Encryption places a message into a code. For a computer, we want to take a string of binary digits and place them into a code. In public key encryption, we have a public key which anyone encrypt a message, and a private key used to decrypt the message. Given the private key, we can generate a public key. We make the public key available to anyone who wants it, but we keep the private key secure. In this way, anyone can encrypt a message to us, but only we can decrypt the message. This allows for e-commerce in that our customers can encrypt their credit card numbers (or other personal information) and only we can decrypt it. For this to work, we need to use some extra math to take the integer number that was the result of encryption and convert it into a number that we can use to decrypt. This example demonstrates how to encrypt a 13-bit binary string using a 13-bit public key, how to convert the resulting number, and how to decrypt it using the 13-bit public key. Notice that the public key's numbers seem to be in a random order while the private key's numbers are strictly in increasing additive order (for any number, it is greater than or equal to the sum of all previous numbers).