Data Representation and Compression

Data and Binary Numbers

• Binary Numbers: Digital data uses binary numbers for numerical representation.
• Bit: The smallest unit of information, either 0 or 1.

Base Conversion

• Binary to Decimal: Convert binary to decimal by recognizing that binary digits represent powers of 2.
  • Example: Binary number 1101.
• Decimal to Binary: Find powers of 2 that sum up to the decimal number.
  • Start with the largest power of 2 less than the number, subtract, and repeat until reaching 0.
  • Example: Decimal number 200.

Digital Images as Bits

• Digital Images: Images are converted to binary, processed, and displayed.
• Pixels: Digital images consist of pixels with binary numbers.
• Black and White Images: Represented using 1 (black/on) and 0 (white/off).
• Grid Creation: Draw a grid and color squares based on binary values.
• Metadata: Data needed to know the image size (e.g., 10 x 10 grid).

Binary and Color Representation

• Color Representation: Computers use binary for colors.
• Color Basis: Colors are created using red, green, and blue light.
• Maximum Color Value: 255 in decimal, represented as 11111111 in binary.
• Minimum Color Value: 0.

Music as Bits

• Analog Signal: Continuous in time and range of values.
• Digital Signal: Sequence of discrete symbols (bits).
• Sampling: Recording analog signals at discrete moments and converting to digital.
• Noise Resilience: Digital signals are more resilient against noise.

Data Compression

• Data Compression Usage: Used in MP3, MP4, RAR, ZIP, JPG, PNG files, etc.
• Importance: Important for backing up and archiving files, especially for internet uploads.
• Two-Way Process: Compression algorithms reduce data size, decompression restores the original form.
• Usefulness: Saves disk space and reduces bandwidth during data transmission.
• Function: Compresses a string of bytes to a smaller set of bytes.
• Lossless Algorithms: Reconstruct the original message exactly.
  • Used for text.
• Lossy Algorithms: Reconstruct an approximation of the original message.
  • Used for images and sound where slight loss is acceptable.

Lossless Compression

• Function: Data is packed and decompressed without any loss of data. Exact reconstruction is possible.
• Text Compression: Crucial to ensure identical reconstruction because minor differences can alter meaning.

Lossy Compression

• Function: Digital data is not decompressed back to 100% of the original.
• Characteristics: Provides high compression but with some loss of original data (pixels, sound waves, etc.).
• Meaning of Lossy: Loss of a quantity such as a frequency component or noise.
• Examples:
  • Images: High compression loss is noticeable when photos are enlarged.
  • Music: Difference between MP3 and high-resolution audio.
  • Video: Moving frames can handle more pixel loss than images.

Using Programs with Data

• Data Increase: Digitization and multiple transactions have led to a surge in data.
• Data Analysis: Analyzing large data sets helps categorize connections and find patterns.
• Data Extraction: Obtaining data from databases or software for use in other software.
• Process: Data extraction → transformation (filters/programs) → analysis (graphs, visualization).
• Steps to Extract and Analyze Data:
  • Analyze data sources (web pages, emails, videos, audio, text, etc.).
  • Determine the purpose of the analysis (trend, effect, cause, quantity).
  • Decide on tools for reading data and repositories for storing data.
  • Clean the data (whitespace, symbols, duplicates).
  • Understand data patterns and text flow using visualization tools.

How to Read and Analyze Graphs

• Graph Definition: Pictorial representation used to depict data relationships.
• Representation: Data is represented in points, lines, bars, pie charts, and scatter plots.
• Types of Graphs:
  • Picture Graphs: Use pictures to represent values.
  • Bar Graphs: Use vertical or horizontal bars to represent values.
  • Line Graphs: Use lines to represent values.
  • Scatter Plots: Use points with a best-fit line.