Encoding Scheme Class 11 Notes consist of ASCII, ISCII, UNICODE, Number System, Conversion between Number System. This Encoding scheme and number system class 11 notes is very handy for the students who are looking for class 11 computer science notes and solutions.

Contents

**Encoding Schemes**

**What is Encoding?**

Process of converting data from one form to another form is called encoding. In Computer Science encoding is converting data (numbers, alphabets, symbols, spaces, graphics etc.) into binary codes.

**Why Encoding?**

- Platform Independency
- Internationalization
- Security
- Effective Communication

There are various standard encoding schemes each part of data is assigned a unique code. Some of the popular encoding schemes are mentioned below:

**ASCII (American Standard Code for Information Interchange)**

- Formally began in 1960 and later promoted by ANSI
- Standard common way to encode and represent keys of keyboard understood by every computer.
- It Uses 7-bits to represent any character.
- It represents (encodes) total 2
^{7}= 128 characters. (Because of 7-bit representation) - It can represent (encode) character set of English language only.

**ASCII Table**

Character | Decimal Value | Character | Decimal Value | Character | Decimal value |

Space | 32 | @ | 64 | , | 96 |

! | 33 | A | 65 | a | 97 |

“ | 34 | B | 66 | b | 98 |

# | 35 | C | 67 | c | 99 |

$ | 36 | D | 68 | d | 100 |

% | 37 | E | 69 | e | 101 |

& | 38 | F | 70 | f | 102 |

‘ | 39 | G | 71 | g | 103 |

( | 40 | H | 72 | h | 104 |

) | 41 | I | 73 | i | 105 |

**ISCII (Indian Standard Code for Information Interchange)**

- Introduced by Bureau of Indian Standard (BIS) in 1991.
- Standard encoding scheme to represent Indian Scripts.
- It uses 8-bits to represent characters.
- It represents total 2
^{8}= 256 characters. - It supports 10 different Indian languages which are: Devanagari, Punjabi, Bengali, Gujarati, Oriya, Telugu, Assamese, Kannada, Malayalam, Tamil and Roman.

**UNICODE**

- It has been developed to represent all the characters of every written language of world.
- It can represent near about 1,000,000 characters
- It may be 8-bit, 16-bit or 32-bit
- It is superset of ASCII
- UTF-8, UTF-16 and UTF-32 are some common Unicode encodings among which UTF-8 is most commonly used.

**Number System**

- Number system is mathematical way to represent numbers using literals such as digits, characters or symbols.
- It is also known as Positional Number System because value of each literal (digit, character or symbol) in a number depends upon its position within number.
- There are different number system and all have their own set of unique literals.
- The count of literals of number system is called Base or Radix.
- The value of each literal in a number is calculated using-
- The literal itself

- Position of the literal

- Base of the number system

- There are four number systems used in the context computer-
- Decimal Number System

- Binary Number System

- Octal Number System

- Hexadecimal Number System

**Decimal Number System**

- It is used by humans
- It uses 10 different digits from 0 to 9 to represent numbers.
- Decimal number system has base 10
- Each place to the left is ten times greater than the place to its right which means each place represent a specific power of the base (10).

Following figure represents the Integer and fractional part of decimal number 1253.76 alongwith calculation of the decimal number using positional values-

**Binary Number System**

- It is used by Computer and other Digital devices.
- It uses two different digits 0 and 1 called as bit to represent any information
- Binary number system has base 2
- Each place in a binary code represents a specific power of the base (2).
- Binary Number System is also referred as Machine Language.

**Application of Binary Number System**

- Used as Machine Language for Computer Hardware and other Electronic Devices.
- Used in ASCII Code and Unicode
- Used in Internet Protocols.
- Used in Image processing, High-end audio recordings, HD Videos recordings and data processing and storage.
- Used in Boolean algebra that is a branch of Mathematics.

**Octal Number System**

- It is used to represent large and complex binary codes into concise manner.
- It uses 8 different digits from 0 to 7 to represent information.
- Octal Number System has base 8.
- Each place in Octal code represents a specific power of the base (8).

**Applications of Octal Number System**

- It is used in register and flip flop of Computer Motherboards.
- It is used in Mainframe such as UNIVAC, PDP etc.

**Hexadecimal Number System**

- It is used to represent large and complex binary codes into concise manner.
- It uses 16 different literals which are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F to represent information.
- Hexadecimal Number System has base 16.
- Each place in a Hexadecimal code represents a specific power of the base (16).

