very hard networking question

[logistic_guy]

here is the question

You are given the network address $\displaystyle 172.16.0.0/27$:

(a) What class does this address belong to?
(b) What is the subnet mask?
(c) Is the IP address $\displaystyle 172.16.3.159$ a network address, host address, or broadcast address?


my attemb
i think the first two part is easy
it belong to class $\displaystyle B$
the subnet mask is $\displaystyle 255.255.255.224$
how to answer part (c)?

 

[logistic_guy]

The main idea of this exercise is to fill the following table:

Network Address​	172.16.0.0​	172.16.0.32​	. . . . . .​	172.16.0.224​
First Host Address​	172.16.0.1​	172.16.0.33​	. . . . . .​	172.16.0.225​
Last Host Address​	172.16.0.30​	172.16.0.62​	. . . . . .​	172.16.0.254​
Broadcast Address​	172.16.0.31​	172.16.0.63​	. . . . . .​	172.16.0.255​

I have shown only $\displaystyle 3$ subnets out of $\displaystyle 8$. I have shown the first, second, and last subnet in this network. In later posts, you will understand why this network has $\displaystyle 8$ subnets and why they are divided in this range.

For now this information is sufficient to show you what kind of ip address is $\displaystyle 172.16.3.159$

I started with the network address $\displaystyle 172.16.0.0$ and I got the table above. If I start with the network address $\displaystyle 172.16.3.0$, I will get the same table above, but instead of having $\displaystyle 0$ in the third octet, I will have $\displaystyle 3$.

The length between the first and second network address is $\displaystyle 32$, this means that each time I add $\displaystyle 32$ I get the next network address. Let us count.

First Network Address: $\displaystyle 172.16.0.0$
Second Network Address: $\displaystyle 172.16.0.32$
Third Network Address: $\displaystyle 172.16.0.64$
Fourth Network Address: $\displaystyle 172.16.0.96$
$\displaystyle 5^{\text{th}}$ Network Address: $\displaystyle 172.16.0.128$
$\displaystyle 6^{\text{th}}$ Network Address: $\displaystyle 172.16.0.160$
$\displaystyle 7^{\text{th}}$ Network Address: $\displaystyle 172.16.0.192$
$\displaystyle 8^{\text{th}}$ Network Address: $\displaystyle 172.16.0.224$

This information tell us that since $\displaystyle 172.16.0.160$ is a network address, the ip that comes before it $\displaystyle 172.16.0.159$ must be a broadcast address.

Then

$\displaystyle 172.16.3.159$ is a broadcast address.