DATA REPRESENTATION Lesson Note

Learning Objectives

By the end of the lesson, students should be able to:

Data representation refers to the way data is converted, organized and stored in a form that a computer or digital device can understand and process.

Computers work electronically and use binary digits (bits) to represent information. A bit can have one of two values: 0 and 1

Therefore, text, numbers, pictures, sounds and videos are all converted into patterns of 0s and 1s before computers process or store them.

Example

The decimal number 5 can be represented in binary as:

5₁₀ = 101₂

Digital computers use electronic circuits that have two basic states, such as:

On / Off

High / Low

True / False

These two states can conveniently be represented using:

1 = ON

0 = OFF

This is why the binary number system is fundamental to digital computers.

Bit

A bit is the smallest unit of digital data.

The word bit comes from binary digit.

A bit can contain either:

0 or 1

Byte

A byte consists of 8 bits.

For example:

10110101

The above contains eight binary digits, so it is one byte.

Common Data Units

Unit Equivalent

1 bit 0 or 1

1 byte 8 bits

1 kilobyte (KB) About 1,024 bytes

1 megabyte (MB) About 1,024 KB

1 gigabyte (GB) About 1,024 MB

1 terabyte (TB) About 1,024 GB

These units are commonly used to describe the size of digital data and storage.

A number system is a method of representing numbers using specific symbols and rules.

The major number systems used in computing include:

The binary number system has a base of 2.

It uses only:

0 and 1

Examples:

101₂

1100₂

10001₂

Binary is the fundamental number system used internally by digital computers.

The decimal number system has a base of 10.

It uses the digits:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

This is the number system humans commonly use in everyday life.

Example:

25₁₀

The octal number system has a base of 8.

It uses:

0, 1, 2, 3, 4, 5, 6 and 7

Example:

17₈

Octal can provide a shorter way of writing some binary values.

The hexadecimal number system has a base of 16.

It uses:

0–9 and A–F

The letters represent values as follows:

Hexadecimal Decimal

A 10

B 11

C 12

D 13

E 14

F 15

Examples:

2A₁₆

FF₁₆

10B₁₆

Hexadecimal is commonly used in computing because each hexadecimal digit represents four binary bits.

To convert a decimal number to binary, the number can be repeatedly divided by 2 and the remainders recorded.

Example: Convert 13₁₀ to binary.

Division Quotient Remainder

13 ÷ 2  6  1

6 ÷ 2  3  0

3 ÷ 2  1  1

1 ÷ 2  0  1

Reading the remainders from bottom to top:

13₁₀ = 1101₂

Binary numbers use place values based on powers of 2.

From right to left, the place values are:

128 64 32 16 8 4 2 1

Example: Convert 1011₂ to decimal.

1 × 8 = 8

0 × 4 = 0

1 × 2 = 2

1 × 1 = 1

Therefore:

8 + 0 + 2 + 1 = 11

So:

1011₂ = 11₁₀

Computers need a way to represent letters, numbers, punctuation marks and other characters.

Character encoding systems are used for this purpose.

Two important examples are:

*ASCII

ASCII means American Standard Code for Information Interchange.

It assigns numerical codes to characters such as:

*Letters

*Numbers

*Punctuation marks

*Some control characters

For example, the letter A has an ASCII code of 65 in decimal.

*Unicode

Unicode is a character-encoding standard designed to represent characters from many writing systems around the world.

It supports:

*English characters

*African languages

*Arabic

*Chinese

*Greek

*Cyrillic

*Mathematical symbols

*Emojis and many other characters

Unicode is more extensive than traditional ASCII.

Digital images are represented using pixels.

A pixel is one of the tiny individual elements that make up a digital image.

A picture on a screen is made up of many pixels arranged in rows and columns.

Image Representation

For a simple black-and-white image, pixels can be represented using binary values:

0 = white

1 = black

For colour images, more information is required to represent the colour of each pixel.

Image Quality

The number of pixels in an image affects its resolution.

For example:

1920 × 1080

Means an image has 1,920 pixels across and 1,080 pixels vertically.

Higher resolution generally allows more visual detail, although file size can also increase.

Digital devices commonly represent colours using numerical values.

One widely used method is RGB.

RGB means:

R – Red

G – Green

B – Blue

Different amounts of red, green and blue can be combined to produce many colours.

For example, a colour may be represented using three numerical values:

R = 255

G = 0

B = 0

This represents a strong red colour in the common RGB model.

Sound is naturally an analogue phenomenon, but computers store and process digital representations of sound.

To convert sound into digital data, a process called sampling is used.

Sampling involves measuring the amplitude of a sound wave at regular intervals.

The number of samples taken per second is called the sampling rate and is measured in hertz (Hz).

For example:

44,100 samples per second = 44.1 kHz

Higher sampling rates can capture more information about the original sound, although they may require more storage.

Bit depth refers to the number of bits used to represent each audio sample.

Greater bit depth can allow a wider range of amplitude values.

A digital video is made up of a sequence of still images called frames.

When frames are displayed rapidly one after another, they create the appearance of motion.

Important video characteristics include:

Frame rate is the number of frames displayed per second.

It is measured in frames per second (fps).

For example:

30 fps means 30 frames are displayed each second.

Digital files can sometimes become very large, especially images, audio and video files.

There are two major types:

Lossless compression reduces file size without permanently removing the original information.

When the file is decompressed, the original data can be reconstructed.

Lossy compression reduces file size by permanently removing some information.

It can produce much smaller files, although some quality may be lost.

Digital Representation  Analogue Representation

Uses discrete values Uses continuously varying values

Commonly represented using binary Uses continuous physical signals

Easy to store and process electronically  Can be more affected by noise

Can be copied without changing Repeated copying can introduce

the basic digital values degradation

Used by computers and many modern devices Used by traditional analogue systems

Data representation is important because it:

Data representation occurs in many everyday digital activities.

When typing a message

The characters are converted into digital codes that the computer or phone can store and process.

When taking a photograph

The camera converts the captured image into digital data represented by pixels and colour information.

When recording music: The sound is sampled and converted into digital values.

When watching a video: The device processes digital video frames, colour information and often digital audio.

When storing a document: The characters, formatting and other information are stored as digital data.

SUMMARY

Data representation is the way information is converted into a form that digital devices can process and store.

Computers fundamentally use binary, consisting of 0 and 1. A bit is the smallest unit of digital data, while 8 bits make one byte.

The major number systems used in computing are binary, decimal, octal and hexadecimal. Text can be represented using encoding systems such as ASCII and Unicode. Images are represented using pixels and colour information, while audio is represented through sampling and video through sequences of digital frames.

Data compression can reduce file sizes, using either lossless or lossy methods.