IP Calculating

 

Calculating IP Address Using the Binary Method

                                                              

An IP address is a 32-bit number that is usually represented in decimal format for human readability. Each bit in the 32-bit number can either be 0 or 1, which means that there are a total of 2^32 (or 4,294,967,296) possible IP addresses.

To represent an IP address in binary format, we can convert each decimal number in the IP address to its binary equivalent. For example:

192 = 11000000 168 = 10101000 42 = 00101010 0 = 00000000

So the binary representation of the IP address 192.168.42.0 would be:

11000000.10101000.00101010.00000000

In binary format, each group of 8 bits is called an octet. So we can also represent the IP address in binary format as a series of 4 octets:

11000000 . 10101000 . 00101010 . 00000000

Each bit in the binary representation of an IP address represents a power of 2, starting from 2^0 (or 1) for the rightmost bit and doubling with each bit to the left. For example:

128 64 32 16 8 4 2 1 1 1 0 0 0 0 0 0 = 192 128 64 32 16 8 4 2 1 1 0 1 0 1 0 0 0 = 168 128 64 32 16 8 4 2 1 0 0 1 0 1 0 1 0 = 42 128 64 32 16 8 4 2 1 0 0 0 0 0 0 0 0 = 0

So the IP address 192.168.42.0 can also be represented in binary format using the power of 2 notation:

11000000.10101000.00101010.00000000 128+64 168 42 0

Culculating a Subnet Mask

To calculate a subnet mask, you need to determine the network portion and the host portion of the IP address. The subnet mask is a 32-bit number that has a series of 1's on the network portion and a series of 0's on the host portion.

The length of the network portion of the subnet mask is determined by the number of subnets you want to create. The length of the host portion is determined by the number of hosts you want to assign to each subnet.

Here are the steps to calculate a subnet mask:

• 1.      Determine the number of subnets you want to create.
• 2.      Determine the number of hosts you want to assign to each subnet.
• 3.      Convert the number of subnets and hosts to binary.
• 4.      Calculate the number of bits needed for the network portion and the host portion.
• 5.      Write the subnet mask in binary using the appropriate number of 1's for the network portion and 0's for the host portion.
• 6.      Convert the binary subnet mask to decimal format for human readability.

 Here is an example:

  Suppose you want to create 4 subnets, each with up to 16 hosts.

• 1.      The number of subnets is 4, which is 100 in binary.
• 2.      The number of hosts is 16, which is 10000 in binary.
• 3.      100 (subnets) and 10000 (hosts) are both 4-bit numbers in binary.
• 4.      You need 2 bits for the network portion (2^2 = 4 subnets) and 4 bits for the host portion (2^4 = 16 hosts).
• 5.      The subnet mask in binary is 11111111.11111111.11111100.00000000.
• 6.      The subnet mask in decimal format is 255.255.252.0.

So the subnet mask for creating 4 subnets, each with up to 16 hosts, is 255.255.252.0.

Converting Binaries to Decimals

To convert a binary number to decimal, you can use the following method

   1.      Write down the binary number.

   2.      Assign each digit of the binary number a power of 2, starting from 0 and increasing by 1 for each subsequent digit. For example, if the binary number is 1011, you would assign powers of 2 as follows:

      ·          1 (the rightmost digit) is 2^0 = 1 

      ·         1 (the second-rightmost digit) is 2^1 = 2

      ·         0 (the third-rightmost digit) is 2^2 = 4

      ·         1 (the leftmost digit) is 2^3 = 8

    3.      Multiply each digit of the binary number by its corresponding power of 2.

    4.      Add up the products from step 3 to get the decimal equivalent of the binary number.

For example, to convert the binary number 1011 to decimal

    1.      Write down 1011.

    2.      Assign powers of 2: 8, 4, 2, 1.

    3.      Multiply each digit by its corresponding power of 2: 1x1 + 1x2 + 0x4 + 1x8 = 1 + 2 + 0 + 8 = 11.

    4.      The decimal equivalent of 1011 in binary is 11 in decimal.

    Therefore, the decimal equivalent of the binary number 1011 is 11.

     To convert a binary number to a decimal a numerical value to each bit, starting from the right with       1b and proceeding to the left, doubling the value each time. The values for an 8-bit number are              therefore as follows.

        128      64        32        16                    8          4          2          1

      You then up the values of your 8-bit binary number with the eight conversion value

     1          1          1          0          0          0          0          0

    128      64        32        16        8          4          2          1

    Final you add together the conversion valu for the1-bit only

 

      1          1          1          0          0          0          0          0

   128      +64      +32      +0        +0        +0        +0        +0   =224

 

    The decimal equivalent to the binary value 11100000 is 224

   

  Calculating IP addresses Using the Subtraction Method

        The subtraction method is a way of calculating the IP address range given an IP address         and a subnet mask. The steps to calculate the IP address range using the subtraction            method are as follows:

  1- Convert the IP address and subnet mask to binary.

  2- Subtract the binary value of the subnet mask from the binary value of the IP address               using the bitwise AND operation.

   3- Add 1 to the result obtained from step 2 to get the first IP address in the range.

   4- Subtract the binary value of the subnet mask from the binary value of all 1's using the            bitwise AND operation. 

   5-  Subtract the result obtained from step 4 from the binary value of the IP address and              add 1 to get the last IP address in the range.

        

                    Let's illustrate the above steps with an example. Suppose we have the IP                  address 192.168.1.100 and the subnet mask 255.255.255.0. we can convert the IP address and subnet mask to binary as Follows

        IP address: 1100000000.10101000.00000001.0100100 

    Subnet Mask: 11111111.11111111.11111111.00000000

    Step 2: Perform a bitwise AND operation between the IP address and the subnet mask.

     11000000.10101000.00000001.01100100(IP address)                                                                11111111.11111111.11111111.00000000(Subnet mask)

    11000000.10101000.00000001.00000000

    Step 3: Add 1 to the result from 2 to get the first IP address in the range.

    11000000.10101000.00000001.00000000 +1 = 11000000.10101000.00000001.00000001           =192.168.1.1

    Step 4: Perform a bitwise AND operation between the subnet mask and all 1's.

    11111111.11111111.11111111.00000000 (subnet mask)                                                              11111111.11111111.11111111.11111111 (All 1's)

     11111111.11111111.11111111.00000000

    Step 5: Subtract the result from step 4 from the IP address, and add 1 to get the last IP             address in the range.

    11000000.10101000.00000001.01100100 (IP address)                                                                11111111.11111111.11111111.00000000 (Result from step4)

    00000000.00000000.00000000.01100100 + 1=00000000.00000000.00000000.01100101         =192.168.1.254

    Therefore, the IP address range for the subnet with IP address 192.168.1.100 and sunet mask 255.255.255.0 is 192.168.1.254.