Understanding IPv4 Addressing, Subnetting, and Binary Calculations

An IP address identifies a node on a network and consists of a network portion and a host portion, where the network bits are represented by continuous 1 s and the host bits by continuous 0 s.

The broadcast address has all host bits set to 1 , e.g., 255.255.255.255 , and cannot be assigned to a single interface.

Classful address ranges are illustrated:

Class A: network 10.0.0.0 , mask 255.0.0.0 , binary 11111111.00000000.00000000.00000000

Class B: network 172.16.0.0 , mask 255.255.0.0 , binary 11111111.11111111.00000000.00000000

Class C: network 192.168.1.0 , mask 255.255.255.0 , binary 11111111.11111111.11111111.00000000

Usable host counts are calculated as 2^n - 2 , where n is the number of host bits; examples include:

10.0.0.0/8 provides 2^24 - 2 = 16,777,214 usable addresses.

128.0.0.0/16 provides 2^16 - 2 = 65,534 usable addresses.

192.168.1.0/24 provides 2^8 - 2 = 254 usable addresses.

Subnetting divides a larger network into smaller ones by extending the subnet mask, which simplifies management and enables policies such as ACLs. The mask distinguishes network bits from host bits; for example, IP 192.168.1.1 with mask 255.255.0.0 has network 192.168.0.0 , while mask 255.255.255.0 yields network 192.168.1.0 .

To design subnets, determine the number of required subnets ( N ) and find the smallest 2^n ≥ N ; the value n indicates how many host bits must be borrowed. Examples:

For 4 subnets, borrow 2 bits ( 2^2 = 4 ).

For 6 subnets, borrow 3 bits ( 2^3 = 8 ≥ 6 ).

Each subnet’s details include network address, first usable IP (network address + 1), last usable IP (broadcast address – 1), broadcast address, and the next network (increment the smallest network bit by 1).

Example calculations:

IP 172.16.36.42/24 converts to binary 10101100.00010000.00100100.00101010 with mask 11111111.11111111.11111111.00000000 (255.255.255.0). The network address is 172.16.36.0 , first host 172.16.36.1 , last host 172.16.36.254 , and next network 172.16.37.0 .

Another example, 192.168.221.37/29 yields binary IP 11000000.10101000.11011101.00100101 and mask 11111111.11111111.11111111.11111000 (255.255.255.248). The network address is 192.168.221.32 , first host 192.168.221.33 , last host 192.168.221.38 , broadcast 192.168.221.39 , and next network 192.168.221.40 .

Binary power tables (2⁰ to 2⁷) are provided to aid manual calculations, and a detailed example for 158.72.68.139/28 shows step‑by‑step conversion to binary, mask derivation ( 255.255.255.240 ), network address 168.72.68.128/28 , first address 168.72.68.129 , last address 168.72.68.142 , and broadcast 168.72.68.143 .

Finally, the article demonstrates splitting 172.16.32.0/20 into four sub‑nets of 50 IPs each, showing the binary representation of each resulting subnet.