**Math in IP Addresses**

History of Binary Math

Binary math (also known as Binary Arithmetic) has existed for a long time. One of the first times was by Indian Scholar, Pingala in the 5th-2nd centuries BC. Pingala used short and long symblos such as Morse code. The modern day binary math is credited to the German mathematician Gottfried Leibniz in 1679.

What is an IP address?

IP addresses are a string of numbers that are uniquely assigned to all devices connected to the internet. For example, here is a real IP Address from Illinois: 50.158.105.184

IP addresses are normally don't look like this. Since computers read in 0s and 1s IP addresses normally look like this:

11000000 10101000 01100100 01010000

Binary Numbers and the Math Behind it

Computers think in 0s and 1s because they run on electricity.

0= Uncharged 1= Charged

00000010 is converted into the number 2.

In IPs each group separated by a period is called an octet. The octet translates into 8 binary digits which is 8 bit. The computer translates the binary numbers into their decimal equivalents to make them more human-readable.

More Math!

When looking for a device's network address the computer/person takes the AND of IP address and subnet mask.

The AND is like a multiplying.

1 AND any number equals that number.

1 AND 1 = 1 1 AND 0 = 0

0 AND any number equals 0

0 AND 1 = 0 0 AND 0 = 0

Real Life Application

Here is a real world example:

**By Carlos Ortega**

Finding out decimal equivalent of binary numbers:

(n-1)

summation of {m*2}

So a number of 11001001 in binary equals 2^7 + 2^6 + 2^3 + 2^0 =

= 128 + 64 + 8 + 1

= 201

Math in IP addresses

A

B

Computer A wants to send Computer B a file. Computer A must find out whether or not Computer B is in the same network. Computer A finds the AND of its own local

network address and its subnet mask.

Continued

It then finds the AND of the Computer B's remote address and A's local subnet mask. The two numbers found are called the network address. If they match it means that Computer B is in the same network as Computer A. Computer A can then look for the B's destination. If the numbers didn't match the file is sent to B's default gateway.

Octets: Here you can see the IP 192.168.100.80 translated from binary numbers.

Here you can see that each number is an 8-digit number. This number is 8-bit which is why it is called an octet. The IP Address itself is considered a 32-bit number

Convert IP Into Binary Terms

To convert an IP into Binary terms we

must follow some steps. First we write down a series of numbers found on the top row of the following image.

The Ip we are trying to convert is

154.31.16.13, we first go through and ask ourselves if we could subtract the numbers. For example for the first

octet we go through and ask. Can we 154-128? If yes we

write down a 1. If no it's a 0. After doing this for all the

numbers we get.

10011010.00011111.00010000.00001101