Summary of Data Representation in Computer Systems

Data Representation in Computer Systems

• Basic Units of Data Representation

  • Bit: Smallest unit of data, can be 0 or 1.
  • Byte: Sequence of 8 bits.
  • Word: Varies in length (16, 32, 64 bits); typically aligned with byte sizes.

• Data Representation Mechanism

  • Computers represent data using two states: ON (1) and OFF (0).
  • Use binary number system (base 2).

• Number Systems

  • Base: Indicates the number of symbols; computers use base 2.
  • Examples:
  • Decimal: (7592)₁₀
  • Binary: (1010)₂

• Decimal System

  • Base 10, left of decimal signifies positive powers, right signifies negative powers.
  • Example: 9735 = 9×10³ + 7×10² + 3×10¹ + 5×10⁰.

• Binary System

  • Uses only 0 and 1 for arithmetic; based on powers of 2.

• Octal System

  • Base 8; uses powers of 8.

• Hexadecimal System

  • Base 16; uses numbers 0-9 and letters A-F to represent values.

• Conversions

  • Decimal to Binary: Repeated division by 2; record remainders.
  • Binary to Decimal: Sum powers of 2 corresponding to binary digits.
  • Decimal to Octal: Repeated division by 8.
  • Octal to Decimal: Multiply each digit by power of 8.
  • Octal to Binary: Convert each octal digit to 3-bit binary.
  • Binary to Octal: Group binary digits in sets of 3.
  • Decimal to Hex: Repeated division by 16.
  • Hex to Decimal: Multiply each hex digit by power of 16.
  • Hex to Binary: Convert each hex digit to 4-bit binary.
  • Binary to Hex: Group binary into sets of 4.

• Memory

  • Electronic components for storing data, and instructions.
  • Each byte has a unique address.
  • Stores OS, application programs, and data.

• Memory Measurement

  • Kilobyte (KB): 1,024 bytes
  • Megabyte (MB): 1,048,576 bytes
  • Gigabyte (GB): 1,073,741,824 bytes
  • Terabyte (TB): 1,099,511,627,776 bytes
  • Larger units follow similar powers of 2 (Peta, Exa, Zetta, Yotta).