*Many IT professionals get scared when the topic of binary numbers and bit manipulation come up. This is not complex, once understood it opens up a whole realm of possibilities. One concrete example where bit manipulation comes in handy is when dealing with subnets. This blog briefly covers bit manipulation and applies the technique to check if a given IP address belong to a Subnet. If you are familiar with bit manipulation skip directly to the code.*

# Binary Numbers

Computer understands
only ‘1’s and ‘0’s (i.e.) binary. All numeric values in computer are stored as
binary numbers. Once you understand the
basics of binary numbers and the binary manipulation you can implement
efficient code in some cases. In the decimal system each place of digit goes by
powers of ten, while in binary system it goes by powers of two. If you are not
familiar read at The Binary System.

# Bit Manipulation

In PowerShell there are
binary equivalent of logical operations. (e.g.) band is binary-and. In that the
binary-and applies the ‘and’ operator for each bit in operand1 with
corresponding bit in operand2 to produce the corresponding bit in the result.
(e.g.) (4 –band 5) will produce 4. How? In the binary 4 and 5 are represented
as ‘100’ and ‘101’ respectively. Logical and of least significant bits will
result in zero, second significant will also result in zero, while most significant
will result in 1 (because both of them are 1). Thus the result in binary is ‘100’
which is decimal ‘4’.

Another nice operator is
the shift operator. Shift left operator shifts the bits by ‘n’ binary digits
and adds ‘n’ zeros on the right. (2 –shl 2) will result in 8 (because ‘10’ is
shifted by two digits and two zeroes added to the right, resulting in ‘1000’,
which is decimal 8)

Likewise binary-not will
flip every single bit in a binary number (i.e.) If it is ‘1’ it will turn to ‘0’,
if it ‘0’ it will turn to ‘1’. ((-bnot
4) –band 7) will result in 3. Why? Decimal ‘4’ is equal to ‘...000100’ will
result in ‘…111011’. Do a binary-and with 7 to retrieve least 3 significant
bits. The result is ‘011’ which is ‘3’. The reason ‘7’ is chosen for binary-and
is, it has all three digits set to ‘1’ (i.e.) ‘111’. Just doing a (-bnot 4)
will result in ‘-5’, can you figure out why? This will lead to the
understanding of how binary form of negative numbers are represented.

There are many other
binary operators in PowerShell like shr, bor, bxor.

# Subnet and IP Address

IP Address is a 32 bit
number consists of two parts the network part and the host part. Classless
Internet Domain Routing (CIDR) is the way to represent the subnet. CIDR has the
network address and the length, which is the number of bits that constitute the
network part of the IP Address. (e.g.) 192.168.0.0/16 means ‘198.168.0.0’ is
the network address and 16 bits are used to represent the network part. This
means the subnet mask is ‘255.255.0.0’.

The network part of any
IP address can easily be obtained by doing binary-and (band) of the subnet mask
with the IP address. Say the IP address is ‘192.168.0.22’ and the subnet mask ‘255.255.0.0’,
doing a binary-and of them will result in 192.168.0.0’.

# Code for CheckSubnet

function checkSubnet
([string]$cidr, [string]$ip)

{

$network, [int]$subnetlen =
$cidr.Split('/')

$a = [uint32[]]$network.split('.')

[uint32] $unetwork =
($a[0] -shl 24) + ($a[1] -shl 16) + ($a[2] -shl 8) + $a[3]

$mask = (-bnot [uint32]0) -shl (32 - $subnetlen)

$a = [uint32[]]$ip.split('.')

[uint32] $uip = ($a[0] -shl 24) + ($a[1] -shl 16) + ($a[2] -shl 8) + $a[3]

$unetwork
-eq ($mask
-band $uip)

}

Sample usage:

PS C:\> checkSubnet ‘192.168.240.0/20’ ‘192.168.250.10’

True

PS C:\> checkSubnet ‘192.168.240.0/20’ ‘192.168.150.10’

False

The code is pretty dense
and requires explanation.

$network, [int]$subnetlen =
$cidr.Split('/')

The above code splits
the CIDR into the network part and the length part and stores it in $network
and $subnetlen respectively. It also converts the length into integer.

$a = [uint32[]]$network.split('.')

[uint32] $unetwork =
($a[0] -shl 24) + ($a[1] -shl 16) + ($a[2] -shl 8) + $a[3]

Uint32 is an unsigned
integer and can store up to 32 bits. Hence this can store the IP address. 32
bits has four bytes. We have the network as a string of four bytes with ‘.’ delimiter
between each byte. To convert to uint32, first extract each byte and put it in appropriate
place of uint32. Extracting each byte is simple, can be achieved by split
operation. The trick is to form the 32 bit number and placing each byte in the
appropriate place. To put $a[3] in least significant byte just add it. To put
$a[2] one byte up, you need to left shift by 8 bits and then add it. (Note: 8
bits corresponds to one byte, which is why you are shifting 8 bits to move one
byte up). Likewise you need to shift $a[1] by 16 bits, $a[0] by 24 bits. That
does the trick!

$mask = (-bnot [uint32]0) -shl (32 - $subnetlen)

To calculate the subnet
mask, first create a 32 bit number with all ‘1’. This can easily be achieved by
taking the binary-not of zero. (-bnot [uint32]0). Zero has to be casted to
uint32 because PowerShell defaults to int32, hence results in a negative number.
Number of zeroes in the subnet mask is equal to (32 - $subnetlen). Just do a
left shift by this amount to achieve the subnet mask.

$a = [uint32[]]$ip.split('.')

[uint32] $uip = ($a[0] -shl 24) + ($a[1] -shl 16) + ($a[2] -shl 8) + $a[3]

Above code does the same
manipulation for the ip address that was done for the network part. Now you
have uint32 version of both network and ip address.

$unetwork
-eq ($mask
-band $uip)

This is the climax.
Compute the network part by doing the binary-and of ip address ($mask –band
$uip). Then compare it with the network!

References

Explore & Enjoy!

/Siva

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