IPv4 Binary-Decimal Conversion

Understanding the IPv4 Address Structure

An IPv4 address is a 32-bit number. To make it easier for humans to read, it's divided into four groups of 8 bits each. Each 8-bit group is called an octet. These octets are then converted to their decimal equivalent and separated by dots. This format is called dotted-decimal notation.

For example, the IP address 172.16.254.1 is the human-readable version of a long 32-bit binary number.

Our main task is to learn how to convert any octet (a decimal number from 0 to 255) into its 8-bit binary equivalent, and vice-versa.

The Key: Powers of Two

The tool we'll use for these conversions is a simple chart representing the positional value of each of the 8 bits in an octet. Since binary is a base-2 system, each position corresponds to a power of 2, starting from $2^0$ on the right.

This sequence—128, 64, 32, 16, 8, 4, 2, 1—is all you need to memorize.

To get a great foundation in this, let's watch a video from Professor Messer. While it's general binary math, it perfectly explains the system we'll be using.

Conversion Practice: From Binary to Decimal

Let's put the chart to use. To convert an 8-bit binary number to decimal, you simply place the binary number under the chart and add up the decimal values that have a 1 below them.

Example: Convert the binary octet 10110100 to decimal.

We add the values corresponding to the '1's: $128+32+16+4=180$.
So, 10110100 in binary is 180 in decimal.

The following video from Neso Academy provides more examples specifically for IPv4 addresses.

Conversion Practice: From Decimal to Binary

To go the other way—from decimal to binary—we use the same chart but with a subtraction method. For a given decimal number, you go from left to right (from 128 down to 1) and ask: "Is this value less than or equal to my remaining number?"

• If yes, you put a 1 in that position and subtract the value from your number.
• If no, you put a 0 and move to the next position.

Example: Convert the decimal number 192 to binary.

1. Start with 192. Is 192 >= 128? Yes.
   • Binary: 1_______
   • Remainder: $192-128=64$
2. Current number is 64. Is 64 >= 64? Yes.
   • Binary: 11______
   • Remainder: $64-64=0$
3. The remainder is 0. All subsequent checks will be "no". We fill the rest with zeros.
   • Binary: 11000000

So, 192 in decimal is 11000000 in binary.

Let's see this method applied to a full IP address.

Test Your Knowledge

Now it's your turn to practice. Use the methods we've just covered to solve these two problems.

Problem 1: Convert the following IP address from dotted-decimal to binary notation:
208.34.54.12

Problem 2: Convert the following IP address from binary to dotted-decimal notation:
00001010.00011001.01011100.10000100

Take a few minutes to work through these on paper. Once you're done, you can check your answers below.

For more practice and a textual summary of the conversion methods, the following article is a great resource.

Conclusion

In this lesson, you've mastered a fundamental skill for network engineering: translating between the human-readable dotted-decimal IP address and the machine-readable binary format.

Key Takeaways:

• An IPv4 address is a 32-bit number, structured as four 8-bit octets.
• The key to conversion is the powers-of-two chart for an octet: 128, 64, 32, 16, 8, 4, 2, 1.
• Binary to Decimal: Add the values of the positions that contain a 1.
• Decimal to Binary: Use the subtraction method, working from 128 down to 1, to determine where to place the 1s.

Preview of the Next Lesson:

Now that you can read and write IP addresses in both formats, you're ready to understand what they actually mean. In our next lesson, we will explore the structure of an IPv4 address, breaking it down into its network and host portions. You'll learn how the subnet mask is used to define the boundary between these two parts, which is the core concept behind creating and managing networks.