie. 2 to the x = ?

comfort with the three classful boundaries...

the thing about ccna and all it's variants, on up through ccie is that you can count on the numbers... if you are afraid of the numbers and their various permutations and calculations, then all of this will be difficult at best...

this site was created for the ccent/ccna candidate... anything more advanced than that is gravy...

if you do a search in the search bar for ccna, you will find over a hundred posts directly related to ccna... and don't forget the hex tutorials...

there is safety in numbers...

the minus 256 technique
this presupposes knowledge of binary and ip addressing conventions
rule 1. remember that the first octet only ever designates the class
of ip, ie. a b or c
rule 2. the first octet that contains a zero bit, is always the octet
where the action occurs, ie,, calculation happens in 4th
octet; or, calculation happens in third octet; or, calculation occurs in 3rd octet, and so on.
rule 3. see rule number 1. The first octet always tells you the class
of address no matter the octet where subnetting occurs.  Subnetting
calculation always happens in the octet of the ip address that the
subnet mask designates with its first instance of less than 255, or
more simply, the first instance of a zero bit.
therefore, given mask of, we know that the
calculation will happen in the ip's 3rd octet.  The mask designates
that with 248.  it is imperative that this is understood.
another way of looking at it in the above example is; the octet in the
subnet mask with the first instance of less than 255, or the first
zero bit, is the multiplier.
rule 4.  when the multiplier (first zero bit octet or octet with first
instance of less than 255) is determined always subtract it from 256
to determine the ranges.
ie. 256-248=8, hence 8 is the multiplier.
using with, it is determined that we have a
class b address 172, our calculation must happen in the 3rd octet, and
we must subtract 256 from 248 to get 8.
the rest is academic:
the multiplier ( has determined our first subnet range
8 16 24 32 40, etc
the first range (excepting the use of subnet zero) begins with 8 and
ends with 15, the second range begins with 16 and ends with 31, next
range begins with 32, and so on up to 255.
Important: there are 256 numbers total comprising the range 0-255,
including the zero.
in the ip /21 (notice the use of bit count; this equals
248 as well.  to determine the number to subtract from 256 in  bit
count form, you need to add the bits...
1st octet 8 bits, second octet 8 bits, third octet 5 bits, hence 8 + 8
+ 5 =/21 or 248 or /21 =
our calculation takes place in the octet designated by the first
instance of a zero, or in our example, /21 or  we
determine that 10 is the number occupying the third octet in our
example, and our multiplier has determined the first possible subnet
is 8 (excepting subnet zero)
so, since 10 falls between 8 and 15 (16 begins the next subnet or
network), our valid range for the address has been determined.
8    16   32...
9    17
14   30
15   31
so our octet 3 number, which is 10 in the example, can only fall
between the range of 8 (the  network), 9 our first valid host, 14 our
last valid host, and 15 which is the broadcast address for the network
our number ten resides in.
if we changed our third octet number to /21 or, we know that our calculation still takes place in the
3rd octet, but the number 20 falls between the network 16, the
broadcast 31, and within the valid range of hosts which is 17-30...
one more example:
the class of address is C
the action takes place in octet 4
subtract 192 from 256 which equals 64 and we can determine the
network, the broadcast and the valid range of hosts because 64 is our
64     128    192
65     129    193
126    190    254
127    191    255
our number in octet 4 is 100, our number 100 falls between 64 (the
first network) and 128 (the second network).  the subnet address is
   the first valid host is
   the last valid host in the range is
   and the broadcast address is
it takes a little time and effort, and a lot of practice, but you'll
eventually be able to do it without paper.

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