IP Addresses
| IP addresses are 32 bits long; like all network-level addresses, they have a network portion and a host portion. The network portion uniquely identifies the data link (that is, the network) and is common to all devices attached to the network. The host portion uniquely identifies a particular device attached to the network. There are several ways to represent the 32 bits of an IP address. For instance, the 32-bit IP address 00001010110101100101011110000011 could be represented in decimal as 181,819,267. The binary format is cumbersome, and the decimal format is time-consuming to calculate. A better format is shown in Figure 2.9. The 32 bits of the address comprise four octets, each of which can be represented with a decimal number between 0 and 255, with dots between the decimal representations. In the figure, the 32-bit address is mapped into a dotted -decimal representation. Figure 2.9. The dotted-decimal format is a convenient way to write IP addresses, but it should not be confused with what the router (or host) sees ”a 32-bit string. An important distinction to remember when working with IP addresses is that dotted decimal is just an easy way for humans to read and write IP addresses. Always remember that the router is not reading an address in terms of four octets; rather, the router sees a 32-bit binary string. Many pitfalls can be avoided by keeping this fact firmly in mind. Probably the most distinctive characteristic of IP addresses is that unlike other network-level addresses, the network and host portions can vary in size within the 32-bit boundaries. That is, the network portion might take up most of the 32 bits or the host portion might or they might divide the bits equally. Protocols, such as NetWare and AppleTalk, were designed for use in relatively small internetworks, [3] and as a result their network-level addresses have fixed-length network and host portions. This arrangement certainly makes life easier; a receiving device knows to read a certain number of bits into the address to find the network part, and the rest is host address.
TCP/IP, however, was designed from the first to be flexible enough to be used in any internetwork, from the tiny to the colossal. This flexibility makes IP addresses more difficult to manage. The basics of administering IP addresses are presented in this section, and then some more advanced techniques are introduced in Chapter 7, "Routing Information Protocol Version 2." The First Octet RuleWithout putting too fine a point on it, it can be said that there are three sizes of internetworks as measured by the number of hosts : big, medium, and small.
This high level of addressing focus requires three types ” classes ”of network address for the three sizes of internetworks. Addresses for big internetworks need to be capable of addressing many hosts, but because so few big internetworks exist, only a few big-network addresses are required. The situation is reversed for small internetworks. Because there are many small internetworks, a large number of small-network addresses are needed. But because a small internetwork has a small number of hosts, each of the many network addresses only requires a few host addresses. For medium- sized internetworks, a medium number of network addresses and a medium number of host addresses will be available for each network address. Figure 2.10 shows how the network and host portions of IP addresses are divvied up for these three classes. Figure 2.10. Class A, B, and C IP address formats. The big, medium, and small networks described thus far map to address classes as follows :
Because all IP addresses are 32-bit binary strings, a way of distinguishing the class to which a particular address belongs is necessary. The first octet rule , illustrated in Figure 2.11, provides the means to make such a distinction and can be described as follows:
Figure 2.11. The first octet rule. So far IP addressing doesn't seem so difficult. A router or host could easily determine the network part of an IP address by using the first octet rule. If the first bit is 0, then read the first eight bits to find the network address. If the first two bits are 10, then read the first 16 bits; and if the first three bits are 110, then read 24 bits in to get the network address. Unfortunately, things are not that easy. Address MasksThe address for an entire data link ”a non-host-specific network address ” is represented by the network portion of an IP address, with all host bits set to zero. For instance, the InterNIC, the body that administers IP addresses, might assign to an applicant an address of 172.21.0.0. [6] This address is a class B address because 172 is between 128 and 191, so the last two octets make up the host bits. Notice that they are all set to zero. The first 16 bits (172.21.) are assigned, but address owners are free to do whatever they please with the host bits.
Each device or interface will be assigned a unique, host-specific address such as 172.21.35.17. The device, whether a host or a router, obviously needs to know its own address, but it also needs to be able to determine the network to which it belongs ” in this case, 172.21.0.0. This task is accomplished by means of an address mask . The address mask is a 32-bit string, one bit for each bit of the IP address. As a 32-bit string, the mask can be represented in dotted-decimal format just like an IP address. This representation tends to be a stumbling block for some beginners : Although the address mask can be written in dotted decimal, it is not an address. Table 2.3 shows the standard address masks for the three classes of IP address. Table 2.3. Address masks for class A, B, and C network addresses.
