Data Representation 3

• epresentation Topic Learning Outcomes

  • Understand numbering systems and the rof data using different numbering systems.

• Comprehend how data is represented, stored, and manipulated inside a computer.

• Learn how to represent data externally for easier understanding and manipulation based on standards.

Numbering Systems and Inter-conversion

• Internal Computer Data format

• Representation of data based on different standards

Binary System in Computers

• Binary (Base 2) is preferred in computers due to:

  • Reduced complexity and cost of binary representation devices.

  • Reliability, as electronic signals can easily represent two states (0 and 1).

• Transistors in processors represent binary states: ON (1) and OFF (0), similar to a light switch.

  • A bit is the smallest unit of data (0 or 1).

  • A byte consists of 8 bits, which represents a character.

Combinations of Bits

• Single bit: 2 outputs (0, 1).

• Two bits: 4 outputs (00, 01, 10, 11).

• General formula:
  n ext{ bits }
  ightarrow 2^n ext{ outputs}

• Doubling outputs with each additional bit: increasing bits leads to exponential growth in data representation capability.

Types of Data Units

• Bit: Basic unit of data,

• Byte: Group of 8 bits (e.g., representing characters),

• Nibble: Half a byte (4 bits),

• Word: 2 or more bytes; varies in size (16, 32, 64 bits).

Types of Numbering Systems

Conversions between Numbering Systems

1. Binary ↔ Decimal

2. Octal ↔ Decimal

3. Hexadecimal ↔ Decimal

4. Octal ↔ Binary

5. Hexadecimal ↔ Binary

6. Octal ↔ Hexadecimal

Practice Conversions

• Represent decimal to binary, octal, and hexadecimal, and vice versa.

• Practice examples in slides 11 - 22.

Binary Arithmetic

Operations

• Addition: Carry over when sums exceed binary limit.

• Subtraction: Use borrow methods similar to decimal.

• Multiplication: Shift-and-add method is effective.

Example Calculations

1. Binary Addition:
   0011 ext{ (3)} + 0010 ext{ (2)} = 0101 ext{ (5)}

2. Binary Multiplication:
   0011 imes 0010 = 000110 ext{ (6)}

3. Binary Subtraction:
   0101 - 0010 = 0011 ext{ (3)}

4. Binary Division provides quotient and remainder.

Data vs. Information

• Data: Raw facts (e.g., name, date of birth).

• Information: Processed data presented meaningfully (e.g., customer details).

Data Processing Cycle

1. Input: Capturing raw data (e.g., user input).

2. Processing: Conversion into useful information.

3. Output: Display or storage of information.

Computer Data Formats

• Different formats for representing data:

  • Alphanumeric (Text): ASCII, Unicode.

  • Audio: WAV, MP3, AIFF, etc.

  • Images: JPEG, GIF, etc.

  • Video: MPEG, QuickTime, etc.

Text Representation Standards

1. ASCII: 7-bit code (128 characters, mainly English).

2. Unicode: 16-bit superset of ASCII (supports global characters, emojis).

3. EBCDIC: Designed for mainframes (not widely used today).

Sound Representation

• Analog signals converted to digital via

  • ADC (Analog to Digital Converter): For converting sound waves to digital.

  • DAC (Digital to Analog Converter): Converts digital data back to sound.

Image Representation

• Pixels: Basic units making up images.

• Resolution: Width x Height, affecting detail quality.

• Color Depth: Number of bits per pixel (e.g., monochrome, RGB, CMYK).

Video Representation

• Comprised of frames (sequences of images).

• Frame Rate (FPS): Affects motion smoothness.

• Compression: REDUCES file sizes (removing redundant data).

Summary / Recap

1. Data conversion is required for processing.

2. Data in modern systems is represented binary.

3. Each data type has a specific format.

4. Compression and encoding standards facilitate storage and transmission.

Review Questions

• Represent numeric data in several numbering systems.

• Explain internal data representation and manipulation by computers.