**Applications of Hexadecimal Number System**

- It is used to represent Memory Address for storage devices used in computers.
- It is used to describe colors in the Web Pages.
- It is used to represent Media Access Control (MAC) addresses.
- It is used to display error messages.

**Conversion Between Number System**

**Decimal to Binary Conversion**

Following are the steps to convert Decimal Number System to Binary Number System:

- Divide the number by the base value of the Binary Number System i.e. 2 you want to convert it from
- Note the remainder
- Keep dividing the quotient by the base value 2 untill it becomes zero and note the remainder of each division
- Write all noted remainders in reverse order (bottom to top)

**Example 1: Convert (45) _{10} to Binary Number.**

**Example 2: Convert (234) _{10} to Binary Number**

**Decimal to Octal Conversion**

Following are the steps to convert Decimal Number System to Octal Number System:

- Divide the number by the base value of the Octal Number System i.e. 8 you want to convert it from
- Note the remainder
- Keep dividing the quotient by the base value 8 until it becomes zero and note the remainder of each division
- Write all noted remainders in reverse order (bottom to top)

**Example 1: Convert (186) _{10} to Octal Number.**

**Example 2: Convert (1683) _{10} to Octal Number.**

**Decimal to Hexadecimal Conversion**

Following are the steps to convert Decimal Number System to Hexadecimal Number System:

- Divide the number by the base value of the Hexadecimal Number System i.e. 16 you want to convert it from
- Note the remainder
- Keep dividing the quotient by the base value 16 untill it becomes zero and note the remainder of each division
- Write all noted remainders in reverse order (bottom to top)

**Example 1: Convert (763) _{10} to Hexadecimal Number.**

**Example 2: Convert (2940) _{10} to Hexadecimal Number.**

**Binary to decimal Conversion**

Following are the steps for converting Binary to Decimal number:

- Write down binary number
- Starting from right to left, Write position number of each bit of given binary code
- Find positional value of each bit by raising its position number as power to the base 2
- Multiply each bit with its positional value and find its corresponding decimal number
- Add all these decimal numbers to find equivalent Decimal number of given Binary Number.

**Example 1: Convert (10011) _{2} to Decimal Number**

**Example 2: Convert (111100) _{2} to Decimal Number**

1 x 2^{5} + 1 x 2^{4} + 1 x 2^{3} + 1 x 2^{2} + 0 x 2^{1} + 0 x 2^{0 }

= 32 + 16 + 8 + 4 + 0 + 0

= (61)_{10}

**Octal to decimal Conversion**

Following are the steps for converting octal to decimal number:

- Write down octal number
- Starting from right to left, Write position number of each digit of given octal code
- Find positional value of each bit by raising its position number as power to the base 8
- Multiply each bit with its positional value and find its corresponding decimal number
- Add all these decimal numbers to find equivalent Decimal number of given Octal Number.

**Example 1: Convert (336) _{8} to Decimal Number**

**Example 2: Convert (1325) _{8} to Decimal Number**

1 x 8^{3} + 3 x 8^{2} + 2 x 8^{1} + 5 x 8^{0}

= 512 + 192 + 16 + 5

= (725)_{10}

**Hexadecimal to decimal Conversion**

Following are the steps for converting Hexadecimal to Decimal number:

- Write down Hexadecimal number
- Starting from right to left, Write position number of each symbol (digit or character) of given hexadecimal code
- Find positional value of each symbol (digit or character) by raising its position number as power to the base 16
- Multiply each bit with its positional value and find its corresponding decimal number
- Add all these decimal numbers to find equivalent Decimal number of given Hexadecimal Number.

**Example 1: Convert (7AC) _{16} to Decimal Number**

**Example 2: Convert (1BF6) _{16} to Decimal Number**

1 x 16^{3} + 11 x 16^{2} + 15 x 16^{1} + 6 x 8^{0}

= 4096 + 2816 + 240 + 6

= (7158)_{10}

**Binary to Octal Conversion**

- Write Binary Number
- From right to left, group all the bits of binary in the set of three
- Add 0 to the left of the last bit of given binary number incase set of 3 bit is not formed
- Write octal no for each corresponding set of 3 bits
- Group these octal digits together to form equivalent octal number

**Example 1: Convert (100110101) _{2} in Octal Number**

**Example 2: Convert (1011) _{2} in Octal Number**

1 0 1 1

001 011

1 3

=(13)_{8}

**Octal to Binary Conversion**

- Write octal number
- Replace each digit of octal number with its equivalent set of 3-bit
- From left to write Arrange and write all 3-bit sets together and form binary equivalent of given given octal number.

