Decimal to binary conversion is an important task to understand in IP addressing and Subnetting. IP addressing is a core functionality of networking today. The knowledge of how to assign an IP address, or determine the network or host ID via a subnet, is vital to any good network engineer. Having a good, solid understanding of the simple things makes more complex tasks easier. Here are steps on how to convert a decimal IP address to its binary form, without memorization.

- The first, and probably most important step, is to put down this row of values:

128 64 32 16 8 4 2 1 In order to remember these values start with the number 1, go from right to left, and double that number seven times. For example, start with 1 on the right side. For your next number, double the 1 (1 x 2 = 2). So, 2 is your next number (remembering to go from right to left). For your third number, double the 2 (2 x 2 = 4); to continue the sequence, double the 4 (4 x 2 = 8). Repeat this process until you’ve doubled your original number, seven times. The key to this is that every single one of the values we put in that row are going to have either number 1 or number 0 assigned to it. To convert the IP address we will take that string of numbers and start from left to right this time. For each value we ask this question: “Can I subtract this value from the decimal remaining?” If the answer is “NO” then you put a “0” under the binary value, and if the answer is “YES” then you put “1” there.

- We take the IP address: 154.31.16.13 and start with the first part, which is 154.
- Question: Can I subtract 128 from 154? Answer: YES. So we assign 1 to 128.

**128**64 32 16 8 4 2 1 **1** - Question: Can I subtract 64 from 26? Answer: NO. So we assign 0 to 64.

128 **64**32 16 8 4 2 1 1 **0** - Question: Can I subtract 32 from 26? Answer: NO. So we assign 0 to 32.

128 64 **32**16 8 4 2 1 1 0 **0** - Question: Can I subtract 16 from 26? Answer: YES. So we assign 1 to 16.

128 64 32 **16**8 4 2 1 1 0 0 **1** - That will give us a remainder of 10. (26-16=10). Question: Can I subtract 8 from 10? Answer: YES. So we assign 1 to 8.

128 64 32 16 **8**4 2 1 1 0 0 1 **1** - That will give us a remainder of 2. (10-8=2). Question: Can I subtract 4 from 2? Answer: NO. So we assign 0 to 4.

128 64 32 16 8 **4**2 1 1 0 0 1 1 **0** - Question: can I subtract 2 from 2? Answer: YES. So we assign 1 to 2.

128 64 32 16 8 4 **2**1 1 0 0 1 1 0 **1** - That will give us a remainder of 0. So for the rest of the values in our row, we can assign 0.

128 64 32 16 8 4 2 **1**1 0 0 1 1 0 1 **0**So now we know that a decimal number 154 is

**10011010**converted to binary form. To double check, we take the values assigned with 1 and add them together: 128+16+8+2=154

- Question: Can I subtract 128 from 154? Answer: YES. So we assign 1 to 128.
- Our next number in the IP address is: 31. So we start with a question from step 2 again
- Can I subtract 128 from 31?

**128**64 32 16 8 4 2 1 **0** - Can I subtract 64 from 31?

128 **64**32 16 8 4 2 1 0 **0** - Can I subtract 32 from 31?

128 64 **32**16 8 4 2 1 0 0 **0** - Can I subtract 16 from 31?

128 64 32 **16**8 4 2 1 0 0 0 **1** - Can I subtract 8 from 15 (remember, it’s the remainder)?

128 64 32 16 **8**4 2 1 0 0 0 1 **1** - Can I subtract 4 from 7?

128 64 32 16 8 **4**2 1 0 0 0 1 1 **1** - Can I subtract 2 from 3?

128 64 32 16 8 4 **2**1 0 0 0 1 1 1 **1** - Can I subtract 1 from 1?

128 64 32 16 8 4 2 **1**0 0 0 1 1 1 1 **1**So the decimal number 31 is

**00011111**converted to binary form. To double check: 16+8+4+2+1=31

- Can I subtract 128 from 31?
- Next number is 16. I will perform the conversion in one step now.

128 64 32 **16**8 4 2 1 0 0 0 **1**0 0 0 0 So the decimal number 16 is

**00010000**converted to binary form. - Next number is 13.

128 64 32 16 **8****4**2 **1**0 0 0 0 **1****1**0 **1**So the decimal number 13 is

**00001101**in binary form. To double check: 8+4+1=13

So the IP address of 154.31.16.13 has its binary form equivalent of:

**10011010.00011111.00010000.00001101**

This is just the start of IP addressing and decimal-to-binary conversions. This is only one of the fundamentals covered in the CompTIA Network+ training video. The following course will teach you everything you need to know about the OSI model, different network protocols, network components, disaster recovery, IP addressing, and much more. It will also prepare you for the Network+ certification through detailed examples and 120 practice exam questions. Here is a direct link to this training video.

