Mathematics in the Workplace

Subnet Mask

by

Alison Hays

Suppose we are given that a subnet mask is /28.  How do we convert this to 255.255.255.240?

The number after the "/" represents the number of ones, starting from the left, in the binary representation of the IP address.  (Recall that all IP address have 32 digits.)

Thus, in binary notation, a /28 subnet mask is written as:

1 1 1 1   1 1 1 1   .   1 1 1 1   1 1 1 1   .   1 1 1 1   1 1 1 1   .   1 1 1 1   0 0 0 0

If we convert each octet into decimal notation, we get the following:

255.255.255.240

Another Example

Suppose we are given that a subnet mask is /20.  Then in binary notation, the IP address of the subnet mask is written as:

1 1 1 1   1 1 1 1   .   1 1 1 1   1 1 1 1   .   1 1 1 1   0 0 0 0   .   0 0 0 0   0 0 0 0

Converting each octet into decimal notation, we get the following IP address for the subnet mask:

255.255.240.0