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Class 11 Computer and Communicatio Notes Chapter 2 (Chapter 2) – CCT Part-I Book

Philoid

Philoid

— 6 min read

CCT Part-I
Alright class, let's get straight into Chapter 2: Encoding Schemes and Number Systems. This is a fundamental chapter, not just for your Class 11 understanding, but also because questions frequently appear from this section in various government exams involving computer awareness. Pay close attention!

Chapter 2: Encoding Schemes and Number System - Detailed Notes

1. Introduction: Why Encoding and Number Systems?

  • Computers, at their core, are electronic machines that understand only two states: ON (represented by 1) and OFF (represented by 0). This is the basis of the Binary System.
  • Humans, however, interact using various data types: numbers (like 1, 99, 3.14), text (like 'A', 'hello', '#'), images, audio, video, etc.
  • To enable computers to process human-understandable data, we need a way to convert this data into the binary format (0s and 1s). This conversion process uses Encoding Schemes and Number Systems.

2. Number Systems

A number system is a way of representing numbers using a set of digits or symbols. The base or radix of a number system defines the total number of unique digits available in that system.

  • a) Decimal Number System:

    • Base: 10
    • Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
    • Description: The system we use in everyday life. Each position represents a power of 10.
    • Example: (253)₁₀ = 2 * 10² + 5 * 10¹ + 3 * 10⁰ = 200 + 50 + 3 = 253

  • b) Binary Number System:

    • Base: 2
    • Digits: 0, 1
    • Description: The system computers use internally. Each position represents a power of 2. A single binary digit (0 or 1) is called a Bit (Binary Digit). A group of 8 bits is called a Byte.
    • Example: (1101)₂ = 1 * 2³ + 1 * 2² + 0 * 2¹ + 1 * 2⁰ = 8 + 4 + 0 + 1 = (13)₁₀

  • c) Octal Number System:

    • Base: 8
    • Digits: 0, 1, 2, 3, 4, 5, 6, 7
    • Description: Used sometimes as a shorthand representation for binary numbers (since 8 = 2³). Each position represents a power of 8.
    • Example: (273)₈ = 2 * 8² + 7 * 8¹ + 3 * 8⁰ = 2 * 64 + 7 * 8 + 3 * 1 = 128 + 56 + 3 = (187)₁₀

  • d) Hexadecimal Number System:

    • Base: 16
    • Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (10), B (11), C (12), D (13), E (14), F (15)
    • Description: Widely used in programming and computing (e.g., memory addresses, color codes like #FF0000). It's a convenient shorthand for binary (since 16 = 2⁴). Each position represents a power of 16.
    • Example: (1A3)₁₆ = 1 * 16² + A * 16¹ + 3 * 16⁰ = 1 * 256 + 10 * 16 + 3 * 1 = 256 + 160 + 3 = (419)₁₀

3. Number System Conversions (Crucial for Exams!)

  • a) Decimal to Any Base (Binary, Octal, Hexadecimal):

    • Method: Repeatedly divide the decimal number by the target base. Record the remainders in reverse order.
    • Example (Decimal 25 to Binary):
      • 25 / 2 = 12 Remainder 1
      • 12 / 2 = 6 Remainder 0
      • 6 / 2 = 3 Remainder 0
      • 3 / 2 = 1 Remainder 1
      • 1 / 2 = 0 Remainder 1
      • Result (Read remainders bottom-up): (11001)₂
    • Example (Decimal 187 to Octal):
      • 187 / 8 = 23 Remainder 3
      • 23 / 8 = 2 Remainder 7
      • 2 / 8 = 0 Remainder 2
      • Result: (273)₈
    • Example (Decimal 419 to Hexadecimal):
      • 419 / 16 = 26 Remainder 3
      • 26 / 16 = 1 Remainder 10 (A)
      • 1 / 16 = 0 Remainder 1
      • Result: (1A3)₁₆

  • b) Any Base (Binary, Octal, Hexadecimal) to Decimal:

    • Method: Multiply each digit by its positional value (base raised to the power of the position, starting from 0 on the right) and sum the results.
    • Example (Binary 11001 to Decimal):
      • 12⁴ + 12³ + 02² + 02¹ + 1*2⁰ = 16 + 8 + 0 + 0 + 1 = (25)₁₀
    • Example (Octal 273 to Decimal):
      • 28² + 78¹ + 38⁰ = 264 + 78 + 31 = 128 + 56 + 3 = (187)₁₀
    • Example (Hexadecimal 1A3 to Decimal):
      • 116² + 1016¹ + 316⁰ = 1256 + 1016 + 31 = 256 + 160 + 3 = (419)₁₀

  • c) Binary to Octal:

    • Method: Group binary digits into sets of three, starting from the right. Convert each group into its octal equivalent. Add leading zeros if needed to complete a group.
    • Example: (11010110)₂
      • Group: (011)(010)(110) (Added a leading 0)
      • Convert: 3 2 6
      • Result: (326)₈

  • d) Octal to Binary:

    • Method: Convert each octal digit into its 3-bit binary equivalent.
    • Example: (326)₈
      • Convert: 3 -> 011, 2 -> 010, 6 -> 110
      • Combine: 011010110
      • Result: (11010110)₂ (Leading zero can be omitted unless significant)

  • e) Binary to Hexadecimal:

