PYTHON PROMISING FUTURE: CLASS 11 CS CHAPTER 13

CLASS -11 COMPUTER SCIENCE

CHAPTER- 13 DATA REPRESENTATION

As all know that computer system stores data in binary form thus we add the word DIGITAL with all the work associated to computer.

Humans adopted Decimal Number System in their day to day life. In the same manner, computer system has adopted Binary Number System, Octal Number System and Hexadecimal Number System which are combinely known as Digital Number System.

These Number Systems are - *Decimal System *Binary System *Octal System *Hexadecimal System
Decimal number system :
Decimal system is a system consisting of 10 digits which are as under
0,1,2,3,4,5,6,7,8,9 – Base of this system is 10
This technique is based on positional value where the weightage of a digit is as per its position.
For ex- in number 526, the value of 5 is 100, value of 2 is 10 and value of 6 is 1. (it is as per the method of hundreds , tens and ones).
The left most digit in any number is called MSD (Most Significant Digit ).
The right most digit in any number is called LSD (Least Significant Digit ).

Binary Number System :
Binary system consists of 2 digits 0 & 1 known as bit.
Base of this system is 2 .
In Digital systems, use of decimal system is impossible therefore use of binary system for a computer system is meaningful. Using circuit to maintain two voltage level is very easy.
The left most digit in any number is called MSB (Most Significant Bit ).
The right most digit in any number is called LSB (Least Significant Bit ).

Decimal to Binary :
For this, decimal value is to be divided by 2 and remainder is arranged in reverse order. Quotient is again to be divide by 2 and remainder is to be again kept in reverse order. This process is repeated until we get the quotient zero. Remainder is then kept in reverse order that results in binary of the given number .(remainder should be either 0 or 1 only).

Binary to Decimal :
For this, every bit of binary is multiplied by 2 after applying power as per its position.
The resultant expression is then solved mathematically.

Decimal to Octal :
For this, decimal value is to be divided by 8 and remainder is to be arrange in reverse order.
Quotient is again divided by 8 and remainder is again kept in order. This process is repeated until we get the quotient zero.
Remainder is then kept in reverse order which results in octal of the given number. (remainder should lie between 0 to 7 only.)

Octal to Decimal :
Every digit of octal is multiplied by 8 after applying power as per its position.
The resultant expression is then solved mathematically.

Decimal to Hexadecimal :
For this, decimal value is divided by 16 and remainder is arranged in reverse order.
Quotient is again divided by 16 & remainder is again kept in order.
This process is repeated until quotient becomes zero. Remainder is then kept in reverse order which results in hexadecimal of the given number. (remainder should lie between 0 to 15 only). A is to be written for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.

Hexadecimal to Decimal :
For this, every digit of Hex is multiplied by 16 after applying power as per its position.
The resultant expression is then solved mathematically.
Octal to binary :
For this, first convert the octal to decimal and then the received one to decimal to binary.
Another method is with the help of Octal Table .

Binary to Octal :
For this we have to take numbers in group of 3 from LSB in reverse order then each group is converted to octal.
If sometimes the number does not have even groups of 3 bits in that case we would have to add zeroes at MSB side .

Binary to Hex :
Binary numbers can be easily converted to hexadecimal by grouping in groups of 4 starting at the binary point .

Binary Addition :
Consider following during Binary Addition :
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
Important point to notice here is that 1 goes for carry which is to be added with next place bit.

ASCII Code :
The ability of a computer system to understand signals/letters depends on its character set.
Character set has standards known as character set code like - ISCII, ASCII, UNICODE etc.
ASCII ( American Standard Code for Information Interchange) is a code used in many of the micro, mini & mainframe computers .
ASCII code has two versions - ASCII – 7 and ASCII – 8.
ASCII – 7 code uses 7 bits of storage for one signal or character.
ASCII – 8 code use 8 bits of storage for one signal or character.

ISCII Code :
Indian Standard Code for Information Interchange is developed in country India.
It identifies signals and characters of almost all indian languages.
It identifies ASCII script along with subscripts of various languages of India.
It also works in the 8 bit grouping.

Unicode :
This is Universal Character Set that represents signal /character in a group of 32 bit.
It has capability of including signals and characters from all scripts of all languages of world.
Various encoding system were in use before the development of Unicode, .
Problems of language on internet is resolved by the use of Unicode.

Unicode uses various encoding systems to represent characters. Like -- 1. UTF – 8 (Unicode Transformation Format) a) UTF – 8 – 1 Octet (8 bits) Representation b) UTF – 8 – 2 Octet (16 bits) Representation c) UTF – 8 – 3 Octet (24 bits) Representation d) UTF – 8 – 4 Octet (32 bits) Representation 2. UTF – 32

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