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Network Working Group P. Tsuchiya
Request for Comments: 1219 Bellcore
April 1991
On the Assignment of Subnet Numbers
Status Of This Memo
This memo suggests a new procedure for assigning subnet numbers. Use
of this assignment technique within a network would be a purely local
matter, and would not effect other networks. Therefore, the use of
these procedures is entirely discretionary.
This memo provides information for the Internet community. It does
not specify an Internet standard. Distribution of this memo is
unlimited.
Overview
RFC-950 [2] specifies a procedure for subnetting Internet addresses
using a bit-mask. While RFC-950 allows the "ones" in the subnet mask
to be non-contiguous, RFC-950 recommends that 1) they be contiguous,
and 2) that they occupy the most significant bits of the "host" part
of the internet address.
RFC-950 did not specify whether different subnets of the same network
may have different masks. This ambiguity was unfortunate, as it
resulted in development of routing protocols that do not support
different masks; see e.g., RIP [6]. The Gateway Requirements RFC [7]
settled the issue in favor of allowing different masks, and therefore
future routing protocols may be expected to support this feature;
OSPF [3] is an example.
The network administrator must of course determine the mask for each
subnet. This involves making an estimate of how many hosts each
subnet is expected to have. As it is often impossible to predict how
large each subnet will grow, inefficient choices are often made, with
some subnets under-utilized, and others possibly requiring
renumbering because of exceeded capacity.
This memo specifies a procedure for assigning subnet numbers that
eliminates the need to estimate subnet size. Essentially, host bits
(mask = 0) are assigned from the least significant bit working
towards the most, and subnet bits (mask = 1) are assigned from the
most significant bit working towards the least. As subnets grow,
more host bits are assigned. As the number of subnets grows, more
subnet bits are assigned. While this process does sometimes result
Tsuchiya [Page 1]
```

RFC 1219 On the Assignment of Subnet Numbers April 1991
in new subnet masks, no host ever need change addresses.
This technique is not new, but it is also not widely known, and even
less widely implemented. With the development of new routing
protocols such as OSPF, it is possible to take full advantage of this
technique. The purpose of this memo, then, is to make this technique
widely known, and to specify it exactly.
This memo requires no changes to existing Internet standards. It
does, however, require that the intra-domain routing protocol handle
multiple different subnet masks.
Acknowledgments
The author would like to thank Phil Karn, Charles Lynn, Jeff Mogul,
and Charles Wolverton for their helpful suggestions. Special thanks
go to Joel Halpern for his painstaking debugging of the detailed
specification and the examples.
## 1. Motivation

The Subnetting standard, RFC-950, specifies that the Host part of the
formally 2-level Internet address can be divided into two fields,
Subnet and Host. This gives the Internet address a third level of
hierarchy, and the concomitant firewalls and savings in routing
overhead. It also introduces increased inefficiency in the
allocation of addresses.
This inefficiency arises from the fact that the network administrator
typically over-estimates the size (number of hosts) of any single
subnetwork, in order to prevent future re-addressing of subnets. It
may also occur if the routing protocol being used does not handle
different length subnets, and the administrator must therefore give
every subnet an amount of space equivalent to that received by the
largest subnet. (This RFC does not help in the latter case, as the
technique herein requires different length subnets.)
The administrative hassle associated with changing the subnet
structure of a network can be considerable. For instance, consider
the following case. A network has three subnets A, B, and C. Assume
that the lowest significant byte is the host part, and the next byte
is the subnet part (that is, the mask is 255.255.255.0). Assume
further that A has subnet 1.0, B has subnet 2.0, and C has subnet
3.0.
Now, assume that B grows beyond its allocation of 254 hosts.
Ideally, we would like to simply change B's mask without changing any
of the host addresses in B. However, the subnets numerically above
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RFC 1219 On the Assignment of Subnet Numbers April 1991
and below B are already taken by A and C. (If say 3.0 was not taken
by C, B's mask could be changed from 255.0 (ff00) to 254.0 (fe00).
In this case, all of B's existing addresses would still match the new
subnet. Indeed, if non-contiguous masks were in use, it might be
possible for B to find some other mask bit to change to 0. However,
non-contiguous masks are generally not in favor, as they impose
limitations on certain forwarding table lookup algorithms. Indeed,
RFC-950 discourages their use.)
