Question

Internet Addresses: IPv4 and IPv6. The Internet requires an address for each machine that is connected to it. The address space of the addressing architecture of Internet Protocol version 4 (IPv4) consists of a 32 -bit field. Since not every combination of bits can be used as an address, plans are underway to change the address space to a 128 -bit field in IPv6. The 32 -bit IPv4 addresses are usually written in a form called dotted decimal. The 32 bit address is broken up into four 8 -bit bytes, and these bytes are then converted to their equivalent decimal form and separated by dots. For example. $$ \begin{array}{ll} 1000000000000011 & 00000010000000011 \end{array} $$ is written as 128.3 .2 .3 , which is obviously more readable. The 128 -bit IPv6 addresses are divided into eight 16 -bit pieces. Each 16 -bit piece is converted to its equivalent hexadecimal value (each sequence of 4 bits is converted to one hexadecimal digit). The eight four-character hexadecimal strings are separated by colons. It is not prac. tical to list 128 bits and show the conversion to the final IPv6 address form. As an example of what you might end up with, however, we show one IPv6 address: \(\mathrm{FFDC} \cdot \mathrm{BA} 98: 7654 \cdot 3210: \mathrm{FEDC}: \mathrm{BA} 98: 7654 \cdot 3210\) How many IPv4 addresses are possible?

Short answer

There are 4,294,967,296 possible IPv4 addresses.

Step-by-step solution

Understand the IPv4 Address Structure

IPv4 addresses are made up of a 32-bit field. Each IPv4 address is composed of four 8-bit sections often represented in decimal form separated by dots. This is known as dotted decimal notation.

Calculate the Number of Possible Addresses

Given that each IPv4 address is a 32-bit binary number, the total number of possible combinations can be calculated using the formula for permutations of binary digits. Since there are 2 possible states for each bit (0 or 1), the number of combinations is given by calculating \(2^{32}\).

Compute the Result

Calculate \(2^{32}\) to find the total number of possible IPv4 addresses. This involves computing the power of 2 with the exponent 32, which results in 4,294,967,296.

Key concepts

IPv4

The Internet Protocol version 4, commonly known as IPv4, is a fundamental aspect of connecting devices across the internet. Each connected device requires a unique address to communicate with other devices, and IPv4 addresses fill this role. These addresses are 32 bits in length, allowing for a significant number of combinations. Each address is constituted by four 8-bit sections.
Each of these sections can take one of 256 values (ranging from 0 to 255), resulting in a total of 2³² possible unique addresses. This means that IPv4 supports approximately 4.3 billion distinct addresses. In practical terms, IPv4 addresses are depicted using dotted decimal notation, which includes separating each of the four groups by dots. This makes it easier to read and understand. For example, the binary sequence 10000000 00000011 00000010 00000011 translates to the more human-readable form of 128.3.2.3.

IPv6

With the explosive growth of internet-enabled devices, IPv4's 4.3 billion addresses became insufficient. To accommodate the expanding need, Internet Protocol version 6 (IPv6) was introduced. IPv6 provides a vastly larger address space than IPv4, using a 128-bit addressing system.
Each IPv6 address is divided into eight segments of 16 bits. Instead of the dotted decimal system used by IPv4, IPv6 addresses are often expressed in hexadecimal, separated by colons. For example, an IPv6 address might appear as FFDC:BA98:7654:3210:FEDC:BA98:7654:3210, indicating its 128-bit structure. This massive increase to 2¹²⁸ possible addresses, equates to a virtually limitless number of combinations, addressing potential at an astronomical scale.

dotted decimal notation

Dotted decimal notation is a method used to represent IPv4 addresses. This format enhances readability and usability by translating 32-bit binary addresses into a four-part decimal format. Each 8-bit binary segment, or "octet," is converted into its decimal equivalent.
This method involves breaking down the binary address into four separate octets. Each octet is then converted into a decimal number and separated by dots, hence the name "dotted decimal." This results in a more comprehensible format of IP numbers such as "192.168.0.1", which is far more user-friendly than its binary counterpart. Dotted decimal notation has been critical in the day-to-day use of IPv4 addresses, simplifying network administration and communication.

hexadecimal

Hexadecimal notation, often used in IPv6 addressing, simplifies the representation of large binary numbers. The hexadecimal system is base-16, meaning it uses sixteen distinct symbols: 0 through 9 to represent values zero to nine, and A through F to represent values ten to fifteen.
In IPv6, the lengthy 128-bit address is broken down into eight 16-bit blocks. Each block is divided into groups of four bits, which are then translated into a single hexadecimal digit. This conversion process makes complex IP addresses more manageable to read and write. An IPv6 address such as FFDC:BA98:7654:3210 presents a meaningful and concise method to handle the otherwise unwieldy binary sequence. Utilizing hexadecimal notation helps in greatly simplifying network tasks and improves overall efficiency when working with IPv6.