Decimal and binary number systems play a crucial role in IP addressing, primarily in the context of IPv4. IP addresses are usually expressed in decimal (base-10) notation for human convenience, while computers use binary (base-2) for efficient data processing and routing.
The translation from decimal to binary in IPv4 addressing involves converting each decimal octet into its binary equivalent. This conversion ensures network devices can work with IP addresses in their native binary format. Conversely, when humans need to read or configure IP addresses, the binary values are converted back to decimal for clarity and ease of use.
The decimal and binary number systems are ways of representing numbers. In the decimal system, numbers are expressed using 10 digits (0-9), and each digit's position carries a specific value. For instance, 10 is written as "10" because it has one ten and zero ones.
In contrast, the binary system uses only two digits, 0 and 1. Each digit's position represents a power of 2, starting with 2^0 (1), 2^1 (2), 2^2 (4), and so on. To convert a decimal number to binary, it's broken down into binary digits (bits) using these powers of 2. For example, the decimal number 10 in binary is "1010" because it's 1*(2^3) + 0*(2^2) + 1*(2^1) + 0*(2^0).
As you can see in the image, each bit has a doubling value from right to left. By setting specific bits to binary 1, we define the values to use. The total sum represents the decimal number. For example, the binary 01100110 equals the decimal 102.
In networking, binary represents IPv4 addresses, where each of the four decimal octets is converted to an 8-bit binary number, allowing devices to locate each other on the network. Understanding the binary's positional value is crucial in comprehending these systems.