If you’re looking for more advanced training with IP Addressing and subnetting, you may be interested in Train Signal’s Cisco CCNA Training course. The CCNA exam requires a near-perfect fluency in conversion, IP addressing, and subnetting. You need to make sure you understand the idea behind decimal- to- binary conversion before you continue to learn subnetting. After that, you need to start practicing so the whole process becomes second nature before you take the exam. Chris Bryant covers this and all the other Cisco Routing and Switching topics required for the CCNA certification; all in 15+ hours of video training.

- The first, and probably most important step, is to put down this row of values:

128 64 32 16 8 4 2 1 In order to remember these values start with the number 1, go from right to left, and double that number seven times. For example, start with 1 on the right side. For your next number, double the 1 (1 x 2 = 2). So, 2 is your next number (remembering to go from right to left). For your third number, double the 2 (2 x 2 = 4); to continue the sequence, double the 4 (4 x 2 = 8). Repeat this process until you’ve doubled your original number, seven times. The key to this is that every single one of the values we put in that row are going to have either number 1 or number 0 assigned to it. To convert the IP address we will take that string of numbers and start from left to right this time. For each value we ask this question: “Can I subtract this value from the decimal remaining?” If the answer is “NO” then you put a “0” under the binary value, and if the answer is “YES” then you put “1” there.

- We take the IP address: 154.31.16.13 and start with the first part, which is 154.
- Question: Can I subtract 128 from 154? Answer: YES. So we assign 1 to 128.

**128**64 32 16 8 4 2 1 **1** - Question: Can I subtract 64 from 26? Answer: NO. So we assign 0 to 64.

128 **64**32 16 8 4 2 1 1 **0** - Question: Can I subtract 32 from 26? Answer: NO. So we assign 0 to 32.

128 64 **32**16 8 4 2 1 1 0 **0** - Question: Can I subtract 16 from 26? Answer: YES. So we assign 1 to 16.

128 64 32 **16**8 4 2 1 1 0 0 **1** - That will give us a remainder of 10. (26-16=10). Question: Can I subtract 8 from 10? Answer: YES. So we assign 1 to 8.

128 64 32 16 **8**4 2 1 1 0 0 1 **1** - That will give us a remainder of 2. (10-8=2). Question: Can I subtract 4 from 2? Answer: NO. So we assign 0 to 4.

128 64 32 16 8 **4**2 1 1 0 0 1 1 **0** - Question: can I subtract 2 from 2? Answer: YES. So we assign 1 to 2.

128 64 32 16 8 4 **2**1 1 0 0 1 1 0 **1** - That will give us a remainder of 0. So for the rest of the values in our row, we can assign 0.

128 64 32 16 8 4 2 **1**1 0 0 1 1 0 1 **0**So now we know that a decimal number 154 is

**10011010**converted to binary form. To double check, we take the values assigned with 1 and add them together: 128+16+8+2=154

- Question: Can I subtract 128 from 154? Answer: YES. So we assign 1 to 128.
- Our next number in the IP address is: 31. So we start with a question from step 2 again
- Can I subtract 128 from 31?

**128**64 32 16 8 4 2 1 **0** - Can I subtract 64 from 31?

128 **64**32 16 8 4 2 1 0 **0** - Can I subtract 32 from 31?

128 64 **32**16 8 4 2 1 0 0 **0** - Can I subtract 16 from 31?

128 64 32 **16**8 4 2 1 0 0 0 **1** - Can I subtract 8 from 15 (remember, it’s the remainder)?

128 64 32 16 **8**4 2 1 0 0 0 1 **1** - Can I subtract 4 from 7?

128 64 32 16 8 **4**2 1 0 0 0 1 1 **1** - Can I subtract 2 from 3?

128 64 32 16 8 4 **2**1 0 0 0 1 1 1 **1** - Can I subtract 1 from 1?

128 64 32 16 8 4 2 **1**0 0 0 1 1 1 1 **1**So the decimal number 31 is

**00011111**converted to binary form. To double check: 16+8+4+2+1=31

- Can I subtract 128 from 31?
- Next number is 16. I will perform the conversion in one step now.

128 64 32 **16**8 4 2 1 0 0 0 **1**0 0 0 0 So the decimal number 16 is

**00010000**converted to binary form. - Next number is 13.

128 64 32 16 **8****4**2 **1**0 0 0 0 **1****1**0 **1**So the decimal number 13 is

**00001101**in binary form. To double check: 8+4+1=13

So the IP address of 154.31.16.13 has its binary form equivalent of: