254 in binary

Guri Bee

2 min read

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20-10-2024

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Demystifying 254 in Binary: A Beginner's Guide

The world of computers is built on a foundation of zeros and ones – the language of binary. Understanding binary is crucial for anyone interested in programming, data storage, or even just the inner workings of a computer. But, how do we represent numbers like 254 in binary? Let's dive in and find out.

Understanding Binary Basics

Before we convert 254, let's grasp the basics of binary:

• Decimal (Base 10): Our everyday number system uses ten digits (0-9). Each place value represents a power of ten. For example, the number 123 means (1 x 10²) + (2 x 10¹) + (3 x 10⁰).
• Binary (Base 2): Binary only uses two digits: 0 and 1. Each place value represents a power of two.

Here's a simple example:

Notice how each binary place value increases by a power of two: 2⁰, 2¹, 2², 2³, and so on.

Converting 254 to Binary

To convert 254 to binary, we'll use the method of successive division by 2:

1. Divide 254 by 2: 254 / 2 = 127 (remainder 0)
2. Divide the quotient (127) by 2: 127 / 2 = 63 (remainder 1)
3. Continue dividing the quotients by 2:
   • 63 / 2 = 31 (remainder 1)
   • 31 / 2 = 15 (remainder 1)
   • 15 / 2 = 7 (remainder 1)
   • 7 / 2 = 3 (remainder 1)
   • 3 / 2 = 1 (remainder 1)
   • 1 / 2 = 0 (remainder 1)
4. Read the remainders from bottom to top: 11111110

Therefore, 254 in binary is 11111110.

Why is 254 Important?

The number 254 holds special significance in networking:

• Subnet Mask: A subnet mask is used to define the network and host portions of an IP address. A common subnet mask is 255.255.255.0, which is represented in binary as 11111111.11111111.11111111.00000000.
• Broadcast Address: The broadcast address for a network is derived from the subnet mask. For example, if the subnet mask is 255.255.255.0, the broadcast address for that network is 255.255.255.255, or 11111111.11111111.11111111.11111111 in binary.

Note: This information is based on responses from GitHub users and is subject to interpretation and variation. It's essential to consult reliable networking resources for a comprehensive understanding of subnets and broadcast addresses.

Conclusion

Converting numbers to binary might seem daunting at first, but with practice, it becomes second nature. The ability to understand and manipulate binary is essential for anyone working in the digital realm. By understanding the relationship between decimal and binary, we gain a deeper understanding of how computers work and the data they process.