In-depth Notes on Information Representation and Multimedia

Chapter 1: Information Representation and Multimedia

Binary Number System

  • Definition: Binary is a two-digit number system utilizing only the digits 0 and 1.
  • Importance: Understanding binary is crucial for many computer science topics and appears frequently in examinations.
  • Example: A binary number is represented as 01001111.

Conversion Between Binary and Decimal

Binary to Decimal

  • Each 1 in a binary number contributes to the total value based on its position (powers of 2).
  • Conversion Method:
    • For example, the binary number 1011 is calculated as:
    • 1 imes 2^3 + 0 imes 2^2 + 1 imes 2^1 + 1 imes 2^0 = 8 + 0 + 2 + 1 = 11

Decimal to Binary

  • Conversion Method: To convert a decimal number to binary:
    1. While the number is greater than zero, divide it by 2.
    2. Record the remainder for each division.
    3. Read remainders from bottom to top.
  • Example: Convert 67 to binary:
    • Division process: 67 / 2 = 33 R1
    • Continue until zero: 33 / 2 = 16 R1, 16 / 2 = 8 R0, 8 / 2 = 4 R0, 4 / 2 = 2 R0, 2 / 2 = 1 R0, 1 / 2 = 0 R1.
    • Result: 67 in binary is 1000011.

One's Complement

  • Definition: One's complement represents negative numbers by flipping all binary digits (changing 0 to 1 and vice versa).
  • Example:
    • For positive binary 0101 (which equals 5), its one's complement would be 1010 (which equals -5).
  • Characteristics:
    • Two representations for zero: +0 (0000) and -0 (1111).

Two's Complement

  • Definition: Provides a more efficient representation for negative numbers compared to one's complement.
  • Conversion:
    1. Flip all the bits (like one's complement).
    2. Add 1 to the least significant bit.
  • Example: For binary 0101:
    • Flip: 1010
    • Add 1: 1010 + 0001 = 1011 (which represents -5).
  • Advantage: Only one representation for zero.

Binary Addition

  • Rules:
    • 0 + 0 = 0
    • 0 + 1 = 1
    • 1 + 0 = 1
    • 1 + 1 = 10 (carry 1)
    • 1 + 1 + 1 = 11 (carry 1)

Binary Subtraction

  • Basic Concept:
    • Similar to base-10 with borrowing.
  • Method:
    • If you need to subtract 1 from 0, borrow from the next left digit, turning 0 into 2 (binary 10). This allows calculations like:
    • 0 - 1 turns into 2 - 1 = 1$$$.

Data Measurement Units

  • Byte: Smallest addressable unit, consisting of 8 bits.
  • Larger units include:
    • Kilobyte (KB) = 1,000 bytes (SI system, base-10), but computers use binary (1 KB = 1024 bytes).
    • Megabyte (MB), Gigabyte (GB), etc.

Hexadecimal System

  • Definition: A base-16 numbering system that uses characters 0-9 and A-F.
  • Purpose: Simplifies the representation of binary numbers; one hex digit corresponds to four binary bits.
  • Conversion:
    • Hexadecimal A = 1010 binary.
    • For binary 11010111, group into nibbles: 1101 (D) and 0111 (7), resulting in D7 in hex.

ASCII and Character Sets

  • ASCII: Codes characters (letters, numbers, symbols) with binary.
  • Character sets:
    • Standard ASCII (7-bit, 128 characters)
    • Extended ASCII (8-bit, 256 characters)
    • Unicode (variable bits, millions of characters).

Bitmap Graphics

  • Definition: Composed of pixels, each pixel represented by binary values indicating its color.
  • Features:
    • Size: Detailed but larger file sizes.
    • Editing Difficulty: Changes require pixel-by-pixel edits.

Image Resolution & Bit Depth

  • Image Resolution: Total pixels = width × height.
  • Bit Depth: Number of bits per pixel.
    • More bits = more colors available.
  • Example:
    • 24-bit image allows for 16.7 million colors.

Vector Graphics

  • Definition: Defined by 2D points, allowing for scalable images without quality loss.
  • Key Features:
    • Editable without pixelation.
    • Commonly used for logos and designs.

Sound Representation

  • Sound is recorded as amplitude at specific time intervals.
  • Sampling Rate: Frequency of measurements taken (Hz). Higher rates yield more accurate representation.

Video Compression

  • Video frames are captured and stitched together at a defined frame rate (commonly 25 fps).
  • File Compression: Reduces size while aiming to retain quality.

Lossless vs. Lossy Compression

  • Lossless: No data loss, original can be perfectly restored (e.g., Run-Length Encoding).
  • Lossy: Some data omitted for smaller file size (e.g., MP3, JPEG), not perfect restoration possible.

MP3 Compression

  • Reduces size significantly by about 90% using perceptual music shaping.
  • Examples of bitrate: 80-320 kbps, affecting sound quality.

Run-Length Encoding (RLE)

  • A lossless technique compressing data by encoding repeated sequences into counts and values.
  • Effective for data with many sequential identical elements, less effective for unique data.
  • Image Example: A black and white 8x8 grid can reduce from 64 bytes to 30 bytes using RLE.