chapter 12

Class A

1-126; 255.0.0.0

Class B

128-191 255.255.0.0

Class C

192-223 255.255.255.0

Key facts about how to calculate the number of subnets and number of hosts per subnet

Number of subnets = 2s Number of hosts per subnet = 2h - 2

Reference table of the private (RFC 1918) IP networks

Private IP Networks Class of Networks Number of Networks 10.0.0.0 through 10.0.0.0 A 1 172.16.0.0 through 172.31.0.0 B 16 192.168.0.0 through 192.168.255.0 C 256

Decimal process to find the structure (network, subnet, and host parts) of an IP address

Step 1 (Same as Step 1 in the binary process.) Compare the first octet of the address to the table of Class A, B, C addresses; write down the number of network bits depending on the address class. Step 2 If the mask is in dotted decimal format, convert the mask to prefix format. Step 3 To find the number of host bits, subtract the prefix length value from 32. Step 4 (Same as Step 4 in the binary process.) Calculate the number of subnet bits by subtracting the number of combined network and host bits from 32.

Binary process to find the structure (network, subnet, and host parts) of an IP address

Step 1 Compare the first octet of the address to the table of Class A, B, C addresses; write down the number of network bits depending on the address class. Step 2 Find the number of hosts bits by: a. Converting the subnet mask to binary. b. Counting the number of binary 0s in the mask. Step 3 Calculate the number of subnet bits by subtracting the number of combined network and host bits from 32.

Binary process, with no binary shortcuts, to find an address's resident subnet by using a Boolean AND

Step 1 Convert the IP address from decimal to binary. Step 2 Convert the subnet mask to binary, writing this number down below the IP address from Step 1. Step 3 Perform a bitwise Boolean AND of the two numbers. To do so: a. AND the first bit of the address with the first bit of the subnet mask, recording the result below those numbers. b. AND the second bit of each number, recording the result below those numbers. c. Repeat for each pair of bits, resulting in a 32-bit binary number. Step 4 Convert the resulting binary number, 8 bits at a time, back to decimal. This value is the subnet number.

Binary process for converting a mask from dotted decimal to prefix notation

Step 1 Convert the dotted decimal mask to binary. Step 2 Count the number of binary 1s in the 32-bit binary mask; this is the value of the prefix notation mask. For example, the dotted decimal mask of 255.255.240.0 converts to 11111111 11111111 11110000 00000000 in binary. The mask has 20 binary 1s, so the prefix notation of the same mask is /20.

Decimal process for converting a mask from prefix to dotted decimal notation

Step 1 Divide x by 8 (x/8), noting the number of times 8 fully goes into x (the dividend, represented as a d), and the number left over (the remainder, represented as an r). Step 2 Write down d octets of value 255. (This in effect begins the mask with 8, 16, or 24 binary 1s.) Step 3 For the next octet, find the decimal number that begins with r binary 1s, followed by all binary 0s. (Table 12-9 will be useful for this step.) Step 4 For any remaining octets, write down a decimal 0.

Summarizes how to choose a subnet mask based on a set of requirements

Step 1 Find the number of network bits (N) based on Class A, B, C rules. Step 2 Find the number of subnet bits (S) based on the formula 2s , such that 2s => the required number of subnets. Step 3 Find the number of host bits (H) based on the formula 2h - 2, such that 2h - 2 => the required number of hosts per subnet. Step 4 Write down, starting on the left, N + S binary 1s. Step 5 Write down, starting on the right, H binary 0s. Step 6 If the number of binary 1s and 0s together adds up to less than 32: a. Fill in the remaining "wildcard" bit positions—between the binary 1s and 0s— with the letter X. b. Find all combinations of bits for the wildcard bit positions that meet the requirements for only having one consecutive string of binary 1s in the binary mask. Step 7 Convert the mask(s) to decimal or prefix format as appropriate. Step 8 To find the mask that maximizes the number of subnets, pick the mask that has the most binary 1s in it. To find the mask that maximizes the number of hosts per subnet, pick the mask that has the largest number of binary 0s in it.

