IPv4 CIDR Address to IP Range Using Boolean Logic and Binary Addition

Given an IPv4 address in CIDR notation (e.g. 192.168.100.10/23), we can find the IP range using boolean logic and binary addition.

Procedure

• IPv4 Address in CIDR Notation

  192.168.100.10/23

• Find Number of Addresses in Range

  • There are 32 bits in an IPv4 address.
  • We know the netmask is 23 bits. Therefore, the address space is 32-23 = 9 bits.
  • Each of those 9 bits can be a 0 or 1.

  • We find the total number of addresses in the space with the power function.

    • base = 2

    • power = 9

      2^9 = 512 addresses (including network and broadcast)

  • We subtract 2 to find the number of available addresses, since the network and broadcast addresses are reserved.

        512 - 2 = 510 addresses (network and broadcast excluded) 

• Find Netmask Bits

  • We were given the netmask as 23 bits.

  • That is 23 1's followed by nine 0's.

    11111111.11111111.11111110.00000000

• Find Wildcard Bits

  • The wildcard bits are the opposite of the netmask bits.
    • Where there is a 0, replace it with a 1.
    • Where there is a 1, replace it with a 0.
    • That is 23 0's followed by nine 1's.

  • The wildcard bits can also be found by taking Number of Addresses in Range - 1 = 511 (decimal).

    00000000.00000000.00000001.11111111

• Convert IPv4 Address to Binary

  • We take each decimal octet and convert it to binary.

    192 (decimal) = 11000000 (binary)168 (decimal) = 10101000 (binary)100 (decimal) = 01100100 (binary) 10 (decimal) = 00001010 (binary)11000000.10101000.01100100.00001010

• Logical AND the IP Address with the Netmask to find the Network Address

  11000000.10101000.01100100.00001010 // 192.168.100.1011111111.11111111.11111110.00000000 // netmask----------------------------------- // logical AND11000000.10101000.01100100.00000000 // network address192     .168     .100      .0       // back to decimal

• Find the Broadcast Address

  • We use binary addition to add the network address to the wildcard bits.

    00000000.00000000.00000001.11111111 // wildcard bits11000000.10101000.01100100.00000000 // network address----------------------------------- // binary addition11000000.10101000.01100101.11111111 // broadcast address192     .168      .101    .255      // back to decimal

Range

    192.168.100.0       // network addr
    192.168.100.1       // first avail ip
    192.168.101.254     // last avail ip
    192.168.101.255     // broadcast addr

Confirmation

• Using the IPv4 Calculator link from the Resources section below, we can check that we applied the procedure properly.

  Address:   192.168.100.10        11000000.10101000.0110010 0.00001010Netmask:   255.255.254.0 = 23    11111111.11111111.1111111 0.00000000Wildcard:  0.0.1.255             00000000.00000000.0000000 1.11111111=>Network:   192.168.100.0/23      11000000.10101000.0110010 0.00000000 (Class C)Broadcast: 192.168.101.255       11000000.10101000.0110010 1.11111111HostMin:   192.168.100.1         11000000.10101000.0110010 0.00000001HostMax:   192.168.101.254       11000000.10101000.0110010 1.11111110Hosts/Net: 510                   (Private Internet)

Resources

• http://jodies.de/ipcalc

• I found the IPv4 Calculator link in IPv4 Subnetting section of the Unix and Linux System Administration Handbook.

  Nemeth, Evi, et al. Unix and Linux System Administration Handbook. 5th ed., Pearson Education, Inc., 2018.