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# Data Representation

Welcome to class!

In today’s class, we will be talking about data representation. Enjoy the class!

### Data Representation

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.

The terms bits, bytes, nibble and word are used widely about 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.

#### Data representation in digital circuits

• Electronic components, such as a 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 the 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.

##### Types of data representation
1. 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.
2. This limitation necessitates the need to develop better ways of handling long streams of binary digits.
3. 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

A number system is a set of symbols used to represent values derived from a common base or radix. As far as computers are concerned, number systems can be classified into two major categories:

• decimal number system
• binary number system
• octal number system
###### Decimal number system
• The term decimal is derived from a Latin prefix deci, which means ten. Decimal number system has ten digits ranging from 0-9. Because this system has ten digits; it is also called a base-ten number system or denary number system.
• A decimal number should always be written with a subscript 10 e.g. X10
• But since this is the most widely used number system in the world, the subscript is usually understood and ignored in written work. However, when many number systems are considered together, the subscript must always be put to differentiate the number systems.

The magnitude of a number can be considered using these parameters.

1. Absolute value
2. Place value or positional value
3. Base value
• The absolute value is the magnitude of a digit in a number. For example, the digit 5 in 7458 has an absolute value of 5 according to its value in the number line.
• The place value of a digit in a number refers to the position of the digit in that number i.e. whether; tens, hundreds, thousands etc.
• The total value of a number is the sum of the place value of each digit making the number.
• The base value of a number also k known as the radix, depends on the type of the number systems that is being used. The value of any number depends on the radix. For example, the number 10010 is not equivalent to 1002.
###### Evaluation
1. A single unit which is composed of a small group of bits is known as (a) bit (b) bug (c) flag (d) byte
2. BCD stands for (a) Binary Coded Decimal (b) Binary Coded Digitals (c) Binary Characters Decimals (d) Binary Conducting Decimals
3. The system in which fractions are written by extending binary rotation is called (a) fixed-point representation (b) floating-point representation (c) binary digits representation (d) single rotation representation
4. ‘megabytes’ of computer storage capacity consists of (a) one million bytes (b) two million bytes (c) three million bytes (d) four million bytes
5. In BCD code, maximum possible characters set size is (a) character set of 64 (b) character set of 84 (c) character set of 94 (d) character set of 104

In our next class, we will be talking more about Data Representation.  We hope you enjoyed the class.

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