So, the choices available to the network administrator are to 1) form
two subnets out of the existing one, or 2) renumber the subnet so
that the subnet ends up with a smaller (fewer 1's) mask. Choice 1
can either be accomplished physically or logically. Physically
forming two subnets requires partitioning the subnet and inserting a
gateway between the two partitions. For obvious reasons, this is not
a desirable course of action. Logically forming two subnets can be
done by simply assigning another subnet number (say 4.0) to the same
subnet, and assigning host addresses under the new subnet. The
result of this logical partition is that the hosts with different
subnet numbers will not recognize that the others are on the same
subnet, and will send packets to the default gateway rather than
directly to the host. In fact, this is not such a bad solution,
because assuming that the gateway is capable of recognizing multiple
subnet numbers on the same subnet, the gateway will simply send the
host an ICMP Redirect [4], and subsequent packets will go directly to
the host [1] (this may not work correctly on all hosts).
If, however, neither choice is acceptable or possible, then the
network administrator must assign a new subnet number to B, thus
renumbering the existing hosts, modifying the Domain Name System
entries, and changing any other configuration files that have
hardwired addresses for hosts in subnet B.
## 2. A More Flexible and Efficient Technique for Assigning Subnet Numbers

In order to help explain the new technique, we shall show what is
wrong with what is currently done now. Currently, most subnets are
assigned by splitting the host part of the address in two fields; the
subnet field and the host field. Mask bits are one for subnet field
bits, and 0 for host field bits. (In all of our addresses, the least
significant bit (LSB) is on the right, the most significant bit (MSB)
is on the left.)
MSB LSB
--------------------------------------
| subnet field | host field |
--------------------------------------
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RFC 1219 On the Assignment of Subnet Numbers April 1991
The subnet field could be different lengths for different size
subnets. For instance, say a network had two large subnets and the
rest small subnets (by large subnet we mean a large number of hosts).
Then the network administrator might assign two types of addresses:
--------------------------------------
| subnet | host | large subnets
--------------------------------------
--------------------------------------
| subnet | host | small subnets
--------------------------------------
In this case, the full range of subnet numbers would not be available
to the small subnets, as the bits in the small subnet that correspond
to those in the large subnet could not have the same values as those
in the large subnets. For instance, say that the large subnets had
4-bit subnet numbers, and the small subnets had 8-bit subnet numbers.
If the large subnets had values 0001 and 0010, then subnet numbers in
the range 00010000 to 00101111 could not be assigned to the small
subnets, otherwise there will be addresses that would match both
subnets.
In any event, a network administrator will typically assign values to
the two fields in numerical order. For example, within a given
subnet, hosts will be numbered 1, 2, 3, etc. Within a given network,
subnets will be numbered 1, 2, 3, etc. The result is that some
number of bits on the right side of the subnet and host fields will
be ones for some hosts and zeros for others, and some number of bits
on the left side of the subnet and host fields will be zeros for all
subnets and hosts. The "all zeros" bits represent room for growth,
and the "ones and zeros" bits represent bits already consumed by
growth.
--------------------------------------
| subnet field | host field |
|-----+-----------+-------+------------|
| | | | |
| 0's | 1's & 0's | 0's | 1's & 0's |
/\ /\
|| ||
subnets can hosts can grow here
grow here
Now, let's assume that the number of hosts in a certain subnet grows
to the maximum allowed, but that there is still room in the subnet
field to assign more addresses. We then have the following:
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RFC 1219 On the Assignment of Subnet Numbers April 1991
--------------------------------------
| subnet field | host field |
|-----+-----------+--------------------|
| | | |
| 0's | 1's & 0's | 1's & 0's |
While the host field can no longer grow, there is still room in the
address for growth. The problem is that because of where the growth
areas are situated, the remaining growth has been effectively
reserved for subnets only.
What should be done instead is to assign subnet numbers so that the
ones start from the left of the subnet field and work right. In this
case we get the following:
--------------------------------------
| subnet field | host field |
|-----------+-------------+------------|
| | | |
| 1's & 0's | 0's | 1's & 0's |
/\
||
Both hosts and subnets can
grow here
Now, both hosts and subnets individually have considerably more
growing space than before, although the combined growing space is the
same. Since one can rarely predict how many hosts might end up in a
subnet, or how many subnets there might eventually be, this
arrangement allows for the maximum flexibility in growth.
Actually, the previous figure is misleading. The boundary between
the host and subnet fields is being shown in the middle of the growth
area. However, the boundary could exist anywhere within the growth
area. Note that it is the mask itself that determines where the
boundary is. Ones in the mask indicate subnet bits, and zeros
indicate host bits. We will show later that in fact the boundary
should lie somewhere in the middle. Putting it there minimizes the
number of times that the masks must be changed in hosts.
