subnets and hosts

[logistic_guy]

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

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

 

[khansaheb]

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

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

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[logistic_guy]

Let us first write down the subnet mask.

$\displaystyle /19$ gives:

subnet mask $\displaystyle = 11111111.11111111.11100000.00000000 = 255.255.224.0$

Once we have the subnet mask in hand, everything else can be solved easily. And that's what we'll do in the next post.

Piece of Cake

 

[logistic_guy]

This formula $\displaystyle 2^x$ gives us the number of subnets,

where $\displaystyle x$ is the number of $\displaystyle 1s$ in the interesting octet

Then, the number of subnets is:

$\displaystyle 2^3 = 8 \ \text{subnets}$

 

[logistic_guy]

This formula $\displaystyle 2^y - 2$ gives the number of hosts per subnet,

where $\displaystyle y$ is the number of all available $\displaystyle 0s$.

Then, the number of hosts is:

$\displaystyle 2^{13} - 2 = 8190$

And the answer is:

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