Binary process to find a subnet broadcast

Step 1 Record the decimal mask in the first row of a table and the decimal IP address in the second row. Step 2 For any mask octets of value decimal 255, copy the IP address's octet value for the same octet of the decimal subnet number. Step 3 Similarly, for any mask octets of value decimal 0, write down a decimal 0 for the same octet of the subnet number. Step 4 If the subnet number still has one remaining octet to be filled in, do the following for that one octet: a. Convert that one remaining octet of the IP address to binary. b. Convert that one remaining octet of the mask to binary. c. AND the two 8-bit numbers together. d. Convert the 8-bit number to decimal, and place that value in the one remaining octet of the subnet number.

Fnding the range of valid IP addresses in a subnet

Step 1 To find the first IP address, copy the subnet number, but add 1 to the fourth octet. Step 2 To find the last IP address, copy the subnet broadcast address, but subtract 1 from the fourth octet.

Decimal process to find the subnet number, broadcast address, and range of addresses in a subnet

Step 1 Write down the subnet mask in the first empty row of the subnet chart and the IP address in the second empty row. Step 2 Find the octet for which the subnet mask's value is not 255 or 0. This octet is called the interesting octet. Draw a dark rectangle around the interesting octet's column of the table, top to bottom. Step 3 Record the subnet number's value for the uninteresting octets, as follows: a. For each octet to the left of the rectangle drawn in Step 2: Copy the IP address's value in that same octet. b. For each octet to the right of the rectangle: Write down a decimal 0. Step 4 To find the subnet number's value for this interesting octet: a. Calculate the magic number by subtracting the subnet mask's interesting octet value from 256. b. Calculate the multiples of the magic number, starting at 0, up through 256. c. Write down the interesting octet's value, calculated as follows: Find the multiple of the magic number that is closest to, but not greater than, the IP address's interesting octet value. Step 5 Find the subnet broadcast address, as follows: a. For each subnet mask octet to the left of the rectangle: Copy the IP address octet value. b. For each subnet mask octet to the right of the rectangle: Write down 255. c. Find the value for the interesting octet by adding the subnet number's value in the interesting octet to the magic number, and subtract 1. Step 6 To find the first IP address, copy the decimal subnet number, but add

Decimal process to find all subnets of a classful network, with one mask and fewer than 8 subnet bits

Step 1 Write down the subnet mask, in decimal, in the first empty row of the table. Step 2 Identify the interesting octet, which is the one octet of the mask with a value other than 255 or 0. Draw a rectangle around the column of the interesting octet. Step 3 Calculate the magic number by subtracting the subnet mask's interesting octet from 256. (Record this number in the list-all-subnets chart, inside the rectangle, for easy reference.) Step 4 Write down the classful network number, which is the same number as the zero subnet, in the next empty row of the list-all-subnets chart. Step 5 To find each successive subnet number: a. For the three uninteresting octets, copy the previous subnet number's values. b. For the interesting octet, add the magic number to the previous subnet number's interesting octet. Step 6 Once the sum calculated in Step 5b reaches 256, stop the process. The number with the 256 in it is out of range, and the previous subnet number is the broadcast subnet.

Decimal process to find all subnets of a classful network, with one mask and more than 8 subnet bits

Step 1 Write down the subnet mask, in decimal, in the first empty row of the table. Step 2 Identify the interesting octet, which is the one octet of the mask with a value other than 255 or 0. Draw a rectangle around the column of the interesting octet. Step 3 Calculate the magic number by subtracting the subnet mask's interesting octet from 256. (Record this number in the list-all-subnets chart, inside the rectangle, for easy reference.) Step 4 Write down the classful network number, which is the same number as the zero subnet, in the next empty row of the list-all-subnets chart. Step 5 To find each successive subnet number: a. For the three uninteresting octets, copy the previous subnet number's values. b. For the interesting octet, add the magic number to the previous subnet number's interesting octet. Step 6 Once the sum calculated in Step 5b reaches 256, stop the process. The number with the 256 in it is out of range, and the previous subnet number is the broadcast subnet.

