Concept:
The Internet Protocol version 4 (IPv4) is the primary protocol used for identifying devices on a network. The capacity of any addressing system is determined by the number of bits used to represent an address. In IPv4, each address is a fixed-length binary number.
Step 1: Determine the bit length of an IPv4 address.
An IPv4 address consists of 32 bits. These bits are traditionally divided into four 8-bit sections known as "octets," separated by dots (dotted-decimal notation, e.g., 192.168.1.1). Since each bit can be either a 0 or a 1, the total number of unique combinations is calculated using base-2.
Step 2: Calculate the total address space.
The formula for the total number of unique addresses is \(2^n\), where \(n\) is the number of bits.
\[ \text{Total Addresses} = 2^{32} \]
Numerically, this equals approximately 4,294,967,296 unique addresses. While this seemed like a vast number in the 1980s, the explosion of internet-connected devices has led to "IPv4 address exhaustion."
Step 3: Comparison with IPv6.
To solve the exhaustion problem, IPv6 was developed using 128-bit addresses. The address space for IPv6 is \(2^{128}\), which is a staggeringly larger number compared to the \(2^{32}\) limit of IPv4.