How does the Computer Store Information in Bits
integer format for representing a limited non-negative integers: By using
powers of 2 instead of 10 to encode integers, the computer uses a binary number
system to encode an integer in bits of 0ís and 1ís (instead of 10 different
digits in the decimal system).
- Exercise 1: Convert each of
the following five binary numbers (each as an 8-bit binary string, 40 bits
all together) into the corresponding decimal numbers: 01000010, 01101001,
01101111, 01101100, and 01100001. (See how to convert between binary and decimal numbers.)
- Exercise 2: Consider 106 and
233 as two decimal numbers. Explain in your report what the corresponding
8-bit binary numbers are. (See how to convert
between binary and decimal numbers.)
- Note: For representing numbers
in general, (i) the signed integer
format can represents both positive and negative integers in a limited
range and (ii) the single-precision
and double-precision floating point formats can represent real numbers
big and small in a much larger but still limited ranges. You can take CSCI
220 Computer Organization to know a lot more details.
code for western characters and symbols: Character are encoded in 8 bits
(i.e. 1 byte) as numbers using the ASCII character set encoding
that maps a character into a number in the range of 0 to 255. The size of a
pure text file (.txt file) in bytes is close to the number of characters in the
file since each character in a plain text file is encoded in 1 byte of memory.
- Exercise 3: Suppose the 5
bytes (i.e. 5 groups of 8 bits each) of information in Step 1 above (i.e
01000010, 01101001, 01101111, 01101100, and 01100001) are stored as a part
of a text file to encode the information of 5 characters (8 bits for each
character) using the ASCII
character set encoding. Explain in your report what the five
- Exercise 4: Use NotePad (or
other simple text editor) to create 4 text files (files with .txt
extension on Windows platform), each of about 100 characters, 200
characters, 400 characters, and 800 characters respectively and save them
as text files. Record and report the sizes of these files (in terms of
bytes). Note that it takes one byte to record a character. Explain in your
report the relationship between the number of characters and the file
sizes you see.
- Note: For characters
and symbols †over the world in
general, Unicode can
represent a much wider range of possible characters and symbols.
format for representing images: The size of a picture in the 24-bit BMP
file format in bytes is about 3 times the number of pixels since the color of
each pixel is encoded in terms of 24 bits, i.e. 3 bytes. With 8 bits each for representing
the intensity of each of the RGB components of the color.
(i) Press the print screen key on
the keyboard to capture the screen as a picture. Open up Microsoft Paint,
paste the image into the canvass, and save it as a 24-bit bitmap
file ( .BMP file). Check the file size and record it in your report.
(ii) On Windows 7 right click on your windows desktop
==> Personalize ==> Screen Resolution (If
it is on Windows XP, instead right click on your windows
desktop ==> property ==> settings) to
get the information regarding the resolution of your screen. What is
your screen resolution X x Y? Record it in your report. For example,
the resolution is 1400 x 1024 for the instructorís computer in Lib 141.
(iii) Note that if you have a screen resolution of X by Y you have
X*Y pixels on the screen in total, the BMP file uses 24 bits (i.e. 3
bytes) to record the color of each pixel, and it will take X*Y*3 bytes in
the BMP file to store the information of your screenshot. Also note
that 1 MB means 1 million bytes. Record in
your progress report whether X*Y*3 is close to the actual BMP file size.
- Note: There are many other formats for representing
images, such as JPG,
GIF, PNG, and so forth.
Common units of storage
KB: ††† About 1 thousand bytes††††††††††††††††††††† (210=1024
MB:†††† About 1 million bytes†††††††††††††††††††††††† (220=1,048,576
GB: ††† About 1 billion bytes††††††††††††††††††††††††† (230=1,073,741,824 bytes)
TB: †††† About 1 tera bytes††††††††††††††††††††††††††††† (240 bytes)