**Example 1: convert (745) _{8} into binary number**

**Binary to Hexadecimal Conversion**

- Write Binary Number
- From right to left, group all the bits of binary in the set of four
- Add 0 to the left of the last bit of given binary number incase set of 4 bit is not formed
- Write hexdecimal no for each corresponding set of 4 bits
- Group these hexadecimal digits together to form equivalent octal number

Example 1: Convert (1100110101)_{2} in hexadecimal Number

**Example 2: Convert (11101001101)2 in Hexadecimal no**

1 1 1 0 1 0 0 1 1 0 1

0111 0100 1101

7 4 D

= (74D)_{16}

**Hexadecimal to binary conversion**

- Write hexadecimal number
- Replace each digit of hexadecimal number with its equivalent set of 4-bit
- From left to write Arrange and write all 4-bit sets together and form binary equivalent of given hexadecimal number.

**Example 1: convert (CA12) _{16} into binary number**

**Conversion of Decimal Number with fractional part to Binary number**

Following are the steps to convert the fractional part of a decimal number to binary number system:

- multiply the fractional part by the base value 2 repeatedly till the fractional part becomes 0.
- from top to bottom, Write integer part of the number to get equivlent binary number.
- If the fractional part does not become 0 in successive multiplication, then stop after 10 multiplications. In some cases, fractional part may start repeating, then stop further calculation.

**Example 1: convert (0.625) _{10} to binary number.**

**Example 2: convert (.36) _{10} to binary number**

**Conversion of Decimal Number with fractional part to Octal number**

Following are the steps to convert the fractional part of a decimal number to Octal number system:

- multiply the fractional part by the base value 8 repeatedly till the fractional part becomes 0.
- from top to bottom, Write integer part of the number to get equivlent Octal number.
- If the fractional part does not become 0 in successive multiplication, then stop after 10 multiplications. In some cases, fractional part may start repeating, then stop further calculation.

**Example 1: convert (0.175) _{10} to Octal number.**

**Example 2: convert (0.345) _{10} to octal number**

**Conversion of Decimal Number with fractional part to Hexadecimal number**

Following are the steps to convert the fractional part of a decimal number to Hexadecimal number system:

- multiply the fractional part by the base value 16 repeatedly till the fractional part becomes 0.
- from top to bottom, Write integer part of the number to get equivlent Hexadecimal number.
- If the fractional part does not become 0 in successive multiplication, then stop after 10 multiplications. In some cases, fractional part may start repeating, then stop further calculation.

**Example 1: convert (0.175) _{10} to Hexadecimal number.**

**Example 2: convert (0.220) _{10} to Hexadecimal number**

**Binary with fractional part to decimal Conversion**

Following are the steps for converting Binary with Fractional part to Decimal number:

- Write down binary number
- Find positional value of each bit by raising its position number as power to the base 2
- Multiply each bit with its positional value and find its corresponding decimal number
- Add all these decimal numbers to find equivalent Decimal number of given Binary Number.

**Example 1: Convert (10011.11) _{2} to Decimal Number**

**Example 2: Convert (101.01) _{2} to Decimal Number**

1×2^{2 } + 0x2^{1} + 1×2^{0} ^{ }. 0x2^{-1} + 1×2^{-2 }

= 4 + 0 + 1 . 0 + 0.25

= (5.25)_{10}

**Binary with fractional part to Octal Conversion**

- Write Binary Number
- Group all the bits of binary in the set of three
- Add 0 to the left of the last bit of integer part and to the right of the last bit if the fractional part of given primary number, incase set of 3 bit is not formed
- Write octal no for each corresponding set of 3 bits
- Group these octal digits together to form equivalent octal number

**Example 1: Convert (10101.01101) _{2} in Octal Number**

**Example 2: Convert (1011.10) _{2} in Octal Number**

1 0 1 1 . 1 0

011 011 . 100

3 3 . 4

=(33.4)_{8}

**Binary with fractional part to Hexadecimal Conversion**

- Write Binary Number
- Group all the bits of binary in the set of four
- Add 0 to the left of the last bit of integer part and to the right of the last bit if the fractional part of given binary number, incase set of 4 bit is not formed
- Write hexadecimal no for each corresponding set of 4 bits
- Group these hexadecimal digits together to form equivalent hexadecimal number

**Example 1: Convert (110101.011011) _{2} in Octal Number**

**Example 2: Convert (1011111011.1011010) _{2} in Octal Number**

1 0 1 1 1 1 1 0 1 1 . 1 0 1 1 0 1 0

0010 1111 1011 . 1011 0100

2 F B . B 4

=(2FB.B4)_{16}

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