Appendix D. Abbreviations | Campus Network Design Fundamentals

To convert from decimal to binary, reverse the above process, taking each octet's decimal value and converting it to binary, as follows:

Step 1.	Referring to the weighting factors in Figure C-2, find the largest weighting factor that is smaller than or equal to the value of the octet. The binary number will have a 1 in the corresponding bit position and will have a 0 in any bit positions to the left of this 1.
Step 2.	Subtract that weighting factor from the decimal octet value.
Step 3.	Repeat this process using the new octet value, until the result is 0.
Step 4.	Set any remaining bit positions in the binary number to 0.

For example, consider the IP address 192.168.19.255. To write this address in binary, follow these steps:

Step 1.

Select an octet to convert. The conversion of the second octet, 168, to binary is shown in Figure C-4.

Figure C-4 describes the following points:

The largest weighting factor that is smaller than or equal to 168 is 128, so the binary number has a 1 in the 2⁷ (128) position.
Subtracting 128 from 168 results in 168 128 = 40.
The largest weighting factor that is smaller than or equal to 40 is 32, so the binary number has a 1 in the 2⁵ (32) position (with a 0 in the intermediary position).
Subtracting 32 from 40 results in 40 32 = 8.
The largest weighting factor that is smaller than or equal to 8 is 8, so the binary number has a 1 in the 2³ (8) position (with a 0 in the intermediary position).
Subtracting 8 from 8 results in 8 8 = 0.
The remaining bit positions in the binary number are set to 0.
Thus, 168 in decimal equals 10101000 in binary.

Step 2.

Repeat this process for the other three octets. The results are as follows:

Note

Again, you can confirm these results using the decimal-to-binary conversion chart in Table C-1.

Therefore, the IP address 192.168.19.255 in binary is as follows:

11000000 10101000 00010011 11111111