IP addresses, subnets, and gateways

An IPv4 address is 32 bits, written as four eight-bit octets. Each octet ranges from 0 to 255. From left to right, the eight bit positions have values 128, 64, 32, 16, 8, 4, 2, and 1. Add the values whose bits are 1 to convert binary to decimal; leading zero bits still occupy positions.

For decimal to binary, work from the largest value down. Subtract a place value when it fits and write 1; otherwise write 0. For 192, subtract 128 and then 64, leaving zero: 11000000. Do this independently for each octet. The binary value of an address and the binary value of its subnet mask have different jobs.

Early IPv4 unicast addressing used classes A, B, and C, selected by leading address bits. Their default network boundaries were /8, /16, and /24. This history explains older training material, but modern routing uses Classless Inter-Domain Routing (CIDR): an explicit prefix length defines the boundary.

Do not infer today’s mask from the first octet. A 10.x.x.x host can be on a /24, /20, or another configured prefix even though 10 falls in the old Class A region. Class labels also do not mean private or public: only specific blocks are reserved for private use. D and E describe multicast and reserved regions, not ordinary unicast subnets with default host masks.

Learn a range’s purpose before treating it as a normal internet destination. Private addresses can be routed inside organisations but are not globally reachable as ordinary public addresses. The entire 172/8 region is not private: the private block only spans second octets 16 through 31.

Not private does not automatically mean publicly usable: other special-purpose blocks exist. A public address also needs appropriate allocation, routing, and access policy to be reachable. The list below is a practical starting point, not the complete IANA registry. A listed block’s endpoints describe its full range, not a guarantee that every address is assignable to a host.

A CIDR prefix /n counts the contiguous network bits at the left of the 32-bit mask. Write n ones followed by 32 − n zeros. Ones retain network bits; zeros identify host positions. For /26, write three full octets of ones and then 11000000. That final octet equals 128 + 64 = 192, giving mask 255.255.255.192.

To reverse the calculation, convert each decimal mask octet to eight bits and count the leading ones. In 255.255.240.0, the first two octets contribute 16 ones and 240 is 11110000, adding four: /20. Count bits in the mask, not ones in the host IP address. A CIDR mask cannot return to 1 after its first 0; 255.0.255.0 is therefore not a valid contiguous CIDR mask.

With h host bits, there are 2^h total addresses because every host-bit position has two possible values. In a conventional IPv4 broadcast subnet with prefix /30 or shorter, reserve the all-zero host part for the network address and the all-one host part for broadcast. The usual assignable capacity is 2^h − 2. A gateway consumes one of those host addresses; it is not an extra address outside the subnet.

For a requirement of H assignable addresses, find the smallest h for which 2^h − 2 ≥ H, then calculate the prefix as 32 − h. For 50 endpoints plus one gateway, H = 51: five host bits give 30 usable addresses, while six give 62. Choose /26. Include infrastructure, reservations, and planned growth in H before sizing the subnet.

Do not apply subtract two blindly. On an IPv4 point-to-point link using /31, both addresses identify endpoints and there is no directed broadcast. A /32 identifies one address, commonly a host route. /0 represents the full IPv4 address space, normally used for a default route, rather than a practical single LAN.

Bitwise AND the IP address with its mask to obtain the network address. AND gives 1 only when both input bits are 1. Set all host bits to 1 for the broadcast address. For an ordinary subnet, the first assignable host is network + 1 and the last is broadcast − 1.

For 192.0.2.130/26, the first three octets are entirely network bits. In the final octet, 130 is 10000010 and mask 192 is 11000000. AND produces 10000000, or 128. Six host bits remain; setting them all to 1 produces 10111111, or 191. The network is 192.0.2.128/26, with hosts .129–.190 and broadcast .191.

A useful decimal shortcut is block size = 256 − mask value in the boundary octet. For /26, 256 − 192 = 64, so last-octet blocks start at 0, 64, 128, and 192. Find the block containing the host and stop one address before the next block. Always use the prefix: an address ending in .0 or .255 is not automatically a network or broadcast address for every subnet size.

The block-size shortcut also works when the prefix ends before the last octet. For 172.20.35.77/20, the mask is 255.255.240.0 and the boundary octet is the third. Its block size is 256 − 240 = 16. Third-octet blocks begin at 0, 16, 32, 48, and so on; 35 is in the 32–47 block.

Keep the first two octets fixed. Set all bits after the /20 boundary to zero for network 172.20.32.0, and to one for broadcast 172.20.47.255. The conventional host range is 172.20.32.1–172.20.47.254. There are 12 host bits, so 4,096 total addresses and 4,094 assignable addresses. This whole subnet lies inside the private 172.16.0.0/12 range.

Subnetting borrows host positions to extend a parent network prefix. Splitting a /24 into /26 networks borrows two bits, giving 2^2 = 4 equal subnets. Each has 64 total addresses and 62 assignable addresses. Do not subtract two from the number of child subnets: all four are usable in modern subnetting.

Variable Length Subnet Masking (VLSM) uses different prefix lengths within one parent allocation to fit different requirements. Allocate larger blocks first and respect their alignment. A /26 boundary must start on a multiple of 64 in the final octet of a /24; writing 192.0.2.70/26 does not create a new block starting at .70. It identifies a host in 192.0.2.64/26.

A host uses its routes to decide how to reach a destination. In a simple LAN with one connected subnet and a default route, a same-subnet destination can be reached directly; a remote destination is sent to the default gateway. The gateway is an address on the local network belonging to a router, not the address of every remote server.

A wrong subnet mask can make a host mistakenly treat a remote address as local. A wrong gateway can allow local traffic while breaking remote access. Before blaming DNS or an application, check the address, prefix, gateway, and relevant route. More specific routes take precedence over the default route.

IPv6 uses 128 bits, written as eight hexadecimal groups. Each hexadecimal digit represents four bits and each full group represents 16. Leading zeros within a group may be omitted; one consecutive run of zero groups may be replaced by ::. Thus 2001:db8::10 expands to 2001:0db8:0000:0000:0000:0000:0000:0010.

A /64 fixes the first four full groups and leaves 64 bits for addresses within that prefix. IPv6 prefixes are written in slash notation, not dotted-decimal masks, and IPv6 has no broadcast. Do not transfer IPv4’s usual minus-two host rule to IPv6. IPv6 address assignment has its own reserved-address and interface-identifier rules.