Networking TCP/IP Math

Example 9

Find the class of the address:           227.12.14.87

Solution

The first byte is 227 (between 224 and 239); the class is D.

Example 10

Find the class of the address:          193.14.56.22

Solution

The first byte is 193 (between 192 and 223); the class is C.

Example 11

In Example 6 we showed that class A has 2³¹ (2,147,483,648) addresses. How can we prove this same fact using dotted-decimal notation?

Solution

The addresses in class A range from 0.0.0.0 to 127.255.255.255. We notice that we are

dealing with base 256 numbers here.

Each byte in the notation has a weight.

The weights are as follows:

256³ , 256², 256¹, 256⁰

Last address:  127 ´ 256³ + 255 ´ 256² +
255 ´ 256¹ + 255 ´ 256⁰ = 2,147,483,647

First address:    =   0

If we subtract the first from the last and add 1, we get 2,147,483,648.

CLASSFUL ADDRESSING networking notes

CLASSFUL ADDRESSING

Occupation of the address space

In classful addressing, the address space is divided into five classes:
                                             A, B, C, D, and E.

Example 6

How can we prove that we have 2,147,483,648 addresses in class A?

Solution

In class A, only 1 bit defines the class.

The remaining 31 bits are available

for the address. With 31 bits,

we can have 2³¹ or 2,147,483,648 addresses.

Example 7

Find the class of the address:            00000001  00001011   00001011 11101111

Solution

The first bit is 0. This is a class A address.

Example 8

Find the class of the address:               11000001  10000011   00011011 11111111

Solution

The first 2 bits are 1; the third bit is 0.

This is a class C address.

All Networking numericals Wbut

Example 1

Change the following IP address from binary notation to dotted-decimal notation.

10000001  00001011   00001011 11101111

Solution

129.11.11.239

Example 2

Change the following IP address from dotted-decimal notation to binary notation. 111.56.45.78

Solution

01101111  00111000  00101101  01001110

Example 3

Find the error, if any, in the following IP address:

111.56.045.78

Solution

There are no leading zeroes in dotted-decimal notation (045).

Example 4

Find the error, if any, in the following IP address:

75.45.301.14

Solution

In dotted-decimal notation, each number Is less than or equal to 255; 301 is

outside this range.

Example 5

Change the following IP addresses from binary notation to hexadecimal notation.

10000001  00001011   00001011 11101111

Solution

0X810B0BEF  or    810B0BEF₁₆

Network layer notes

Network  layer

•       Logical Addressing-The network layer is responsible for the source-to-destination delivery of a packet, possibly across multiple networks.

•       The network layer adds a header that includes a logical address(IP address) of the sender and the receiver to the  packet coming from the upper layer.

•        Routing- When independent networks or links are connected together to create an internetwork, routers or switches routes the packets to their final destination.

IP Addresses

An IP address is a 32-bit address.

The IP addresses are unique.

RULE:

If a protocol uses N bits to define an address, the address space is 2^N because each bit can have two

different values (0 and 1) and N bits can have 2^N values.

The address space of IPv4 is

2³²
or
4,294,967,296.

NOTATIONS

•       Binary Notation

01110101   10010101   00011101   11101010

•       Dotted-decimal notation

•       Hexadecimal Notation

0111 0101   1001 0101   0001 1101   1110 1010

                       75               95             1D               EA

                                            0x75951DEA

•       Some rules regarding the different notations of IP  addresses:-

1)      There should not  be any leading zero.

2)      There should  not be more than four numbers in an IPv4 address.

3)      Each number should be less than or equal to 255.

4)      A mixture of any two notation in IP addressing is not allowed.