1.1 Demonstrate and apply representation of decimal integers within computer systems.
1. concepts of data representation in digital
computers
• Data and instructions cannot be entered and processed directly into computers using
human language. Any type of data be it numbers, letters, special symbols, sound or
pictures must first be converted into machine-readable form i.e. binary form. Due to
this reason, it is important to understand how a computer together with its peripheral
devices handles data in its electronic circuits, on magnetic media and in optical
devices.
Data representation in digital circuits
• Electronic components, such as microprocessor, are made up of millions of
electronic circuits. The availability of high voltage(on) in these circuits is interpreted
as ‘1’ while a low voltage (off) is interpreted as ‘0’.This concept can be compared to
switching on and off an electric circuit. When the switch is closed the high voltage in
the circuit causes the bulb to light (‘1’ state).on the other hand when the switch is
open, the bulb goes off (‘0’ state). This forms a basis for describing data
representation in digital computers using the binary number system.
Data representation on magnetic media
• The laser beam reflected from the land is interpreted, as 1.The laser entering the pot
is not reflected. This is interpreted as 0.The reflected pattern of light from the
rotating disk falls on a receiving photoelectric detector that transforms the patterns
into digital form.The presence of a magnetic field in one direction on magnetic
media is interpreted as 1; while the field in the opposite direction is interpreted as
“0”.Magnetic technology is mostly used on storage devices that are coated with
special magnetic materials such as iron oxide. Data is written on the media by
arranging the magnetic dipoles of some iron oxide particles to face in the same
direction and some others in the opposite direction
Data representation on optical media
In optical devices, the presence of light is interpreted as ‘1’ while its absence is interpreted
as ‘0’.Optical devices use this technology to read or store data. Take example of a CD-
ROM, if the shiny surface is placed under a powerful microscope, the surface is observed to
have very tiny holes called pits. The areas that do not have pits are called land.
Reason for use of binary system in
computers
, • It has proved difficult to develop devices that can understand natural language
directly due to the complexity of natural languages. However, it is easier to construct
electric circuits based on the binary or ON and OFF logic. All forms of data can be
represented in binary system format. Other reasons for the use of binary are that
digital devices are more reliable, small and use less energy as compared to analog
devices.
Bits, bytes, nibble and word
• The terms bits, bytes, nibble and word are used widely in reference to computer
memory and data size.
• Bits: can be defined as either a binary, which can be 0, or 1.It is the basic unit of data
or information in digital computers.
• Byte: a group of bits (8 bits) used to represent a character. A byte is considered as
the basic unit of measuring memory size in computer.
• A nibble: is half a byte, which is usually a grouping of 4 bytes.
• Word: two or more bits make a word. The term word length is used as the measure
of the number of bits in each word. For example, a word can have a length of 16 bits,
32 bits, 64 bits etc.
Types of data representation
• Computers not only process numbers, letters and special symbols but also complex
types of data such as sound and pictures. However, these complex types of data take
a lot of memory and processor time when coded in binary form.
• This limitation necessitates the need to develop better ways of handling long streams
of binary digits.
• Higher number systems are used in computing to reduce these streams of binary
digits into manageable form. This helps to improve the processing speed and
optimize memory usage.
Number systems and their representation
o A number system is a set of symbols used to represent values derived from a
common base or radix.
o As far as computers are concerned, number systems can be classified into two major
categories:
o decimal number system
o binary number system
o octal number system
o hexadecimal number system
Decimal number system
1. concepts of data representation in digital
computers
• Data and instructions cannot be entered and processed directly into computers using
human language. Any type of data be it numbers, letters, special symbols, sound or
pictures must first be converted into machine-readable form i.e. binary form. Due to
this reason, it is important to understand how a computer together with its peripheral
devices handles data in its electronic circuits, on magnetic media and in optical
devices.
Data representation in digital circuits
• Electronic components, such as microprocessor, are made up of millions of
electronic circuits. The availability of high voltage(on) in these circuits is interpreted
as ‘1’ while a low voltage (off) is interpreted as ‘0’.This concept can be compared to
switching on and off an electric circuit. When the switch is closed the high voltage in
the circuit causes the bulb to light (‘1’ state).on the other hand when the switch is
open, the bulb goes off (‘0’ state). This forms a basis for describing data
representation in digital computers using the binary number system.
Data representation on magnetic media
• The laser beam reflected from the land is interpreted, as 1.The laser entering the pot
is not reflected. This is interpreted as 0.The reflected pattern of light from the
rotating disk falls on a receiving photoelectric detector that transforms the patterns
into digital form.The presence of a magnetic field in one direction on magnetic
media is interpreted as 1; while the field in the opposite direction is interpreted as
“0”.Magnetic technology is mostly used on storage devices that are coated with
special magnetic materials such as iron oxide. Data is written on the media by
arranging the magnetic dipoles of some iron oxide particles to face in the same
direction and some others in the opposite direction
Data representation on optical media
In optical devices, the presence of light is interpreted as ‘1’ while its absence is interpreted
as ‘0’.Optical devices use this technology to read or store data. Take example of a CD-
ROM, if the shiny surface is placed under a powerful microscope, the surface is observed to
have very tiny holes called pits. The areas that do not have pits are called land.
Reason for use of binary system in
computers
, • It has proved difficult to develop devices that can understand natural language
directly due to the complexity of natural languages. However, it is easier to construct
electric circuits based on the binary or ON and OFF logic. All forms of data can be
represented in binary system format. Other reasons for the use of binary are that
digital devices are more reliable, small and use less energy as compared to analog
devices.
Bits, bytes, nibble and word
• The terms bits, bytes, nibble and word are used widely in reference to computer
memory and data size.
• Bits: can be defined as either a binary, which can be 0, or 1.It is the basic unit of data
or information in digital computers.
• Byte: a group of bits (8 bits) used to represent a character. A byte is considered as
the basic unit of measuring memory size in computer.
• A nibble: is half a byte, which is usually a grouping of 4 bytes.
• Word: two or more bits make a word. The term word length is used as the measure
of the number of bits in each word. For example, a word can have a length of 16 bits,
32 bits, 64 bits etc.
Types of data representation
• Computers not only process numbers, letters and special symbols but also complex
types of data such as sound and pictures. However, these complex types of data take
a lot of memory and processor time when coded in binary form.
• This limitation necessitates the need to develop better ways of handling long streams
of binary digits.
• Higher number systems are used in computing to reduce these streams of binary
digits into manageable form. This helps to improve the processing speed and
optimize memory usage.
Number systems and their representation
o A number system is a set of symbols used to represent values derived from a
common base or radix.
o As far as computers are concerned, number systems can be classified into two major
categories:
o decimal number system
o binary number system
o octal number system
o hexadecimal number system
Decimal number system
