LESSON NOTE
WHY BINARY?
Computers are made up of millions of tiny
circuits. These circuits can either hold a low voltage of 0 volts
or a high voltage of 5 volts. (Values may
vary.) Therefore, the circuits have two possible states – a low
state (zero) and a high state (one). By grouping circuits
together, we get strings of 0s and 1s – binary.
COMPUTERS WITH
DIFFERENT BASES
Some experimental computers use different
bases such as tertiary (base-3) and even decimal (base-10). However,
such computers have been mostly unreliable to date. This is why
all mass-produced computers use binary.
One approach to implement a higher base
number is to allow the computer circuits to store more values than just 0 or
5 volts. For example, a tertiary circuit could store 0 volts, 2.5
volts and 5 volts. However, this is not as simple as it sounds and
has lead to many unreliability issues.
BITS & BYTES
In computers, each value of either 0 or 1 is
called a bit. A byte is a series of eight bits stored together in
memory.
Example: 01110011
FILE
SIZE
A file is
a sequence of bits stored as a single unit.
The size
of a file is the amount of bits or bytes that the file uses up in
memory (RAM, hard drive, flash disk, …).
The
file size depends on the amount of data that is stored in the file.
Example 1:
In
text files, each character is stored as a single byte. Therefore,
a text file with 25 characters takes up 25 bytes.
Example 2:
A
newer BMP image file that is 10 pixels by 10 pixels (100 total pixels) stores
the colour for each pixel in 3 bytes. The file size will be about
300 bytes.
Note:
BMP images have a 54 byte file header. There is also some extra bytes placed in some situations also
having a small effect on file size.
Note:
It is 24-bit BMP images have store colours in 3 bytes of data.
GREEK
PREFIXES
Usually,
the prefix kilo means 1000. However, in computers, its value is
1024. Therefore, a kilobyte is 1024 bytes.
Consider
this table:
|
Prefix
|
Power
|
Computer
Value
|
Usual Value
|
|
Kilo-
|
210
|
1024
|
1000 (one
thousand)
|
|
Mega-
|
220
|
1 048 576
|
1 000 000
(one million)
|
|
Giga-
|
230
|
1 073 741 824
|
1 000 000
000 (one billion)
|
|
Tera-
|
240
|
1 099 511 627 776
|
1 000 000
000 000 (one trillion)
|
Note
that it is common to assume the math value during casual conversations.
Examples
a) Convert 234 kilobytes into bytes.
234
kilobytes x 1024 bytes / kilobytes = 239616 bytes
b) Convert 2 349 203 bytes into
megabytes.
2
349 203 bytes / 1048576 bytes / megabytes = 2.24 megabytes
UNIT
SYMBOLS
|
Unit
|
Symbol
|
|
Bit(s)
|
b
|
|
Byte(s)
|
B
|
|
Kilobits
|
Kb
|
|
Kilobytes
|
KB
|
|
Megabits
|
Mb
|
|
Megabytes
|
MB
|
|
Gigabits
|
Gb
|
|
Gigabytes
|
GB
|
|