"Cyber Space" is a name for this global information system consisting of many familiar pieces — like web sites, distributed video games, email — and many less familiar pieces as well, that work behind the scenes. All of these systems do little more than process, store and retrieve digital data. So to even begin to understand Cyber Space, we need to get a handle on what "digital data" is all about. That's what this lesson will do.

Submarine Radio Communications

Ballistic missile submarines remain undetected beneath the ocean's surface awaiting the order to launch their missiles. The launch order must be sent via radio transmission, but sea water blocks those radio waves typically used with satellites or for long-range radio because of their high frequencies. For submarines, very low frequency (VLF) radio waves must be used (3-30kHz) to penetrate the ocean and reach the submarine's VLF antenna.

Communicating with submarines while completely submerged comes at a cost. VLF radio waves have a severely limited capacity for carrying data. VLF data transmission rates are around 300 bps. Compare that with a data transmission rate of 10 Mbps for a 4G wireless phone. Your smart phone is 33,000 times faster than VLF! In other words, it would take 2 hours and 47 minutes to download one MP3 song using submarine VLF communications, where it would only take 0.3 seconds using your 4G phone.

(Image courtesy of Jim Hawkins)
This is a picture of the VLF antenna array that used to be at Greenbury Point. The three small antennas you see today are all that's left. The rest were pulled down in the late 90's.

Bits and Bytes

Digital data consists solely of 0's and 1's. An individual 0 or 1 value is called a bit. So to represent a piece of information, you need to be able to express that information as a sequence of 0's and 1's. For the remainder of this lesson, we'll explore how this is done for many different kinds of information. First, however, there's a practical issue to take care of. All computational devices group bits into chunks of eight, and that's usually the smallest unit of data they actually operate on. An 8-bit chunk is called a byte. The difference between bit and byte is really important.

A computer is typically capable of storing and processing an immense number of bits and bytes. So we often speak of kilo, mega, giga and tera bytes or bits. What do those mean? Normally kilo means thousand, mega means million, giga means billion, and tera means trillion, and that's approximately true in the context of digital data, but not exactly. In the context of digital data:

... so "megabyte" means 220 bytes, which is 8 × 220 = 223 bits. Finally, you often see these abbreviated as K=kilo, M=mega, G=giga, T=tera and b=bit and B=byte. So, Gb means "gigabit" whereas GB means "gigabyte", which is eight times as many bits. In fact, it's not always easy to know whether the "decimal" or "binary" interpretation of "kilo", "mega" etc. is meant, especially in marketing material.

Binary Numbers

"There are 10 kinds of people: those who know binary, and those who don't."
On the face of it, it's pretty amazing that all information can be somehow expressed as sequences of bits. Actually though, it's all possible because numbers can be expressed as sequences of bits. A number expressed as a sequence of 0's and 1's is called a binary number, and the idea is no different from how we use sequences of decimal digits to represent numbers. Recall how that works: When we write 467 we mean 4×102 + 6×101 + 7×100. Now, in a binary number we only allow bits as digits, and instead of powers of 10, we have powers of 2. So in binary, 1101 means 1×23 + 1×22 + 0×21 + 1×20 which is 13 in decimal. Numbers of any size can be represented by sequences of 0's and 1's, though larger numbers require longer sequences.
In fact, it's easy to compute how many bits you need to represent a number of a specific size. With k bits, you can represent any number from 0 up to and including 2k-1. To represent a positive integer N, you need 1 + log2N bits. In a byte, i.e. eight bits, we can represent numbers up to 28-1 = 256 - 1 = 255.
Because of the importance of bytes, we will concentrate on being able to write numbers as 8-bit sequences, and being able to interpret an 8-bit sequence as a number. The smallest number we can represent in 8-bits is 0, which is the byte 00000000. The largest is 255 which, in binary, is 11111111. Of course, anything in between is possible as well.

Videos showing how to convert from binary to decimal and back


Bytes are all-important in computing, and after a while it becomes cumbersome to write out all eight bits of a byte. So we often write out bytes as two hexadecimal digits. Hexadecimal is actually the base 16 number system, but for our purposes that is irrelevant. The important point is that it gives us a concise representation for bytes, since each hex digit represents a 4-bit pattern. Thus two hex-digits represent an 8-bit pattern, i.e. a byte. The following table gives the mapping between the hex digits (0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f) and 4-bit patterns.
hex digit 0 1 2 3 4 5 6 7 8 9 a b c d e f
4-bit pattern 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Using this table, you should be able to convert 3cf6 into a byte sequence, and convert the byte 01101110 into two hex digits.

ASCII Encoding and Plain Text

Other than numbers, the most fundamental data is text. The method for representing text digitally (i.e. as bits and bytes) depends on the alphabet the text uses, of course. However, in the cyber world, English is the base language and everything else is an add-on. Convenient for us, eh? Plain text is represented using one byte (i.e. one number in the range 0-255, although in reality we only use 0-127) for each character, where the characters allowed and the byte values (i.e. numbers) they correspond to are given by the ASCII Table. So, for example, the letter a has ASCII value 97 which is byte 01100001. ASCII values 32-126 are the printable characters, and any sequence of bytes consisting solely of them is considered to be plain text. We might allow the additional values 9 ← tab, 10 ← newline, 13 ← carriage return, which provide limited formatting.
String to ASCII Demo
input a string and press enter
You can actually enter ASCII values into the address bar in your browser. Although you have to write them in hexadecimal notation rather than decimal or binary. (Hexadecimal is a base 16 (rather than 10 or 2) number system, whose digits are 0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f.) For example, c has ASCII value 99 which is 63 in hex, so a c can be written in the address bar as %63. Thus, entering %63nn.com in your browser's address bar gets you go cnn.com! BTW: Firefox might have this turned off by default, since there are actually security implications with this.

