Lecture Notes: Notational Systems and Data Representation

Introduction

• Presented by Technology G (Tech G)
• Topics covered include binary, hexadecimal, decimal systems, and data representation through ASCII and Unicode.

Notational Systems

Binary System

• Definition: A number system using base-2, composed of two symbols: 0 and 1.
  • Zero represents off/no electricity flow.
  • One represents on/electricity flow.
• Usage: Core to binary code, used in computing for processor instructions.
• Structure: Numbers in binary are read as a sequence of bits (8 bits form an octet).
  • Each bit has a place value (1, 2, 4, 8, 16, 32, 64, 128).

Decimal System (Base 10)

• Definition: A numeral system using base 10, includes digits 0-9.
• Common Use: Everyday counting, base system for most human-centric numeral systems.

Powers of 2

• Definition: Mathematical doubling starting from base number 2.
• Example:
  • 2^1 = 2 (binary 10)
  • 2^2 = 4 (binary 100)
  • 2^3 = 8 (binary 1000)

Hexadecimal System (Base 16)

• Definition: A numeral system using 16 symbols: 0-9 and A-F (A=10, F=15).
• Usage: Common in HTML for color codes, IP addressing (IPv6), and MAC addresses.

Data Representation

ASCII

• Definition: American Standard Code for Information Interchange.
• Features:
  • 7-bit character set with 128 characters.
  • Includes letters, numbers, punctuation.

ANSI

• Definition: American National Standards Institute.
• Extension: Extends ASCII to include special symbols and language accents.

Code Pages

• Purpose: Allow operating systems to display characters from different languages that don’t use Latin alphabets.
• Functionality: Selects characters based on user's language and region settings.

Unicode

• Purpose: Replaces ASCII and ANSI, supports a broader range of characters.
• Coverage: Includes Latin and non-Latin alphabets; up to 576 displayable characters.

IP Addresses

IPv4

• Definition: An older protocol for IP addresses, consists of four octets (e.g., 172.16.254.1).
• Limitation: 4.3 billion addresses; inadequate for modern needs due to device proliferation.

IPv6

• Definition: New protocol with longer address space to accommodate more devices.
• Structure: 128 bits long, divided into 8 groups of 16 bits each.
• Capacity: 340 undecillion addresses, theoretically sufficient for future needs.

Applications and Examples

• HTML Color Codes: Use hexadecimal to represent colors (e.g., "#FF0000" for red).
• IP Addressing and DNS: DNS translates human-readable addresses to IP addresses for routing.

Conclusion

• Summary: Covered binary, hexadecimal, decimal systems, ASCII, Unicode, and IP addressing.
• Further Resources: More information available on Technology G's website.