"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 2^{20} bytes,
which is 8 × 2^{20} = 2^{23}
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.
"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
4×10^{2} + 6×10^{1} + 7×10^{0}.
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
1×2^{3} + 1×2^{2} + 0×2^{1} + 1×2^{0}
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 2^{k}-1.
To represent a positive integer N, you need 1 + log_{2}N bits.
In a byte, i.e. eight bits, we can represent numbers up to
2^{8}-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 binary digits, and convert 01101110 into two hex digits.
ASCII Encoding and Text
Encoding is converting data from one system of communication into another. There are other encoding schemes beyond ASCII; for example: base64, Unicode, UTF-8.
Other than numbers, the most fundamental data is plain 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? Basic 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 0110 0001 (spaced for readability). 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
You can actually enter ASCII values into the address bar in
Google Chrome. 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: Mozilla Firefox no longer supports this feature for the server name (cnn.com 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).