## Internet of Networks

Previously, we have discussed that IPv4 addressing are done in two categories;

In these days, classful addressing is almost obsolete and are replaced by Classless Addressing.

To overcome the flaws  of classful addressing such as the address depletion and to provide more organizations to access the internet, classless addressing was designed and implemented.

In this type of addressing, there are no classes but still the addresses are granted in blocks.

In classless addressing, when an organization , small or large needs to connect the internet; it is granted a block (means a range) of addresses. The size of the block means the number of addresses varies based on the nature and need of the organization.

Although, there are some restrictions before implementation of classless addresses.

### Restrictions

To facilitate the handling of addresses, the authority of Internet imposed three restrictions on classless address blocks, such as:

1. All the addresses in a block must be contiguous, one after the another.
2. The number of addresses in block must be a  power of 2, means 1, 2, 4 6 8 ...n (Where n is an even number)
3. The first address of the block must be divisible by the number of addresses in the block.

Let us come to the mathematics then.

For First Address: The first address of any block can be found by setting the rightmost 32-n bits to 0's, where 'n' is mask.

Example 1.

A block of addresses is granted to a small organization, where one of the address is 205.16.37.39/28. What is the first address of the block?

Solution.
The binary representation of 205.16.37.39 is :

11001101 00010000 00100101 00100111

if we set the right most 32-n bit  to 0, i.e 32-28 = 4

We get, 11001101 00010000 00100101 00100000

which is, 205.16.37.32

So, the first address of the block is 205.16.37.32.

For Last Address: The last address of any block can be found by setting the rightmost 32-n bits to 1's, where 'n' is the mask.

Example 2.

Find the last address of Example 1.

Solution.
The binary representation of 205.16.37.39 is :

11001101 00010000 00100101 00100111

if we set the right most 32-n bit  to 1, i.e 32-28 = 4

We get, 11001101 00010000 00100101 00101111

So, the last address of the block is 205.16.37.47.

For Total Number of Addresses: The total number of addresses in the block can be found by using the formula 232-n

where 'n' is the musk.

Example 3.

Find the number of addresses of Example 1.

Solution.
The value of n is 28, which means the number of addresses is 232-28

which is 16.

### There is another way to solve the above problems:

There is another way to find the first address, last address, no. of address is to represent mask into 32-bit binary format. Like, from example 1. the musk is 28, so the 32-bit binary format is:

11111111 11111111 11111111 11110000 (twenty eight 1s and four 0s)

For first address: Perform a Logical AND between the given address and the 32-bit binary format of the mask.

For No. of addresses in the block: No. of addresses can be found by complementing the mask, then interpreting it as a decimal no., and adding 1 to it.

This way is particularly useful when you are writing programs to find any piece of information. Free image downloaded from unsplash.com