For each bit of the IP address, the device performs a Boolean (logical) AND function with the corresponding bit of the address mask. The AND function can be stated as follows: Compare two bits and derive a result. The result will be one if and only if both bits are one. If either or both bits are zero, the result will be zero. Figure 2.12 shows how, for a given IP address, the address mask is used to determine the network address. The mask has a one in every bit position corresponding to a network bit of the address and a zero in every bit position corresponding to a host bit. Because 172.21.35.17 is a class B address , the mask must have the first two octets set to all ones and the last two octets, the host part, set to all zeros. As Table 2.3 shows, this mask can be represented in dotted decimal as 255.255.0.0. Figure 2.12. Each bit of this class B address is ANDed with the corresponding bit of the address mask to derive the network address. A logical AND is performed on the IP address and its mask for every bit position; the result is shown in Figure 2.12. In the result, every network bit is repeated, and all the host bits become zeros. So by assigning an address of 172.21.35.17 and a mask of 255.255.0.0 to an interface, the device will know that the interface belongs to network 172.21.0.0. Applying the AND operator to an IP address and its address mask always reveals the network address. An address and mask are assigned to an interface of a Cisco router (in this example, the E0 interface) by means of the following commands:
But why use address masks at all? So far, using the first octet rule seems much simpler. Subnets and Subnet MasksNote The need for network-level addressing Never lose sight of why network-level addresses are necessary in the first place. For routing to be accomplished, each and every data link (network) must have a unique address; in addition, each and every host on that data link must have an address that both identifies it as a member of the network and distinguishes it from any other host on that network. As defined so far, a single class A, B, or C address can be used only on a single data link. To build an internetwork, separate addresses must be used for each data link so that those networks are uniquely identifiable. If a separate class A, B, or C address were assigned to each data link, less than 17 million data links could be addressed before all IP addresses were depleted. This approach is obviously impractical , [7] as is the fact that to make full use of the host address space in the previous example, more than 65,000 devices would have to reside on data link 172.21.0.0!
The only way to make class A, B, or C addresses practical is by dividing each major address, such as 172.21.0.0, into subnetwork addresses. Recall two facts:
Figure 2.13 shows an internetwork to which the major class B address 172.21.0.0 has been assigned. Five data links are interconnecting the routers, each one of which requires a network address. As it stands, 172.21.0.0 would have to be assigned to a single data link, and then four more addresses would have to be requested for the other four data links. Figure 2.13. Subnet masks allow a single network address to be used on multiple data links by " borrowing " some of the host bits for use as subnet bits. Notice what was done in Figure 2.13. The address mask is not a standard 16-bit mask for class B addresses; the mask has been extended another eight bits so that the first 24 bits of the IP address are interpreted as network bits. In other words, the routers and hosts have been given a mask that causes them to read the first eight host bits as part of the network address. The result is that the major network address applies to the entire internetwork, and each data link has become a subnetwork, or subnet. A subnet is a subset of a major class A, B, or C address space. Note Subnet Note Subnet mask The IP address now has three parts : the network part, the subnet part, and the host part. The address mask is now a subnet mask , or a mask that is longer than the standard address mask. The first two octets of the address will always be 172.21, but the third octet ”whose bits are now subnet bits instead of host bits ”may range from 0 to 255. The internetwork in Figure 2.12 has subnets 1, 2, 3, 4, and 5 (172.21. 1 .0 through 172.21. 5 .0). Up to 256 subnets may be assigned under the single class B address, using the mask shown. Two words of caution are in order. First, not all routing protocols can support subnet addresses in which the subnet bits are all zeros or all ones. The reason is that these protocols, called classful protocols, cannot differentiate between an all-zero subnet and the major network number. For instance, subnet 0 in Figure 2.13 would be 172.21.0.0; the major IP address is also 172.21.0.0. The two cannot be distinguished without further information. Note Classful protocols Likewise, classful routing protocols cannot differentiate a broadcast on the all-ones subnet from an all-subnets broadcast address. [8] For example, the all-ones subnet in Figure 2.13 would be 172.21.255.0. For that subnet, the all-hosts broadcast address would be 172.21.255.255, but that is also the broadcast for all hosts on all subnets of major network 172.21.0.0. Again, the two addresses cannot be distinguished without further information. RIP version 1 and IGRP are both classful routing protocols; Chapter 7 introduces classless routing protocols, which can indeed use the all-zeros and all-ones subnets.
