Detailed Notes -Chapter 2 : Encoding Schemes and Number System -Class 11

Text Interpretation and Encoding in Computer Systems

1. Key Interpretation:

• 1. • When a key is pressed on the keyboard, it’s internally mapped to a unique code.
     • This code is then converted into binary form for the computer to process.
     • Example: Pressing the letter ‘A’ might be mapped to the decimal value 65, then converted to binary.

  2. Encoding:

     • Encoding is the process of converting data into a cipher using a specific code.
     • Each character, numeral, and symbol is assigned a unique code for representation.
     • Standard encoding schemes ensure compatibility across systems and keyboards.

  3. ASCII (American Standard Code for Information Interchange):

     • Developed in the 1960s to standardize character representation.
     • Originally used 7 bits to represent characters, allowing for 128 different characters.
     • Primarily used for the English language.

  4. ISCII (Indian Script Code for Information Interchange):

     • Developed in the 1980s for Indian languages.
     • An 8-bit code representation.
     • Retains ASCII codes and uses additional codes for Indian language characters.

  5. UNICODE:

     • Developed to incorporate characters from all written languages.
     • Provides a unique number for each character, ensuring compatibility across devices and systems.
     • Includes encodings like UTF-8, UTF-16, and UTF-32.
     • A superset of ASCII, with values 0–128 having the same characters as ASCII.

  6. Introduction to Number Systems:

     • Each keyboard key is mapped to an ASCII code, which is then converted into binary for computer understanding.
     • A number system represents numbers using unique characters or literals, with the count of these characters called the radix or base.
     • Number systems are positional, meaning the value of each symbol depends on its position within the number.

  7. Decimal Number System (Base-10):

     • Used in daily life, consisting of 10 digits (0 to 9).
     • Numbers are represented by symbol value (0 to 9) and positional value.

  8. Binary Number System (Base-2):

     • Utilized in computer circuits, representing on/off states with 1 and 0.
     • Base-2 system with only two digits (1 and 0).
     • Binary numbers can be converted to decimal for human understanding.

  9. Octal Number System (Base-8):

     • Designed for compact representation of binary numbers.
     • Base-8 system with eight digits (0 to 7), positional value expressed in powers of 8.
     • Each octal digit is represented by three binary digits.

  10. Hexadecimal Number System (Base-16):

      • Offers compact representation of binary numbers.
      • Consists of 16 symbols (0–9, A–F), with each alphanumeric digit represented by a group of four binary digits.
      • Used in memory addressing and color representation on webpages for its ease of use and compactness.

Applications of Hexadecimal Number System:

• Simplifies memory address representation and color description on webpages.
• Memory addresses and color codes are often written in hexadecimal form for ease of use and compact representation.

Conversion between Number Systems

1. Introduction:

   • Decimal system is used by humans, while computers understand binary.
   • Octal and hexadecimal systems simplify binary representation for human understanding.

2. Conversion from Decimal to other Number Systems:

   • Steps:
     • Divide the decimal number by the base value of the target system.
     • Record the remainders and write them in reverse order.

   a) Decimal to Binary Conversion:

   • Divide by 2 and record remainders until quotient is 0.
   • Write remainders in reverse order.

   b) Decimal to Octal Conversion:

   • Divide by 8 to obtain the equivalent octal number.

   c) Decimal to Hexadecimal Conversion:

   • Divide by 16 to obtain the equivalent hexadecimal number.

3. Conversion from other Number Systems to Decimal:

   • Steps:
     • Write position numbers for each symbol.
     • Obtain positional values by raising the position number to the base value.
     • Multiply each digit with its positional value and sum them up.

   a) Binary Number to Decimal:

   • Positional values are computed in terms of powers of 2.

   b) Octal Number to Decimal:

   • Positional values are computed in terms of powers of 8.

   c) Hexadecimal Number to Decimal:

   • Positional values are computed in terms of powers of 16.
   • Use decimal value equivalents for alphabet symbols.

Conversion between Binary, Octal, and Hexadecimal Numbers

1. Binary to Octal/Hexadecimal Conversion:

   • Group binary digits into sets of 3 or 4 bits for octal or hexadecimal conversion, respectively.
   • Replace each group with its equivalent octal or hexadecimal digit.

   a) Binary to Octal:

   • Example: Convert (10101100)₂ to octal: Group into sets of 3 bits: 010 101 100 → Octal digits: 2 5 4 → Result: (254)₈

   b) Octal to Binary:

   • Example: Convert (705)₈ to binary: Octal digits: 7 0 5 → Binary: 111 000 101 → Result: (111000101)₂

   c) Binary to Hexadecimal:

   • Example: Convert (0110101100)₂ to hexadecimal: Group into sets of 4 bits: 0001 1010 1100 → Hexadecimal: 1 AC → Result: (1AC)₁₆

   d) Hexadecimal to Binary:

   • Each hexadecimal symbol represents a 4-digit binary number.
   • Substitute each hexadecimal digit with its 4-bit binary equivalent.

Conversion of Numbers with Fractional Part

1. Decimal Number with Fractional Part to another Number System:

   • Multiply the fractional part of a decimal number by the base value of the target system until it becomes 0.
   • Use the integer part from top to bottom to get the equivalent number in the target system.
   • Stop if the fractional part repeats or after a certain number of multiplications.

2. Non-decimal Number with Fractional Part to Decimal Number System:

   • Compute the positional value of each digit using its base value.
   • Add the product of positional value and the digit to get the equivalent decimal number with the fractional part.

3. Fractional Binary Number to Octal or Hexadecimal Number:

   • Substitute groups of 3 or 4 bits in the integer part with the corresponding digit for octal or hexadecimal.
   • Similarly, group bits in the fractional part and substitute them with the equivalent digit or symbol in the target system.
   • Add 0s at the end of the fractional part to ensure groups of 3 or 4 bits.