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Converting IP addresses to binary using math.

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  1. Use mathematics to convert an IP address to binary
  2. Use a simple command-line application to convert an IP address to binary from decimal

Use mathematics to convert an IP address to binary

There is an advantageous way to convert an IP address from decimal to binary using mathematics. This is not too hard after all.

  1. Write down the decimal number of the first octet of the IP address.
  2. Convert the decimal number to binary by dividing it by 2 repeatedly and writing down the remainder (0 or 1) each time, starting from the bottom.
  3. Continue this process with the remaining three octets of the IP address.

For example, we are converting the IP address 192.168.0.1, which is /24 to binary.

  1. Write down the decimal number of the first octet: 192
  2. Convert 192 to binary:192 / 2 = 96,
    remainder 096 / 2 = 48,
    remainder 048 / 2 = 24,
    remainder 024 / 2 = 12,
    remainder 012 / 2 = 6,
    remainder 06 / 2 = 3,
    remainder 03 / 2 = 1,
    remainder 11 / 2 = 0,
    remainder 1
    So, the binary representation of 192 is 11000000.
  3. Repeat this process for the remaining octets:
    168 -> 101010000 -> 000000001 -> 00000001.

Therefore, the binary representation of the IP address 192.168.0.1 is 11000000.10101000.00000000.00000001.

This is an easy way to convert an IP address to binary using simple math.

Use a simple command-line application to convert an IP address to binary from decimal

There is also a nice command-line application to convert an IP address to binary. The ipcalc app is very useful for working with IP addresses. Below is an example, of converting a /24 IP address to binary.

┌──(john㉿DESKTOP-PF01IEE)-[~]
└─$ ipcalc 192.168.0.1/24
Address:   192.168.0.1          11000000.10101000.00000000. 00000001
Netmask:   255.255.255.0 = 24   11111111.11111111.11111111. 00000000
Wildcard:  0.0.0.255            00000000.00000000.00000000. 11111111
=>
Network:   192.168.0.0/24       11000000.10101000.00000000. 00000000
HostMin:   192.168.0.1          11000000.10101000.00000000. 00000001
HostMax:   192.168.0.254        11000000.10101000.00000000. 11111110
Broadcast: 192.168.0.255        11000000.10101000.00000000. 11111111
Hosts/Net: 254                   Class C, Private Internet

Another way is to use sipcalc. This is a very good application for calculating networks.

This shows that a network using these IP addresses would have 28 possible addresses.

┌──(john㉿DESKTOP-PF01IEE)-[~]
└─$ sipcalc -a 10.2.0.1/28
-[ipv4 : 10.2.0.1/28] - 0
 
[Classful]
Host address            - 10.2.0.1
Host address (decimal)  - 167903233
Host address (hex)      - A020001
Network address         - 10.0.0.0
Network class           - A
Network mask            - 255.0.0.0
Network mask (hex)      - FF000000
Broadcast address       - 10.255.255.255
 
[CIDR]
Host address            - 10.2.0.1
Host address (decimal)  - 167903233
Host address (hex)      - A020001
Network address         - 10.2.0.0
Network mask            - 255.255.255.240
Network mask (bits)     - 28
Network mask (hex)      - FFFFFFF0
Broadcast address       - 10.2.0.15
Cisco wildcard          - 0.0.0.15
Addresses in network    - 16
Network range           - 10.2.0.0 - 10.2.0.15
Usable range            - 10.2.0.1 - 10.2.0.14
 
[Classful bitmaps]
Network address         - 00001010.00000000.00000000.00000000
Network mask            - 11111111.00000000.00000000.00000000
 
[CIDR bitmaps]
Host address            - 00001010.00000010.00000000.00000001
Network address         - 00001010.00000010.00000000.00000000
Network mask            - 11111111.11111111.11111111.11110000
Broadcast address       - 00001010.00000010.00000000.00001111
Cisco wildcard          - 00000000.00000000.00000000.00001111
Network range           - 00001010.00000010.00000000.00000000 -
                          00001010.00000010.00000000.00001111
Usable range            - 00001010.00000010.00000000.00000001 -
                          00001010.00000010.00000000.00001110
 
[Networks]
Network                 - 10.2.0.0        - 10.2.0.15 (current)
Network                 - 10.2.0.16       - 10.2.0.31
Network                 - 10.2.0.32       - 10.2.0.47
Network                 - 10.2.0.48       - 10.2.0.63
Network                 - 10.2.0.64       - 10.2.0.79
Network                 - 10.2.0.80       - 10.2.0.95
Network                 - 10.2.0.96       - 10.2.0.111
Network                 - 10.2.0.112      - 10.2.0.127
Network                 - 10.2.0.128      - 10.2.0.143
Network                 - 10.2.0.144      - 10.2.0.159
Network                 - 10.2.0.160      - 10.2.0.175
Network                 - 10.2.0.176      - 10.2.0.191
Network                 - 10.2.0.192      - 10.2.0.207
Network                 - 10.2.0.208      - 10.2.0.223
Network                 - 10.2.0.224      - 10.2.0.239
Network                 - 10.2.0.240      - 10.2.0.255

This is a most useful tool to calculate a subnet easily. Subnets can be very challenging, and this takes the pain out of this for everyone.


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