    • Method: Group binary digits into sets of four, starting from the right. Convert each group into its hexadecimal equivalent. Add leading zeros if needed.
    • Example: (11010110)₂
      • Group: (1101)(0110)
      • Convert: D 6
      • Result: (D6)₁₆

  • f) Hexadecimal to Binary:

    • Method: Convert each hexadecimal digit into its 4-bit binary equivalent.
    • Example: (D6)₁₆
      • Convert: D (13) -> 1101, 6 -> 0110
      • Combine: 11010110
      • Result: (11010110)₂

  • g) Octal to Hexadecimal & Hexadecimal to Octal:

    • Method: Convert to Binary first, then convert the binary representation to the target base (Hexadecimal or Octal).
    • Example (Octal 326 to Hex): (326)₈ -> (011 010 110)₂ -> (1101 0110)₂ -> (D6)₁₆
    • Example (Hex D6 to Octal): (D6)₁₆ -> (1101 0110)₂ -> (011 010 110)₂ -> (326)₈

4. Encoding Schemes for Characters

These schemes map characters (letters, numbers, symbols) to unique numerical codes (usually binary).

  • a) ASCII (American Standard Code for Information Interchange):

    • Purpose: Early standard, primarily for English characters.
    • Versions:
      • ASCII-7: Uses 7 bits, represents 128 characters (0-127). Includes uppercase/lowercase English letters, digits 0-9, punctuation, and control characters.
      • ASCII-8 (Extended ASCII): Uses 8 bits (1 byte), represents 256 characters (0-255). Includes ASCII-7 plus additional symbols, graphic characters, and accented letters for some European languages.
    • Limitation: Cannot represent characters from most other languages (e.g., Hindi, Chinese).

  • b) ISCII (Indian Script Code for Information Interchange):

    • Purpose: Developed to represent characters from various Indian scripts (Devanagari, Tamil, Telugu, Bengali, etc.) along with English.
    • Mechanism: Uses 8 bits. It retains the lower 128 characters of ASCII-7 and uses the upper 128 positions (128-255) for Indian script characters. A mechanism allows switching between different Indian scripts.
    • Limitation: Not a global standard; primarily focused on Indian scripts.

  • c) Unicode:

    • Purpose: A universal character encoding standard designed to represent characters from all major writing systems of the world (past and present).
    • Advantage: Solves the limitations of ASCII and ISCII by providing a unique code point (a number) for every character, regardless of platform, program, or language.
    • Encodings (Ways to store Unicode code points in bytes):
      • UTF-8: Variable-width encoding (uses 1 to 4 bytes per character). Very common on the web. Backward compatible with ASCII (ASCII characters use only 1 byte).
      • UTF-16: Variable-width encoding (uses 2 or 4 bytes per character). Used by systems like Windows and Java.
      • UTF-32: Fixed-width encoding (uses 4 bytes per character). Simpler but less space-efficient.
    • Key takeaway: Unicode defines the code, UTF defines how to store that code in bytes.

Key Points for Government Exams:

  • Master the number system conversions, especially Decimal <-> Binary, Binary <-> Hexadecimal, Binary <-> Octal.
  • Understand the base and digits of each number system.
  • Know the definitions of Bit and Byte (1 Byte = 8 Bits).
  • Understand the purpose and limitations of ASCII.
  • Know the purpose of ISCII (for Indian scripts).
  • Understand the goal of Unicode (universal standard) and its advantage over ASCII/ISCII. Know that UTF-8 is a common implementation.

Multiple Choice Questions (MCQs)

Here are 10 MCQs based on this chapter for your practice:

  1. Which number system forms the basis for computer operations?
    a) Decimal
    b) Hexadecimal
    c) Binary
    d) Octal

  2. How many unique digits are used in the Octal number system?
    a) 2
    b) 10
    c) 16
    d) 8

  3. The value (25)₁₀ is equivalent to which binary number?
    a) 10011
    b) 11001
    c) 10101
    d) 11100

  4. What is the decimal equivalent of the binary number (10110)₂?
    a) 20
    b) 22
    c) 26
    d) 18

  5. Which encoding scheme was specifically developed for representing Indian scripts?
    a) ASCII
    b) Unicode
    c) ISCII
    d) EBCDIC

  6. The hexadecimal number system uses digits 0-9 and letters:
    a) A-E
    b) A-F
    c) A-G
    d) A-Z

  7. How many bits are typically used in the standard ASCII-7 encoding?
    a) 4
    b) 7
    c) 8
    d) 16

  8. Which of the following is a major advantage of Unicode over ASCII?
    a) It uses fewer bits per character.
    b) It is only for English characters.
    c) It can represent characters from almost all writing systems globally.
    d) It is an older standard.

  9. To convert a binary number to hexadecimal, we group the bits in sets of:
    a) 2
    b) 3
    c) 4
    d) 8

  10. What does the term 'Bit' stand for?
    a) Binary Integer
    b) Byte Information Transfer
    c) Binary Digit
    d) Basic Input Task

Answers to MCQs:

  1. c) Binary
  2. d) 8
  3. b) 11001
  4. b) 22 (116 + 08 + 14 + 12 + 0*1 = 16 + 4 + 2 = 22)
  5. c) ISCII
  6. b) A-F
  7. b) 7
  8. c) It can represent characters from almost all writing systems globally.
  9. c) 4
  10. c) Binary Digit

Make sure you understand the concepts behind these answers, especially the conversions. Keep practicing!

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