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Understanding Data Representations in IGCSE

May 23, 2025

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Xero to Hero in IGCSE Computer Science: Data Representations

Overview

  • Introduction to a series focusing on IGCSE Computer Science.
  • The first video covers Chapter 1: Data Representations.

Number Systems

Binary System

  • Computers process data in binary (0 and 1) due to millions of tiny switches that turn on (1) or off (0).
  • Binary to Decimal Conversion:
    • Multiply each binary digit by its place value (2^position).
    • Example: Binary 1011 = 1x8 + 0x4 + 1x2 + 1x1 = 11 in decimal.

Decimal to Binary Conversion

  • Continuously divide the decimal number by 2, noting remainders.
  • Example: Decimal 39 is binary 100111.

Hexadecimal System

  • Base 16 system using digits 0-9 and letters A-F.
  • Conversions:
    • Binary to Hexadecimal: Group binary into chunks of 4 and map to hex.
    • Hexadecimal to Binary: Reverse the mapping process.

Usage of Hexadecimal

  • Advantages: Easier visualization and shorter representation than binary.
  • Applications: Error codes, MAC addresses, IP addresses, HTML color codes.

Binary Arithmetic

Addition

  • Similar to decimal addition with carries.
  • Overflow can occur if an extra bit (9th bit) is generated beyond an 8-bit register.

Multiplication & Division (Binary Shifting)

  • Left Shift: Multiplies binary number by powers of 2.
  • Right Shift: Divides binary number by powers of 2.

Two's Complement

  • Method for representing negative numbers in binary.
  • Positive numbers start with 0, negative numbers start with 1.
  • Conversion involves inverting digits and adding 1.

Data Representation

Text

  • Character Sets: ASCII and Unicode (supports more characters, including emojis).

Sound

  • Conversion of analog sound to digital involves sampling.
  • Key Terms:
    • Sample: Captured sound at intervals.
    • Sampling Resolution: Bits used to represent amplitude.
    • Sample Rate: Samples taken per second.

Images

  • Bitmap: Images made of pixels, each represented by a binary number.
  • Resolution: Number of pixels in an image.
  • Color Depth: Number of bits per pixel, influencing the range of colors.

Storage Measurements

  • Units:
    • Bit: 0 or 1.
    • Byte: 8 bits.
    • Nibble: 4 bits.
  • Size Conversions: Use base 1024 for kilobyte, megabyte, etc.

File Size Calculations

Images

  • Formula: Image Resolution x Color Depth.

Sound

  • Formula: Sample Rate x Sampling Resolution x Length (in seconds).
  • Adjustments for mono and stereo sounds.

Data Compression

Types of Compression

  • Lossy Compression: Reduces file size by removing data (e.g., MP3, JPEG).
  • Lossless Compression: No data loss; original file can be reconstructed (e.g., run-length encoding).

Benefits of Compression

  • Reduces file size for easier storage and faster upload/download.
  • Reduces costs and saves storage space.

These notes summarize key points from the video on data representations, covering number systems, data representation techniques for text, sound, images, storage measurements, and data compression. The information is crucial for IGCSE Computer Science exam preparation.

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