Problem 13 - Computer Networking: A Top-Down Approach

Question

What is the 32 -bit binary equivalent of the IP address \(223.1 .3 .27 ?\)

Step-by-Step Solution

Answer

The 32-bit binary equivalent of 223.1.3.27 is 11111111.00000001.00000011.00011011.

Step 1: Understand the IP Address

An IP address is made up of four numbers separated by dots. Each number can be between 0 and 255. In this problem, the IP address is given as 223.1.3.27.

Step 2: Convert Each Octet to Binary

Each of the four numbers, also called octets, should be converted to an 8-bit binary number. Start with the first octet. 1. Convert 223 to binary: 223 divided by 2 gives 11111111 2. Convert 1 to binary: 1 divided by 2 gives 00000001 3. Convert 3 to binary: 3 divided by 2 gives 00000011 4. Convert 27 to binary: 27 divided by 2 gives 00011011

Step 3: Combine the Binary Numbers

Take each 8-bit binary number from the previous step and combine them to form a complete 32-bit binary sequence for the IP address. So, the combination is 11111111.00000001.00000011.00011011.

Key Concepts

Binary Conversion

Binary conversion refers to the process of translating a decimal (base-10) number into a binary (base-2) number. This transformation is crucial in computing, as computers primarily process data in binary form. Binary numbers use only two digits, 0 and 1, compared to the ten digits used in the decimal system.

For any decimal number, converting it to binary involves repeatedly dividing the number by 2 and keeping track of the remainder. You continue this process until the quotient is 0. The binary number is read from the remainders, starting from the bottom to the top.

For example, to convert the number 5 to binary:

• 5 divided by 2 gives quotient 2 and remainder 1
• 2 divided by 2 gives quotient 1 and remainder 0
• 1 divided by 2 gives quotient 0 and remainder 1

Reading from bottom to top, the binary equivalent is 101. Remember, binary conversion is essential for operations involving network configurations, such as IP addresses.

32-bit Binary

A 32-bit binary system consists of a sequence of 32 digits, where each digit is either 0 or 1. This is the standard format for many computing systems, including IPv4 addresses.

• Each bit represents a power of 2, from 2^0 to 2^31.
• The sum of these weighted bits can represent a range of values, making it powerful for both storage and processing tasks.
• For a standard IP address, each set of 8 bits is known as an octet, and there are four octets in total.

In networking, 32-bit binary numbers are used to represent IP addresses. This allows for the representation of up to 4,294,967,296 unique addresses, accommodating a vast number of devices on the internet.

To handle binary numbers efficiently, one must often transition between human-readable decimal format and machine-readable binary format, especially when configuring network settings.

Octet Conversion

Octet conversion is the method of transforming each decimal number in an IP address into an 8-bit binary number. An IP address like 223.1.3.27 is typically expressed in decimal form as four distinct numbers separated by dots, each ranging from 0 to 255.

Each of these numbers is known as an 'octet'. In binary, this means creating an 8-digit sequence for each one.

• The value 223 converts to binary as 11111111.
• The value 1 becomes 00000001.
• The value 3 translates to 00000011.
• The value 27 is converted to 00011011.

Each octet is combined to form a 32-bit binary string representing the entire IP address. This process is fundamental when working with computer networks. It ensures uniformity in communication, as all network devices convert and interpret IP addresses in the same binary format. Understanding octet conversion not only aids in addressing but also in tasks like subnetting and configuring network hardware.