1 IPv4 Addressing and CIDR Fundamentals

IPv4 address structure

An IPv4 address is a 32-bit value presented as four decimal octets separated by periods. For example, 192.168.10.77 contains the octets 192, 168, 10, and 77; each octet contains $8$ bits and ranges from $0$ to $255$.

An address can be understood as two parts: the network prefix, which identifies a block of addresses, and the remaining host bits, which identify an address within that block. A subnet mask or CIDR prefix length specifies where the network bits end and the host bits begin.

Binary and decimal conversion

Each bit in an octet has a place value. From the leftmost bit to the rightmost bit, the values are $128$, $64$, $32$, $16$, $8$, $4$, $2$, and $1$. To convert binary to decimal, add the place values corresponding to bits that are $1$.

For example, $11000000$ represents $128+64=192$, while $01001101$ represents $64+8+4+1=77$. To convert decimal to binary, express the decimal value as a sum of place values and mark those positions with $1$. Thus, $77=64+8+4+1$, giving $01001101$.

The address 192.168.10.77 in binary is:

The binary representation has four octets of $8$ bits each, for a total of $32$ bits.

Subnet masks and network addresses

A subnet mask is another 32-bit value. Its leading $1$ bits mark the network prefix, and its remaining $0$ bits mark the host portion. In a valid contiguous mask, all the $1$ bits come first, followed by all the $0$ bits.

For example, 255.255.255.192 is represented in binary as:

This mask has $26$ leading $1$ bits and $6$ trailing $0$ bits. To find the network address, apply a bitwise AND between the IP address and its mask: each result bit is $1$ only when both corresponding input bits are $1$.

For 192.168.10.77 with mask 255.255.255.192, the operation is:

The result is 192.168.10.64. The first three octets remain unchanged because their mask bits are all $1$; in the last octet, $77$ AND $192$ equals $64$.

CIDR prefixes and address blocks

CIDR notation writes an IPv4 address followed by a slash and a decimal prefix length from $0$ through $32$. The number after the slash specifies how many leading bits belong to the network prefix. For example, /26 means $26$ network bits and $6$ host bits.

To convert a prefix length to a mask, write that many $1$ bits from the left, fill the remaining bits with $0$ bits, and group them into octets. These examples show the prefix, corresponding mask, and number of network and host bits:

• /8: mask 255.0.0.0; $8$ network bits and $24$ host bits.

• /16: mask 255.255.0.0; $16$ network bits and $16$ host bits.

• /24: mask 255.255.255.0; $24$ network bits and $8$ host bits.

• /26: mask 255.255.255.192; $26$ network bits and $6$ host bits.

• /30: mask 255.255.255.252; $30$ network bits and $2$ host bits.

• /32: mask 255.255.255.255; $32$ network bits and $0$ host bits.

For example, 172.16.5.9/16 means that the first $16$ bits—172.16—are the prefix. CIDR makes the prefix length explicit; it is not inferred from the address’s first octet.

For a prefix of length $p$, the number of addresses in its block is:

Thus, a /26 block contains $2^6=64$ addresses. The address written before the slash is not necessarily the block’s starting network address. Apply the mask to find the network address, as in the example using 192.168.10.77 and 255.255.255.192.