For this essay, I wanted to examine the mathematics in a workplace environment. I do not have very much work experience, so I could not rely on my on experiences in the work place. The next logical person to turn to, of course, was my fiancé. I asked Curtis, "Do you use math at work?" I knew the answer would be yes because I have actually had to help him with some of it! He works with computers, and he did not understand base-2 arithmetic until I explained it to him. :-)

Since I knew that Curtis uses base-2 arithmetic at work, I decided to ask him what he uses it for.

In the staging department, which is the department that Curtis manages, a
main topic is IP addressing. IP addresses consist of four decimal numbers
that are separated by a "dot". For example, if you are using a
Windows computer and go to Start --> Run, and then type in *winipcfg*,
you will see the IP address of your computer (if you are connected to the
internet). The IP address of the computer that I am using right now, for
example, is 10.1.0.2.

Each of these four numbers (10, 1, 0, 2) are called **octets**. This
comes from the fact they the computer reads them in binary notation. In
binary notation, this IP address is written as

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

The decimal point divides these numbers into four bytes. Each byte consists of eight binary digits, so they are called octets. The largest octet possible contains all 1's, so it would be 255.

When a network is designed, each device on the network is given an IP
address. Each device is called a **host**, and a group of hosts make up
a **subnet**. A subset of the subnet makes up a **network**, and
devices can only "talk to each other" if they are part of the same
network. Part of Curtis's job is to determine if two hosts can talk to
each other. He is given their IP addresses and the size of the networks,
and he must determine if they are in the same network. Here is an example.

A **full subnet** has the address 255.255.255.255. Suppose the **subnet
mask** for a particular subnet is 255.255.255.240. To determine the size
of the networks, subtract these two numbers

255.255.255.255

255.255.255.240

________________

0.0.0.15

This last octet, 15, gives the size of the network. Thus, the networks have the following ranges for their last octets:

0 | 15 |

16 | 31 |

32 | 47 |

48 | 63 |

64 | 79 |

80 | 95 |

96 | 111 |

112 | 127 |

128 | 143 |

144 | 159 |

160 | 175 |

176 | 191 |

192 | 207 |

208 | 223 |

224 | 239 |

240 | 255 |

Suppose we are given the following IP addresses and asked if the devices with these addresses can talk to each other:

209.215.17.65

209.215.17.66

209.215.17.81

If we look at the above table, we see that one network has a range of 64-79 for its last octet, and another network has a range of 80-95 for its last octet. Therefore, 209.215.17.65 and 209.215.17.66 are on the same network, and 209.215.17.81 is on a different network. The first two devices can talk to each other, but the third one cannot.

1. Curtis does not use binary number system on a *regular
basis*, but he does use it to explain the concept of IP addressing to his
employees. Click here for an introduction to
the binary number system.

2. When Curtis is given a subnet mask, it is not given to him as 255.255.255.240. It is given to him as /28. Click here to find out how he figures out that /28 is 255.255.255.240.