2.1 Specification of the New Technique
Having given the appropriate explanatory material, we can now specify
the procedure for subnet number assignment. We need the following
definitions:
Host-assigned Bits (h-bits): These are the bits, contiguous from
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RFC 1219 On the Assignment of Subnet Numbers April 1991
the right, for which host values, within a given subnet, contain
both ones and zeros. Different subnets may have different h-bits.
Subnet-assigned Bits (s-bits): These are the bits, contiguous from
the left, which 1) are not h-bits, AND 2) are required to
distinguish one subnet from another, AND 3) include all bits
to the left of and including the right-most one. Notice that
different subnets may have different s-bits.
Growth Bits (g-bits): These are the "all zeros" bits in between
the h-bits and s-bits.
s-mask: For a given subnet, the mask whereby all s-bits are one,
and all g-bits and h-bits are zero.
g-mask: For a given subnet, the mask whereby all s-bits and g-bits
are one, and all h-bits are zero.
Subnet Field: These are the one bits in the subnet mask (as
defined in RFC-950). These bits are on the left. The subnet
field must at least include all of the s-bits, and may
additionally include some or all of the g-bits.
Host Field: These are the zero bits in the subnet mask.
These bits are on the right. The host field must at least
include all of the h-bits, and may additionally include some
or all of the g-bits.
Mirror-image Counting: Normal counting, in binary, causes one
bits to start at the right and work left. This is how host
values are assigned. However, for subnet assignment, we want
the one bits to start at the left and work right. This process
is the mirror image of normal counting, where the MSB is swapped
with the LSB, the second MSB is swapped with the second LSB, and
so on. So, where normal counting is:
0 (reserved to mean "this host")
01
10
011
100
101
:
:
11...1110
11...1111 (reserved to mean "all hosts")
and so on, Mirror-image, or MI counting, is:
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RFC 1219 On the Assignment of Subnet Numbers April 1991
0 (reserved to mean "this subnet")
10
01
110
001
101
:
:
011...11
111...11 (reserved to mean "all subnets")
and so on. If the current MI counting value is, say, 001,
the "next" MI value is 101, and the "previous" MI value is 11.
Now we can specify the algorithm. We have the following functions:
Initialize(), AddSubnet(), RemoveSubnet(subnet#), AddHost(subnet#),
and RemoveHost(subnet#,host#).
Notice that the algorithm is described as though one state machine is
executing it. In reality, there may be a root Address Authority
(RootAA) that assigns subnet numbers (Initialize, AddSubnet, and
RemoveSubnet), and subnet AA, that assign host numbers within a
subnet (AddHost and RemoveHost). While in general the AAs can act
independently, there are two cases where "coordination" is required
between the rootAA and a subnetAA. These are the cases where either
the rootAA or the subnetAA "grabs" the last growth bit (in the former
case because another subnet has been added, and in the latter because
another host has been added). Since it is impossible for the rootAA
and a subnetAA to simultaneously grab the last growth bit, either one
or the other must do it.
Finally, note that the following C language style notation is used:
& bit-wise AND function
== is equal to
!= is not equal to
x-mask(X) the x-mask of X (where x is s or g)
Initialize():
Assign the first subnet value to be 0 (the value reserved to mean
"this subnet"). This is not assigned to any real subnet.
AddSubnet():
1. Find the lowest non-zero (in MI counting) non-assigned subnet
number S such that (S & g-mask(Y)) != (Y & g-mask(Y)) for all
existing subnet numbers Y, (Y != S).
2. If all bits in S from the rightmost one bit left are ones,
then label all bits to the left of and including one bit
position to the right of the rightmost one bit in S to be
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RFC 1219 On the Assignment of Subnet Numbers April 1991
s-bits. Else, label all bits to the left of and including the
rightmost one bit in S to be s-bits. This prevents the "all
ones" value (which is the "all subnets" broadcast address)
from being assigned to a subnet. (Since no hosts have been
added, the rightmost one bit is a subnet bit.)
3. Label all other bits in the address to be g-bits. (By
address, we mean that part of the IP address not including
the network number.)
4. Set the subnet mask to include at least all s-bits, and
optionally some g-bits. The subnet mask must be contiguous.
(Section 2.2 discusses the pros and cons of choosing a mask.)
5. For all existing subnet numbers Y (Y != S):
51. If (S & s-mask(Y)) == (Y & s-mask(Y)), then:
511. Change the leftmost g-bit of Y to an s-bit. If
the rootAA and YAA (the address authority for Y) are
separate AAs, then the YAA must be informed of the
change of bit status. If this is the last g-bit,
then this change must be coordinated with YAA.
512. Expand the subnet mask for all hosts in Y if
necessary (that is, if the subnet mask no longer
includes all s-bits).
