GCSE Lesson - Data Representation in Computers

1. DATA REPRESENTATION IN
COMPUTERS

2. Units
 8 bits = 1 byte
 1024 bytes = 1 kilobyte
 1024 kilobytes = 1 megabyte
 1024 megabytes = 1 gigabyte
 1024 gigabytes = 1 terabyte
Four bits, half a byte, is called a nibble

3. Denary to Binary conversion

4. Denary to Binary conversion
11100
1
Start from the bottom and get the reminders
00000011 is binary for 3 but so is 11. You
do not need the leading zeros for it to be a
valid number but we tend to write groups of
8 bits because computers usually store
data in bytes.

5. Addition and Subtraction in
binary
10010+101
10101100 + 00010001
00101101+ 10000101
00101101+ 10000111
What is the biggest decimal number you
can store using:
• 4 bits?
• 2 bytes?

6. Addition and Subtraction in
binary
11111100 + 00001111
If you cannot represent the number in that
amount of space because it is too big, then we
get overflow.
8 bits is 255

7. Addition and Subtraction in
binary
11111100 + 00001111
If you cannot represent the number in that
amount of space because it is too big, then we
get overflow.
8 bits is 255

8. Hexadecimal (hex)
8 bits is 255

9. Hexadecimal (hex)
8 bits is 255
1011100
Separate them by 4 units:
0101 1100
5 12
5C in hex

10. Hexadecimal (hex)
8 bits is 255
182
182/16=11 remainder 6
11=B in hexa
182 in denary=B6 in hex

11. Characters
 PCs mainly uses ASCII, American
Standard Code for Information
Interchange
 ASCII uses 7bits
 From 0000000 to 1111111
 Can represent up to 128 characters
 Unicode: or 32 bits per character
so can code or 4,294,967,296
 EBCDIC(pronounced eb-sid-ic):
Extended Binary Coded Decimal
Interchange Code,
 8-bit encoding.
 256 different characters in its character set.

12. Images
 Computer to interpret an image and
rebuild the picture it must know
some other things about the data
file.
 Picture’s resolution is 8x11 pixels and
the colour depth is 2 bits per pixel.
 Data about the data file itself is called
metadata.
 The number of bits per pixel is
referred to as the colour depth.

13. Images
 To store an image on a computer
the image is broken down into very
small elements called .

14. Sound
 Sound waves are analogue,
which means continuously
changing.
 In order to store sound waves
in the computer these signals
have to be converted in to
numerical values(binaries).
 This is achieve with
Analogue-to-Digital Converter
(ADC).
For sound waves, the analogue
signal is converted as follows:
• Measure the amplitude (height of
wave) at regular intervals
(sampling)
• Store the values as a series of
binary numbers in a file

15. Quality of Sound
 Sample Resolution
 The number of bits used to store each
sample.
 The more bits that are used, the better the
accuracy of the sound file.
 Sample Interval
 The time period between taking
samples/measurements.
 The more frequently the sound is sampled,
the better the quality of playback.
Synthesis:
Sound synthesis is when the sound is recreated
from this file by the computer, and played
through speakers.

16. Instructions
 Each type of processor has its own
type of machine code – a specific
set of instructions that it can
execute. This is called an
instruction set.
The group of bits that represents the operation is
called the opcode
If the programming language allowed us to specify how many steps to move
RIGHT 90 (Turn 90° to the right)
MOVE 2

17. Instructions
If the programming language allowed us to specify how many steps to
move
RIGHT 90 (Turn 90° to the right)
MOVE 2
In the program, number steps to move can be stored in a variable.
Move numSteps
An opcode, which is the binary number representing the operation to be carried
out.
e.g. RIGHT, MOVE
The operand (data) that the operation will use.
The data can be an actual value (e.g. 5) or an address in memory where the data
can be found (a variable).