Sizing the Prefix From Counted Demand

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Sizing the Prefix From Counted Demand

The chapter’s practitioner example tallies 180 sensors, 12 infrastructure addresses, 8 reserved maintenance addresses, and 40 documented spares, then asks for a prefix with at least 240 usable hosts. A planner who sized on the 180 sensors alone would badly understate the real demand. This audit adds up every address consumer to find which prefix actually clears the counted total.

Companion to the chapter Subnetting and CIDR for IoT Networks — every number here comes from that chapter.

Ada: The practitioner example counts 180 sensors, 12 infrastructure addresses, 8 reserved maintenance addresses, and 40 documented spares, then asks for a prefix whose usable capacity is “at least 240.” Let me check the demand total and see exactly which prefix clears it, using the chapter’s own rule that usable hosts equal 2^(32 - p) - 2.

The demand is the sum of every address consumer, not just the sensors:

• Counted demand: 180 + 12 + 8 + 40 = 240 addresses.

Now test the prefixes against that 240:

• /25: 2^(32 - 25) - 2 = 2^7 - 2 = 128 - 2 = 126 usable — short of 240, rejected.
• /24: 2^(32 - 24) - 2 = 2^8 - 2 = 256 - 2 = 254 usable — clears 240 with 254 - 240 = 14 to spare.

The two subtracted addresses are the same pair the chapter derives for a /26: 6 host bits give 2^6 = 64 total, and removing the all-zeros network address and the all-ones broadcast address leaves 64 - 2 = 62 usable — the pattern that makes 192.168.10.45/26 span .0 to .63 with hosts .1 through .62.

The design meaning is that headroom must be measured against counted demand, not device count. A /24 clears 240 but leaves only 14 free addresses, so a planner who sized on the 180 sensors alone would believe there were 254 - 180 = 74 spare when only 14 remain — and the next dozen infrastructure or replacement devices would force a /23 or a disruptive renumber. The prefix is chosen from the whole record precisely so that the spare margin is real.

Every number above is taken from the chapter’s own material and re-derived step by step.