networking - 2

[logistic_guy]

The network address of \(\displaystyle 172.16.0.0/19\) provides how many subnets and hosts?

\(\displaystyle \bold{A.}\) \(\displaystyle 7\) subnets, \(\displaystyle 30\) hosts each
\(\displaystyle \bold{B.}\) \(\displaystyle 7\) subnets, \(\displaystyle 2,046\) hosts each
\(\displaystyle \bold{C.}\) \(\displaystyle 7\) subnets, \(\displaystyle 8,190\) hosts each
\(\displaystyle \bold{D.}\) \(\displaystyle 8\) subnets, \(\displaystyle 30\) hosts each
\(\displaystyle \bold{E.}\) \(\displaystyle 8\) subnets, \(\displaystyle 2,046\) hosts each
\(\displaystyle \bold{F.}\) \(\displaystyle 8\) subnets, \(\displaystyle 8,190\) hosts each

 

[logistic_guy]

\(\displaystyle \bold{F.}\) \(\displaystyle 8\) subnets, \(\displaystyle 8,190\) hosts each

My intuition tells me that the correct answer is \(\displaystyle \bold{F}\). We will see later why this might be the correct answer!

 

[logistic_guy]

\(\displaystyle 172.16.0.0/19\)

\(\displaystyle /19\) is the number of network bits.

In other words,

\(\displaystyle /19\) means the \(\displaystyle \bold{Subnet \ Mask}\) contains \(\displaystyle 19 \ \textcolor{green}{\bold{network}}\) bits.

Or

\(\displaystyle \bold{Subnet \ Mask} = 11111111.11111111.11100000.00000000\)

This also means that it has \(\displaystyle 13 \ \textcolor{indigo}{\bold{host}}\) bits \(\displaystyle \longrightarrow\) the number of zeros

What should we do with this information?

Well, first look at the \(\displaystyle \bold{Subnet \ Mask}\) above. You will notice that it has \(\displaystyle 4\) octets, each contains \(\displaystyle 8\) bits.

If you look closer, you will see that the third octet has a mixture of \(\displaystyle \textcolor{blue}{\bold{ones}}\) and \(\displaystyle \textcolor{red}{\bold{zeros}}\). And there where we are interested in.

We are interested mainly in this octet: \(\displaystyle 11100000\)

Before we say anything about this interesting octet, let us familiarize ourselves with the other form of the \(\displaystyle \bold{Subnet \ Mask}\). That is:

\(\displaystyle 11111111.11111111.11100000.00000000 = 255.255.224.0\)

 

[logistic_guy]

We go back to the interesting octet \(\displaystyle 11100000\).

This octet has \(\displaystyle \textcolor{red}{\bold{3}}\) network bits, so:

\(\displaystyle 2^{\textcolor{red}{\bold{3}}} = \textcolor{blue}{\bold{8}} \longrightarrow\) number of subnets

So far, we are sure that the answer is not \(\displaystyle \bold{A}\), \(\displaystyle \bold{B}\), or \(\displaystyle \bold{C}\)

 

[logistic_guy]

Another way to calculate the number of subnets is to convert the interesting octet to base \(\displaystyle 10\).

\(\displaystyle 11100000 = 224\)

Then, you can find the length of one subnet by this simple subtraction:

\(\displaystyle 256 - 224 = 32\)

This means that the total number of subnets is:

\(\displaystyle \frac{256}{32} = \textcolor{green}{\bold{8}}\)