RemoveSubnet(S):
1. Consider B to be the bit position of the rightmost s-bit in S.
2. Remove S.
3. For all existing subnet numbers Y:
31. If the bit in position B is not an s-bit, or if the bit
in bit position B is a one, or if the bit in bit position
B is a zero and all bits to the left of bit position B
are ones, then do nothing (skip steps 32 and 33).
32. Change the s-bit in position B to a g-bit.
33. If for any other existing subnet numbers X
(X & s-mask(Y)) == (Y & s-mask(Y)), then change the
g-bit in position B back into an s-bit for Y. Else,
inform YAA that of the change of bit status.
AddHost(S):
1. Create an address A consisting of subnet number S concatenated
with zeros.
2. Assign to A the same h-bits, g-bits, and s-bits as the
other host addresses.
3. Find the lowest non-zero (using normal counting) non-assigned
host number H.
4. If all bits from the leftmost one bit to bit position 0 are
ones, then execute steps 5 and 6 using bit position B equals
one bit position to the left of the leftmost one bit in H.
Else, execute steps 5 and 6 with bit position B equals
the leftmost one bit in H. This prevents the "all ones" value
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RFC 1219 On the Assignment of Subnet Numbers April 1991
(which is the "all hosts" broadcast address) from being
assigned to a host.
5. If bit position B is an s-bit, then the host cannot be added.
Skip the remaining steps.
6. If bit position B is a g-bit:
61. Change the g-bit to an h-bit for all hosts in S. Note
that if this is the last g-bit, this change must be
coordinated with the address authority assigning subnet
numbers (see section 2.2).
62. Modify the subnet mask in all hosts if necessary.
7. Create a new address A consisting of S concatenated with H
8. Assign A to the host.
RemoveHost(S,H):
1. Remove H.
2. If for all remaining host numbers in S, the value of the bit
position of the leftmost h-bit is zero, and there is a zero in
at least one of the bit positions to the right of the leftmost
h-bit, then for all hosts change the leftmost h-bit into a
g-bit.
It is worth noting here that this technique is a 2-level subset of
the more general n-level kampai addressing [5]. The main
difference here is that n-level kampai results in non-contiguous
masks, while 2-level does not. In the description of kampai
addressing in [5], g-bits are called a-bits, h-bits are called
g-bits, and s-bits are called i-bits.
2.2 An Example
For this example, we assume a class C network, so we will only need
to work with 8 bits. We start with 3 subnets, A, B, and C. Our
nomenclature is h for h-bit and g for g-bit. Note that h-bits can be
one or zero, but g-bits are all zero. The remaining bits are s-bits,
but are shown as 1's and 0's according to the subnet number
assignment. The space is just to make the addresses and masks easier
to read. Finally, we number our bits 0 to 7 from right to left as
shown below.
Subnet Address Mask
A 10gg ghhh 1111 0000
B 01gg ghhh 1111 0000
C 110g ghhh 1111 0000
bit 7 bit 0
We see that each subnet has at most 6 hosts (because of the three h-
bits). Notice that we have chosen the masks so that there is room
for growth in both hosts and subnets without requiring a mask change.
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RFC 1219 On the Assignment of Subnet Numbers April 1991
However, we have generally allowed for more growth in subnets than in
hosts because adding new subnets can cause mask changes in existing
subnets, while adding new hosts in a subnet only causes that subnet's
mask to change.
Further, if a subnet's mask must change, but not all hosts are
reconfigured at the same time, then it is less damaging if the not
yet reconfigured hosts have too large a mask (too many ones) than if
they have too small a mask. This is because with too large a mask, a
host may think that another host which is in fact on the subnet is on
another subnet. In this case, the host will send packets to the
gateway, and will be redirected to the host.
However, with too small a mask, a host may think that another host
which is in fact not on the subnet is on the subnet, and will ARP for
that host but receive no reply. (Note that broadcasts may fail if
all masks do not match.)
Finally, notice that subnet C requires three s-bits instead of just
two. This is because with just two, the subnet address of C could be
"11" (rather than "110"), which is a broadcast value. Step 2 of
AddSubnet checks for this case.
Now, a fourth subnet, D, also with 6 hosts, is added. We get:
Subnet Addr Mask
A 10gg ghhh 1111 0000
B 01gg ghhh 1111 0000
C 110g ghhh 1111 0000
D 001g ghhh 1111 0000
Notice that none of the original subnets required a change in any of
their status bits. This is because, when D compared its subnet
number with the others (step 5 of AddSubnet(), using the s-mask),
they were all different. In other words, a router would be able to
distinguish an address in D from addresses in A, B, and C.
