Binary, Decimal, Hexadecimal

Binary, Decimal, Hexadecimal and Compression Study Guide

1. Binary, Decimal, Hexadecimal Relationships

• Binary (Base 2): Uses two digits (0 and 1). Example: 1010 in binary is 10 in decimal.

• Decimal (Base 10): Uses ten digits (0-9). Example: 10 in decimal is A in hexadecimal.

• Hexadecimal (Base 16): Uses sixteen digits (0-9 and A-F). Example: A in hexadecimal is 10 in decimal.

Conversion Examples:

• Binary to Decimal: Multiply each bit by 2 raised to its position (right to left).

  • Example: 1010 = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 10.

• Decimal to Binary: Repeatedly divide the decimal number by 2, recording the remainders.

• Hexadecimal to Decimal: Multiply each digit by 16 raised to its position.

  • Example: 1A = (1 × 16¹) + (10 × 16⁰) = 16 + 10 = 26.

2. Determining the Number of Bits Needed

• Formula: Number of Bits = ⌈log₂(Number)⌉

• Example: To represent the decimal number 100:

  • ⌈log₂(100)⌉ = ⌈6.64⌉ = 7 bits.

3. Computer Hardware/Software Elements and Network Configurations

Hardware Elements:

• CPU: Executes instructions.

• RAM: Temporary storage for active processes.

• Storage (HDD/SSD): Permanent storage for data.

• Motherboard: Connects all hardware components.

• NIC: Manages network connections.

Software Elements:

• Operating System (OS): Manages hardware and software resources.

• Applications: Software for specific tasks (e.g., Word, Chrome).

• Drivers: Allow the OS to communicate with hardware.

Network Configurations:

• Client-Server Model: Central server provides services to clients.

• Peer-to-Peer Network: Devices communicate directly.

• LAN: Local Area Network for a specific area (e.g., home, office).

• WAN: Wide Area Network covering a large geographical area.

4. Lossy vs. Lossless Compression

• Lossy Compression:

  • Some data is permanently removed.

  • Common for audio, video, images (e.g., JPEG, MP3).

• Lossless Compression:

  • No data is lost, can be perfectly restored.

  • Used for text, documents, and some images (e.g., PNG, ZIP).