Question

Suppose the address of an end system on the Internet is quoted as 134.48.4.122. What is the 32-bit address in hexadecimal notation?

Short answer

The 32-bit address in hexadecimal is 8630047A.

Step-by-step solution

Understand the Problem

We are given an IP address in dotted decimal notation (134.48.4.122) and need to convert it to a 32-bit address in hexadecimal format. An IP address consists of four octets (8 bits each) and needs to be represented as a single 32-bit number.

Convert Each Octet to Binary

First, we need to convert each of the four octets in the given IP address to their binary equivalents. - 134 in binary is \( 10000110 \).- 48 in binary is \( 00110000 \).- 4 in binary is \( 00000100 \).- 122 in binary is \( 01111010 \).

Combine Binary Representations

Combine the binary representations of all octets to form a 32-bit binary number:\[ 10000110.00110000.00000100.01111010 \] By removing the dots, we get:\[ 10000110001100000000010001111010 \]

Convert Binary to Hexadecimal

Convert the 32-bit binary number to hexadecimal by dividing it into 4-bit segments:- 1000 is 8 in hexadecimal.- 0110 is 6 in hexadecimal.- 0011 is 3 in hexadecimal.- 0000 is 0 in hexadecimal.- 0000 is 0 in hexadecimal.- 0100 is 4 in hexadecimal.- 0111 is 7 in hexadecimal.- 1010 is A in hexadecimal.Thus, the 32-bit binary number \( 10000110001100000000010001111010 \) converts to hexadecimal as \( 8630047A \).

Key concepts

Dotted Decimal Notation

The IP address is a fundamental part of networking. When we look at an IP address like 134.48.4.122, it is presented in what's called Dotted Decimal Notation. This format makes it easier for humans to read and memorize IP addresses. An IP address in this notation is composed of four separate numbers known as octets. Each octet represents 8 bits of the address. For example:

• The first octet, 134, is one segment of the full address.
• The second octet, 48, is the next, and so on.
• Each of these numbers ranges from 0 to 255.

Each octet is actually part of a greater whole—a 32-bit address—and it helps in uniquely identifying a device on a network. This segmented structure using periods (.) makes the IP address more manageable for human operators.

Binary Representation

Binary numbers form the backbone of network addressing. Computers operate using binary, a base-2 numeral system utilizing only 0s and 1s. Converting our dotted decimal IP address to its binary form is the first step in transitioning to other notations.

• The IP address 134.48.4.122 expressed in binary becomes 10000110.00110000.00000100.01111010.
• Each number in the dotted decimal corresponds to an 8-bit octet in binary.

Translating each octet into binary means rewriting it into an easy-to-manage format for computers. For instance, the decimal number 134 becomes 10000110 in binary. Understanding binary is core to networking, as computers and networking equipment communicate using this straightforward language.

Hexadecimal Notation

Hexadecimal notation is another way to express IP addresses, offering a compressed format that simplifies representation. It is a base-16 numeral system, using numbers 0-9 and letters A-F. Converting from binary to hexadecimal involves breaking the binary number into 4-bit segments.

• The 32-bit binary number 10000110001100000000010001111010 converts to hexadecimal as 8630047A.
• Each group of four binary digits converts directly into a single hexadecimal digit.
• For example, 1000 in binary becomes 8 in hexadecimal.

Hexadecimal notation efficiently condenses lengthy binary numbers, simplifying tasks like coding and debugging for IT professionals.

32-bit Address

An IP address being a 32-bit address means it consists of 32 individual bits. These bits are the smallest unit of data in a computer, representing binary digits that can be 0 or 1. A 32-bit address constructs a wide number of possible combinations, making it capable of supporting approximately 4.3 billion unique addresses.

• These addresses are divided into network and host portions, allowing networks to be subdivided.
• IPv4, the protocol version utilizing 32-bit addresses, was designed to manage a vast number of devices.

The 32-bit structure is crucial for routing data across the globe, providing a unique identifier that directs traffic from one device to another accurately.