Decimal process to find the range of addresses in a subnet, after having found the subnet number and subnet broadcast address

Step 1 Write down the subnet number (or IP address), and subnet mask, in binary form. Make sure that the binary digits line up directly on top of the other. Step 2 Separate the host part of these numbers from the network/subnet part by drawing a vertical line. Place this line between the rightmost binary 1 in the mask and the leftmost binary 0. Extend this line up and down an inch or two. Step 3 To find the subnet broadcast address, in binary: a. Copy the bits of the subnet number (or IP address) that are to the left of the vertical line. Step 4 Convert the 32-bit binary subnet broadcast address to decimal, 8 bits at a time, ignoring the vertical line.

Binary process for converting a mask from prefix to dotted decimal notation

Step 1 Write down x binary 1s, where x is the value listed in the prefix version of the mask. Step 2 Write down binary 0s after the binary 1s until you have written down a 32-bit number. Step 3 Convert this binary number, 8 bits at a time, to decimal, to create a dotted decimal number; this value is the dotted decimal version of the subnet mask. For example, with a /20 prefix, you would first write: 11111111 11111111 1111

Important fact about the binary values in subnet masks

The network and subnet bits in a subnet mask are, by definition, all binary 1s. Similarly, the host bits in a subnet mask are, by definition, all binary 0s. So, the only valid subnet mask, in binary, is 11111111 11111111 11111111 00000000

A note that the subnet numbers of a classful network are multiples of the magic number

The various subnet numbers' interesting octet values are multiples of the magic number. For example, as you read in the previous section, with Class B network 130.4.0.0, mask 255.255.252.0, the magic number is 256 - 252 = 4. So, the subnets of 130.4.0.0/ 255.255.252.0, in the third octet, are multiples of 4—namely, 130.4.0.0 (zero subnet), 130.4.4.0, 130.4.8.0, 130.4.12.0, 130.4.16.0, and so on, up through 130.4.252.0 (broadcast subnet).

Decimal process for converting a mask from dotted decimal to prefix notation

To convert a mask from dotted decimal to prefix format, use the following process: Step 1 Start with a prefix value of 0. Step 2 For each dotted decimal octet, add the number of binary 1s listed for that decimal value in Table 12-9. Step 3 The prefix length is /x, where x is the sum calculated at Step 2. For example, with a mask of 255.255.240.0 again, for Step 1, you start with a value of 0. At Step 2, you add the following: Because of the first octet value of 255, add 8. Because of the second octet value of 255, add 8. Because of the third octet value of 240, add 4. Because of the fourth octet value of 0, add 0. The end result, 20, is the prefix length, written as /20.

Tips for doing binary-to-decimal and decimal-to-binary conversion for IP addresses

When you convert from one format to the other, each decimal number represents 8 bits. When you convert from decimal to binary, each decimal number converts to an 8-bit number. When you convert from binary to decimal, each set of 8 consecutive bits converts to one decimal number.

IP Subnet-Zero

allows you to use the first and last subnet in your network design; turned this command on by default

Nine decimal values allowed in subnet masks, with the binary equivalent values

pg 353

How to determine which formula to use to calculate the number of available subnets

pg 361

[no] ip subnet-zero

then an IP address in a zero subnet cannot be configured

Tips for understanding how to find the mask that provides the most subnets or most hosts per subnet

■ The mask with the most subnet bits: The mask for which the wildcard bits were set to binary 1, thereby making the subnet part of the addresses larger, maximizes the number of subnets and minimizes the number of hosts per subnet. ■ The mask with the most host bits: The mask for which the wildcard bits were set to binary 0, thereby making the host part of the addresses larger, maximizes the number of hosts per subnet and minimizes the number of subnets.

Facts about how the subnet mask identifies part of the structure of an IP address

■ The mask's binary 1s define the combined network and subnet parts of the addresses. ■ The mask's binary 0s define the host part of the addresses. ■ The class rules define the size of the network part.

Facts about how to analyze and find the size of the network, subnet, and host parts of an IP address

■ The network part of the address is always defined by class rules. ■ The host part of the address is always defined by the subnet mask. The number of binary 0s in the mask (always found at the end of the mask) defines the number of host bits in the host part of the address. ■ The subnet part of the address is what is left over in the 32-bit address.