Next, a fifth subnet, E, is added. We get:
Subnet Addr Mask
A 100g ghhh 1111 0000
B 01gg ghhh 1111 0000
C 110g ghhh 1111 0000
D 001g ghhh 1111 0000
E 101g ghhh 1111 0000
Notice that this time, A was forced to change its leftmost g-bit (bit
5) into an s-bit, because bit 5 is needed to distinguish subnet A
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RFC 1219 On the Assignment of Subnet Numbers April 1991
from subnet E (step 511 of AddSubnet()). Changing bit 5 into an s-
bit prevents hosts from being added to A to the point where bit 5
would be changed into a one (that is, step 5 of AddHost() would
fail).
Notice also that if the masks in A, B, and C were originally set to
1100.0000, then the addition of E would have caused A's mask to
change to 1110.0000 (Step 512 of AddSubnet()).
Next, 8 hosts each are added to subnets A and C, thus causing the
right-most g-bit in each to change to an h-bit.
Subnet Addr Mask
A 100g hhhh 1111 0000
B 01gg ghhh 1111 0000
C 110g hhhh 1111 0000
D 001g ghhh 1111 0000
E 101g ghhh 1111 0000
Notice again that no masks have changed. If the masks for A, B, and
C were originally set to 1111 1000, then they would have required
changing (step 62 of AddHost()).
Next, enough hosts are added to subnet B that all of its remaining
g-bits become h-bits.
Subnet Addr Mask
A 100g hhhh 1111 0000
B 01hh hhhh 1100 0000
C 110g hhhh 1111 0000
D 001g ghhh 1111 0000
E 101g ghhh 1111 0000
Notice here that the masks in B's subnet had to be changed to
accommodate the new h-bits (step 62 of AddHost()). Notice also that
if the person assigning host addresses for B (B Address Authority, or
BAA) is different than the person assigning network numbers (RootAA),
then BAA must coordinate the change of its last g-bit to an h-bit
with the RootAA. This allows the RootAA to properly assign
additional subnet numbers, as in the next step, where we add another
subnet F:
Subnet Addr Mask
A 100g hhhh 1111 0000
B 01hh hhhh 1100 0000
C 110g hhhh 1111 0000
D 001g ghhh 1111 0000
E 101g ghhh 1111 0000
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RFC 1219 On the Assignment of Subnet Numbers April 1991
F 1110 ghhh 1111 0000
Notice that F received subnet number 1110 rather than subnet number
011 (which is what comes after 101 in MI counting). The reason is
that 1) 011 is not distinguishable from B's subnet address using B's
mask, and 2) we can't increase B's mask to make it distinguishable
because B has already assigned hosts at bit position 5. In other
words, when the comparison of step 1 in AddSubnet() was tried on
number 011, the two values were equal, and so the next number was
tried. In fact, no subnet numbers with 01 in bit positions 7 and 6
can be assigned (unless B loses hosts).
Next, subnet E is removed:
Subnet Addr Mask
A 10gg hhhh 1111 0000
B 01hh hhhh 1100 0000
C 110g hhhh 1111 0000
D 001g ghhh 1111 0000
F 1110 ghhh 1111 0000
Notice that this caused subnet A to change an s-bit back into a g-
bit. This is because the equality of step 33 of RemoveSubnet() did
not hold true for subnet A with respect to the remaining subnets.
References
[1] Braden, R., "Requirements for Internet Hosts -- Communication
Layers", RFC 1122, USC/Information Sciences Institute, October
1989.
[2] Mogul, J., and J. Postel, "Internet Standard Subnetting
Procedure", RFC 950, USC/Information Sciences Institute, August
1985.
[3] Moy, J., "OSPF Specification", RFC 1131, Proteon, October 1989.
[4] Postel, J., "Internet Control Message Protocol", RFC 792,
USC/Information Sciences Institute, September 1981.
[5] Tsuchiya, P., "Efficient and Flexible Hierarchical Address
Assignment", TM-ARH-018495, Bellcore, February 1991.
[6] Hedrick, C., "Routing Information Protocol" RFC 1058, Rutgers
University, June 1988.
[7] Braden, R., and J. Postel, "Requirements for Internet Gateways",
RFC 1009, USC/Information Sciences Institute, June 1987.
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RFC 1219 On the Assignment of Subnet Numbers April 1991
Security Considerations
Security issues are not discussed in this memo.
Author's Address
Paul F. Tsuchiya
Bellcore
435 South St.5 South St.
MRE 2L-281
Morristown, NJ 07960
Phone: 201 829-4484
EMail: tsuchiya@thumper.bellcore.com
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