Computer Number Systems (Binary, Decimal, Octal, and Hexadecimal)

Introduction

You sit at your computer or smartphone playing your favourite video game or texting a friend. The images on your screen are vibrant, the text clear and the videos fluid. However, nothing actually exists in your computers digital brain.

Computers do not understand languages such as English or even Filipino. Instead, everything within your computer is converted into billions of tiny switches that turn ON (1) and OFF (0) in the electronic circuits of your computer. This includes photos, songs, characters and levels within your games.

Welcome Secret Agent! You have been recruited by the Global Cyber Defense Network (GCDA). We have intercepted an encrypted message from an Alien Satellite. You must learn the four digital languages: Decimal, Binary, Octal and Hexadecimal to decode the secret message and save our global communication!

Are you ready to learn how to read the secret language of machines? Let's get started!

Task

Working in teams of 3 to 4 agents, your team will create a Cyber Codebreaker’s Survival Guide & Decoder Kit.

By the end of this WebQuest, your team will submit and present:

  1. The Codebreaker's Survival Manual: A creative visual handbook (digital slide deck or mini-booklet) that explains the 4 number systems and step-by-step conversion rules with examples.
  2. Decoded Mission File: A completed activity sheet showing how your team converted and decoded the alien's secret message.
  3. Team Presentation: A 3-minute quick briefing demonstrating how to convert a number between Decimal and Binary to the rest of the class.

Process

Your mission is broken down into 4 Phase Steps.

Assign roles within your team:
a. Base 10 & Base 2 Specialist: Focuses on Decimal and Binary mechanics.
b. Base 8 Specialist: Focuses on Octal grouping and conversions.
c. Base 16 Specialist: Focuses on Hexadecimal (letters A–F) and conversions.
d. Chief Editor / Presenter: Oversees the design of the Survival Guide and leads the oral presentation.

PHASE 1: Explore the curated resources below to learn about the four main computer number systems:
a. Decimal System (Base 10): The human counting system using digits 0–9.
b. Binary System (Base 2): The machine language using only 0s and 1s.
c. Octal System (Base 8): A shorthand system using digits 0–7 (3 binary digits = 1 octal digit).
d. Hexadecimal System (Base 16): Used in web design (color codes) and memory addresses using digits 0–9 and letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15).

Curated Web Resources:
Khan Academy: Journey into Information Theory & Binary (https://youtube.com/playlistlist=PLSQl0a2vh4HC9lvrBhVt4UUkhzpp3N5_x&si=…)
Math is Fun: Binary, Octal, and Hexadecimal Number Systems (https://www.mathsisfun.com/binary-number-system.html)
GeeksforGeeks: Number Systems in Computer Architecture (https://www.geeksforgeeks.org/maths/number-system-in-maths/)
YouTube: Computer Number Systems Explained Simply (https://youtu.be/2Z03p3yhGmk?si=s7LnMlF1jxKmx3j5)


PHASE 2: Practice Conversions 
Work together to master the following conversions in your group notebook:
Decimal to Binary (Repeated division by 2) & Binary to Decimal (Positional values: 16, 8, 4, 2, 1).
Binary to Octal (Group binary bits into sets of 3 from right to left).
Binary to Hexadecimal (Group binary bits into sets of 4 from right to left).

PHASE 3: Decode the Intercepted Message
Using your conversion skills, translate the following encrypted mission codes into Decimal numbers:
Code Alpha (Binary): 1 0 1 1 0  =>  Decimal: ____
Code Bravo (Octal): 3 7  =>  Decimal: ____
Code Charlie (Hexadecimal): 1 A   =>  Decimal: ____
Secret Word Challenge: Convert these Binary numbers to Decimal, then use the alphabet position (1=A, 2=B, 3=C, etc.) to reveal the secret word:
  a. 001002 = _________
  b. 000012 = _________
  c. 101002 = _________
  d. 000012 = _________

PHASE 4: Create the Survival Guide
Synthesize your findings into your Codebreaker's Survival Guide. Make sure your guide includes:
a. A comparison chart showing bases, allowable digits, and real-world uses (e.g., Hex for HTML color codes like #FFFFFF).
b. Simple step-by-step conversion guides with annotated examples.
c. Clear visual layouts, diagrams, or memory tricks.

Evaluation

Your performance will be evaluated based on the following rubric:

Criteria Excellent (4 pts) Proficient (3 pts) Developing (2 pts) Beginning (1 pt)
Mathematical Accuracy All number conversions (Binary, Octal, Hex, Decimal) are 100% correct. 80–90% of conversions are correct; minor computational errors. 60–79% of conversions are correct; shows conceptual confusion. Less than 60% accurate; major conversion errors.
Survival Guide Quality Exceptionally clear, visually engaging, well-organized, and includes real-world uses. Clear and organized with step-by-step rules and neat formatting. Missing key sections or explanations are hard to follow. Disorganized, incomplete, or lacks required explanations.
Decoded Mission File All secret codes and the Secret Word Challenge are accurately decoded. Secret codes decoded with 1 minor mistake in the challenge. Multiple errors in decoding the mission file. Mission file incomplete or mostly inaccurate.
Collaboration & Presentation All team members actively participated and presented clearly within the time limit. Good teamwork; most members contributed to the presentation. Equal participation was lacking; presentation was rushed. Minimal teamwork; presentation was unprepared.

Grading Scale:

  • 15 – 16 Points: Master Codebreaker (Grade A)
  • 12 – 14 Points: Senior Cyber Agent (Grade B)
  • 9 – 11 Points: Agent in Training (Grade C)
  • Below 9 Points: Needs Re-training (Grade D)

Conclusion

Congratulations, Secret Agents! Mission Accomplished!

By completing this WebQuest, you have unlocked the foundational language of all digital technology. You now understand that behind every app, image, game, and website lies a simple yet powerful world of numbers, bases, and positional math.