Address space is a hierarchy of bit prefixes

IPv4 addresses contain 32 bits; IPv6 addresses contain 128. A slash followed by a prefix length fixes that many leading bits. The remaining bits enumerate suffixes. A /26 IPv4 block contains 64 addresses because six bits remain free. Its starting address must align to a 64-address boundary in the final octet when the first 24 bits are fixed. Writing 192.0.2.70/26 describes an address inside the block whose network prefix is 192.0.2.64/26.

Splitting a prefix into equal children increases the prefix length. A /24 divided into /27 blocks has eight children, each containing 32 addresses. Count raw addresses before subtracting reservations or infrastructure assignments. For IPv6, a /48 can contain 65,536 distinct /64 subnets; that is a count of subnet prefixes, not a recommended number of hosts on one link. Hierarchy makes allocations understandable and aggregatable, but operational topology determines whether the summaries remain useful.

On an ordinary IPv4 broadcast subnet, the all-zero host suffix identifies the network and the all-one suffix identifies its directed broadcast. This motivates the familiar raw-count-minus-two rule, but only within that context. RFC 3021 permits both addresses of a /31 on an appropriate point-to-point link. A /32 identifies one IPv4 address as a host route. Applying a blanket subtraction to those prefixes produces nonsense and obscures the link model that justifies their use.

IPv6 has no broadcast address type; multicast provides relevant group-delivery functions. Do not subtract an IPv4 broadcast reservation from an IPv6 allocation. Also do not infer that every bit pattern is an ordinary assignable interface address: subnet-router anycast and other architectural conventions still matter. A common /64 link allocation is not a license to disregard the requirements of address configuration or neighbor discovery. Address width, prefix boundaries, and interface assignment policy answer different questions.

An assigned address still needs a correct interface configuration, on-link determination, a usable next hop, return routing, and permitted traffic. IPv4 and IPv6 can fail independently on a dual-stack service. A DNS answer for both families is therefore an invitation to test both, not evidence that either path succeeds. Keep allocation records separate from route advertisements and from application health so a change in one layer does not silently invalidate assumptions in another.

Use the probability lab to examine the limits of random reachability sampling. Set independent per-test failure probability p and trial count n; predict the probability of seeing zero failures before reading the binomial bars. At p=0.1 and n=10 it remains about 0.349. A clean small sample therefore cannot certify every address in a prefix. Real outages often correlate by subnet or next hop, violating independence; stratify tests by family and route boundary rather than treating this illustrative binomial model as a network audit.