Let's see if I can completely strike-out, with a third unanswered post:

I would like to know how to store binary data in the app.config file for a C# application.

These are basically text strings, but they do include one or two "binary" characters, such as decimal 12.

I need these strings in my application, but would like to store them in the app.config file and get them with ConfigurationSettings.AppSettings.Get().

Are you wanting to store it as

<somesetting>12</somesetting>
or
<somesetting>1100</somesetting>
?
What I'm asking is, by binary data, are you wanting to write is as binary, or just write it, or write it using something like a binarywriter? If I figure that out, I bet I could help you ;)