Usable Hosts in a Subnet

1. Background Knowledge

IPv4 addresses are 32-bit integers. A subnet prefix length $p$ determines how many leading bits are fixed for the network portion, leaving $32 - p$ bits for the host portion. The total number of addresses in a subnet is therefore $2^{32-p}$.

In traditional subnetting, two addresses are reserved: the network address (all host bits zero) and the broadcast address (all host bits one). This leaves $2^{32-p} - 2$ usable host addresses for most prefix lengths. However, two special cases exist defined by RFCs:

• A /31 subnet (point-to-point link, RFC 3021) has exactly 2 usable addresses because there is no separate broadcast address on a point-to-point link.
• A /32 subnet (host route) represents a single specific host, so it has exactly 1 usable address.

Understanding these edge cases is critical because blindly applying the $2^{32-p} - 2$ formula would yield 0 for /31 and $-1$ for /32, which are incorrect.

2. Algorithm Approach

This is a conditional arithmetic problem. The core logic involves:

1. Computing the total address count via bit shifting: $2^{32-p}$.
2. Applying the standard subtraction of 2 for normal subnets.
3. Handling the two special cases (prefix == 31 and prefix == 32) with explicit conditional branches that override the standard formula.

The pattern is: compute the general case, then check for exceptions. This is a common structure in networking problems where RFC-defined edge cases deviate from the general rule.

3. Step-by-Step Strategy