Convert an IP Address from Decimal to Binary Form

Decimal to binary conversion is an important task to understand in IP addressing and Subnetting.

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:

th bit	7th bit	6th bit	5th bit	4th bit	3rd bit	2nd bit	1st bit
128 (27)	64 (26)	32 (25)	16 (24)	8 (23)	4 (22)	2 (21)	1 (20)

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

128

64

32

16

8

4

2

1

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

      128	64	32	16	8	4	2	1
      1

   2. 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

   3. 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

   4. 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

   5. 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

   6. 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

   7. 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

   8. 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  
2. Our next number in the IP address is: 31. So we start with a question from step 2 again
   1. Can I subtract 128 from 31?  
      

      128	64	32	16	8	4	2	1
      0

   2. Can I subtract 64 from 31?  
      

      128	64	32	16	8	4	2	1
      0	0

   3. Can I subtract 32 from 31?  
      

      128	64	32	16	8	4	2	1
      0	0	0

   4. Can I subtract 16 from 31?  
      

      128	64	32	16	8	4	2	1
      0	0	0	1

   5. Can I subtract 8 from 15 (remember, it’s the remainder)?  
      

      128	64	32	16	8	4	2	1
      0	0	0	1	1

   6. Can I subtract 4 from 7?  
      

      128	64	32	16	8	4	2	1
      0	0	0	1	1	1

   7. Can I subtract 2 from 3?  
      

      128	64	32	16	8	4	2	1
      0	0	0	1	1	1	1

   8. 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
3. 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.  
4. 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