The second caution has to do with the verbal description of subnets and their masks. Subnetting the third octet of a class B address, as is done is Figure 2.13, is very common; also common is hearing people describe such a subnet design as "using a class C mask with a class B address," or "subnetting a class B address into a class C." Both descriptions are wrong! Such descriptions frequently lead to misunderstandings about the subnet design or to a poor understanding of subnetting itself. The proper way to describe the subnetting scheme of Figure 2.12 is either as "a class B address with 8 bits of subnetting," or as "a class B address with a 24-bit mask." The subnet mask may be represented in any of three formats ”dotted decimal, bitcount, and hexadecimal ”as shown in Figure 2.14. Dotted decimal is still the most common format, although the bitcount format is becoming increasingly popular. Compared to dotted decimal, the bitcount format is easier to write (the address is followed by a forward slash and the number of bits that are masked for the network part). In addition, the bitcount format is more descriptive of what the mask is really doing and therefore avoids the type of semantic misunderstandings described in the previous paragraph. Many UNIX systems use the hexadecimal format. Figure 2.14. The subnet mask in Figure 2.13 may be represented in three different formats. Although the address mask must be specified to Cisco routers in dotted decimal, using the command shown previously, the mask may be displayed by various show commands in any of the three formats by using the command ip netmask -format [dechexbit] in line configuration mode. For example, to configure a router to display its masks in bitcount format, use:
Designing SubnetsAs established in the previous section, subnet bits cannot be all zeros or all ones in classful environments. Likewise, an IP host address cannot have all its host bits set to zero ” this setting is reserved for the address router's use to represent the network or subnet itself. And the host bits cannot be set to all ones, as this setting is the broadcast address. These restrictions apply to the host bits with no exceptions and are starting points for designing subnets. Beyond these starting points, network designers need to choose the most appropriate subnetting scheme in terms of matching the address space to the particulars of an internetwork. When designing subnets and their masks, the number of available subnets under a major network address and the number of available hosts on each subnet are both calculated with the same formula: 2 n “ 2, where n is the number of bits in the subnet or host space and 2 is subtracted to account for the unavailable all-zeros and all-ones addresses. For example, given a class A address of 10.0.0.0, a subnet mask of 10.0.0.0/16 (255.255.0.0) means that the 8-bit subnet space will yield 2 8 “ 2 = 254 available subnets and 2 16 “ 2 = 65,534 host addresses available on each of those subnets. On the other hand, a mask of 10.0.0.0/24 (255.255.255.0) means that a 16-bit subnet space is yielding 65,534 subnets and an 8-bit host space is yielding 254 host addresses for each subnet. The following steps are used to subnet an IP address: Note A stepwise method for designing subnets
Note When configuring subnets, always work in binary instead of dotted decimal. The importance of doing the last two steps in binary cannot be overemphasized. The single greatest source of mistakes when working with subnets is trying to work with them in dotted deci mal without under standing what is happening at the binary level . Again, dotted decimal is for convenience in reading and writing IP addresses. Routers and hosts see the addresses as 32-bit binary strings; to successfully work with IP addresses, they must be seen the way the routers and hosts see them. The last paragraph may seem a bit overzealous in light of the examples given so far; the patterns of subnet and host addresses have been quite apparent without having to see the addresses and masks in binary. The next section uses the four design steps to derive a subnet design in which the dotted-decimal representations are not so obvious. Breaking the Octet BoundaryIn the examples given so far, the subnet spaces have fallen on octet boundaries. This arrangement is not always the most practical or efficient choice. What if, for instance, you need to subnet a class B address across 500 data links, each with a maximum of 100 hosts? This requirement is easily met, but only by using nine bits in the subnet field: 2 9 “ 2 = 510 available subnets, leaving seven bits for the host field, and 2 7 “ 2 = 126 available hosts per subnet. No other bit combination will satisfy this requirement. Notice, also, that there is no way to subnet a class C address on an octet boundary ”doing so would use up all of the last byte, leaving no room for host bits. The subnet bits and host bits must share the last octet, as the following example shows. Step 1: Figure 2.15 shows the internetwork of Figure 2.13 but with a class C address of 192.168.100.0 assigned. There are five data links; therefore, the address must be subnetted to provide for at least five subnet addresses. The illustration also indicates the number of hosts (including router interfaces) that need to be addressed on each subnet. The maximum host address requirement is 25 for the two ethernets . Therefore, the full subnetting requirements are at least five subnets and at least 25 host addresses per subnet. Figure 2.15. The network from Figure 2.13 but with a class C mask assigned. Subnetting an entire octet will not work here; there would be no space left for host bits. Step 2: Applying the 2 n “ 2 formula, three subnet bits and five host bits will satisfy the requirements: 2 3 “ 2 = 6 and 2 5 “ 2 = 30. A class C mask with three bits of subnetting is represented as 255.255.255.224 in dotted decimal. Step 3: Figure 2.16 shows the derivation of the subnet bits. The subnet mask derived in step 2 is written in binary, and the IP address is written below it. Vertical lines are drawn as markers for the subnet space, and within this space all possible bit combinations are written by counting up from zero in binary. Figure 2.16. The subnet bits are derived by marking the masked subnet bit space and then writing all possible bit combinations in the space by counting up from zero in binary. In Figure 2.17, the unchanged network bits are filled in to the left of the subnet space and the host bits, which are all zeros in the subnet addresses, are filled in to the right of the subnet space. The results are converted to dotted decimal, and these are the six subnet addresses (remembering that the first and last addresses, which have 000 and 111 in the subnet space, cannot be used). Figure 2.17. The subnet addresses are derived by filling in the network address to the left of the subnet space, setting all host bits to zero to the right of the subnet space, and converting the results to dotted decimal. Step 4: The last step is to calculate the host addresses available to each subnet. This step is done by choosing a subnet and, keeping the network and subnet bits unchanged, writing all bit combinations in the host space by counting up from zero in binary. Figure 2.18 shows this step for subnet 192.168.100.32. Notice the patterns in the results: The first address, in which the host bits are all zero, is the subnet address. The last address, in which the host bits are all one, is the broadcast address for subnet 192.168.100.32. The host addresses count up from the subnet address to the broadcast address, and if the sequence were to continue, the next address would be the second subnet, 192.168.100.64. Figure 2.18. The host addresses for a subnet are derived by writing all possible bit combinations in the host space. These are the host bits for subnet 192.168.100.32. The importance of understanding subnetting at the binary level should now be clear. Presented with an address such as 192.168.100.160, you cannot be sure whether it is a host address, a subnet address, or a broadcast address. Even when the subnet mask is known, things are not always readily apparent. Readers are encouraged to calculate all host addresses for all the remaining subnets in the example and to carefully observe the patterns that result in the addresses. Understanding these patterns will help in situations such as the one presented in the next section. Troubleshooting a Subnet MaskThe necessity frequently arises to "dissect" a given host address and mask, usually to identify the subnet to which it belongs. For instance, if an address is to be configured on an interface, a good practice is to first verify that the address is valid for the subnet to which the subnet is connected. Use the following steps to reverse-engineer an IP address: Note A stepwise method for finding the subnet and broadcast address of a host address
Figure 2.19 shows these steps applied to 172.30.0.141/25. The address is a class B, so it is known that the first 16 bits are the network bits; therefore, the last nine bits of the 25-bit mask mark the subnet space. The subnet address is found to be 172.30.0.128, and the broadcast address is 172.30.0.255. Knowing that the valid host addresses for the subnet are bounded by these two addresses, it is determined that the host addresses for subnet 172.30.0.128 are 172.30.0.129 through 172.30.0.254. Figure 2.19. Given an IP address and a subnet mask, follow these steps to find the subnet, the broadcast, and the host addresses. Several things about this example tend to bother folks who are new to subnetting . Some are bothered by the third octet of the address, which is all zeros. Some are bothered by the single subnet bit in the last octet. Some think that the broadcast address looks suspiciously invalid. All of these uneasy feelings arise from reading the addresses in dotted decimal. When the addresses and the mask are seen in binary, these suspicions are assuaged and everything is seen to be legitimate ; the mask sets a nine-bit subnet space ”all of the third octet, and the first bit of the fourth octet. The moral of the story is that if everything is known to be correct in binary, don't worry if the dotted-decimal representation looks funny . |
![Routing TCP[s]IP (Vol. 11998)](/icons/blank_book.jpg "Routing TCP[s]IP (Vol. 11998)"){kind=icon}