A sequence of characters is called a string, and what we've just seen is that ASCII gives us a way to encode strings as sequences of bits (or, if you prefer, bytes).


A file on a computer is simply a sequence of bytes, nothing more, nothing less. What imbues the file with meaning is how we (or a program) choose to interpret those bytes. This is actually the same with language. The string bow has no intrinsic meaning. It's up to us to decide whether it means something you shoot with, put in a little girl's hair, or whether it means bending over in a polite manner. If each byte of a file corresponds to a printable ASCII character, we could choose to interpret the file as containing text, so such files are called text files. However, many text files have a more specific meaning. What you're reading right now is contained within a plain text file of a special type: an HTML file.
If you right-click in this browser window and select "view source" you can actually see the plain text file that produced this pretty page.
Many files are not plain text, but even though such files don't immediately mean something to us, there's usually some program out there that understands how to interpret those bytes in a meaningful way.

The rules that define how the bytes of a particular file are supposed to be interpreted are called a file format. We described the format of a plain text file in the previous paragraph. You might have heard of .jpg files (JPEG files). JPEG is a file format for images, and any file whose bytes conform to the JPG rules can be viewed as an image with the proper program. So usually to use a file you need to know what kind it is (i.e. what format it follows) and what program(s) to use to operate on that kind of file. Here are some common formats:

One of the most important file types is one you might not have thought of: a program. A program is a regular old file whose bytes can be interpreted by the physical computer as instructions to be executed.

The Role of File Extensions

Filenames typically (by tradition) end in a '.' followed by
Windows by default hides the file extension from you. For this course (and life) you really want to see this information. Follow these instructions to turn off the extension hiding, so you actually know the true names of files.
  1. Under the Windows Start button, click on Computer.
  2. Under the 'Organize' menu, select 'Folder and search options'
  3. Click on the 'View' tab.
  4. Uncheck the box for 'Hide extensions for known file types'
  5. Click 'Apply' at the bottom of the window. Done!
Why is hiding file extensions bad?
Well, aside from making it hard for you to know what a file's real name is, hidden file extensions can be used to trick people. Check out #1 on this list of ways to trick users into executing malicious programs .
three letters — like fact.jpg ends in .jpg. This last part of the filename is called the file extension. The Operating System (Windows) and many programs trust the extension to tell them the file type, and thus choose, for example, what program to use when opening the file. However, this trust is misplaced. The extension does not tell you the file type reliably. Try this:
  1. right-click on this link and choose to save the link to the desktop.
  2. go to Start->Documents->Desktop and find the file CSL.png (which is an image). Right-click on it and change its name to CSL.doc (the .doc extension is for MS Word). Notice how the icon changed. Windows thinks this is a Word file now.
  3. double-click on CSL.doc to open it up. Windows will try to open it with Word. What happens?
The moral of the story here was that extensions can lie! The only real way to know the type of the file is to examine its bytes and see what format it's in. Usually, the first few bytes tell you the type reliably as you saw in the above activity.

Here's a common example of playing games with file extensions. The mail server here at USNA won't let you send a zip file. Any .zip attachment just mysteriously disappears. In fact, the server only looks at the file name, not at the bytes that make up the file. So you can simply rename the file, say changing foo.zip into foo.piz, and then attach it. The file will be sent, no problem, and the recipient merely needs to change the extension back to .zip when he saves it. So: don't believe what file extensions tell you!

How many bytes does it take ...

File headers

Because files have a format, there must be some parts of the format that are the same for all files of the same type. For instance, something has to be common to all pdf files. One common feature across file formats is a header. A header is a short sequence of data at the head, or beginning, of the file data. This can readily be recognized when viewing a file in a hex editor. In general you really need a hex editor, not just a text editor, because for many non-text files the header contains some non-printable characters. For instance, a pdf file always has a header of %PDF, which in hex is 25 50 44 46. Below are some common headers (in hex). Open a few files on your computer and see if you can corroborate this information. Headers are many different lengths, and one particular file type may have multiple valid headers. Remember, it's easy to lie with extensions, but quite hard to lie with headers!

Follow this link to an activity that should help you to understand a) that files really are just a bunch of bits/bytes, b) that changing the bits in a file changes what happens when the file is opened with the appropriate program, and c) that since many file formats have rules about what bytes a file starts with, you can often determine the type of a file by examining the first few bytes. We'll see that this can be important!

"GIFAR" Files

you can play games with file format rules — sometimes for unsavory purposes. One interesting example is the "gifar". Basically, we can create a single file (sequence of bytes) that satisfies the formatting rules both for an image format and for an "archive" format. Specifically, for instance, we can create a single file that is a valid .jpg image file and a valid Java .jar (a file that's intended to be processed by the program "java"). The gist is the first part of the file is the jpg image, and the second part is the Java jar file. This works because a jpg file must have a jpg header as its first several bytes, and must have a jpg footer indicating the end of the image data, but not necessarily the end of the file. There can be more bytes after the jpg footer, but any jpg viewer simply ignores them. Meanwhile, Java processes a jar file starting with the bytes at the back end of the file. These bytes act as a sort of "table of contents" that tells Java how far forward in the file to jump for other pieces of Java-specific data. The table of contents in a gifar never tells Java to look as far forward in the file as the jpg footer or beyond.

You might ask: "what's the point?" Java jar files can instruct the Java program to do seriously bad things to your computer — they can really be evil. Jpg image files, on the other hand, are pretty benign. So websites that allow users to post content will often allow jpg image files to be posted, but definitely not Java jar files. What the bad guys figured out, is that by posting a gifar, they could post files to these websites that the websites thought were innocuous jpg image files (and so would allow to be posted), but which were also malicious Java jar files.