Binary System

Every image, video, and message on the internet is ultimately a sequence of 0s and 1s — understanding binary is understanding how computers think.

🔢 2. Binary System - The Language of Computers

🎯 Challenge 2: The Light Switch Language

Scenario: Imagine you're in a room with only a light switch. You can only communicate using ON and OFF.

Challenge: How would you represent:

• Numbers (0, 1, 2, 3...)
• Letters (A, B, C...)
• Colors (Red, Green, Blue...)
• Your vacation photos?

Pause and think: With just ON and OFF, can you really represent everything?

💡 The Binary Revelation

The Answer: YES! Computers do exactly this with electricity:

BINARY = The language of ON and OFF

Physical reality in computer:

i) Voltage HIGH (5 volts) = 1 (ON)

ii) Voltage LOW (0 volts) = 0 (OFF)

Everything in your computer is just:

0 0 1 1 0 1 0 1 1 0 0 1 1 1 0...

But from these simple 0s and 1s, we get:

✓ Documents

✓ Photos

✓ Videos

✓ Music

✓ Games

✓ The entire internet!

Key insight: Binary is like Morse code - simple signals that combine to express complex ideas!

🎓 Understanding Binary: From Bits to Terabytes

The Hierarchy of Data

🔍 THE BUILDING BLOCKS:

1️⃣ BIT (Binary Digit) Smallest unit of data Can be: 0 or 1

Example: 1

Real-world: A single light switch

2️⃣ BYTE (8 Bits) Basic unit of storage 8 bits = 1 byte

Example: 01001000

Can represent:

i) Number 0-255

ii) Single letter (H)

iii) Small instruction

Real-world: Its like 8 light switches in a row

3️⃣ KILOBYTE (1,024 Bytes) 1 KB ≈ 1 thousand bytes

Examples:

You have a short email: 2 KB

A small text file: 5 KB

Tiny image: 10 KB

4️⃣ MEGABYTE (1,024 KB) 1 MB ≈ 1 million bytes

Examples:

A high-res photo: 3 MB

A 1 minute MP3 song: 1 MB

A short document: 0.5 MB

A typical app install: 50 MB

5️⃣ GIGABYTE (1,024 MB) 1 GB ≈ 1 billion bytes

Examples:

HD movie (1080p): 4 GB

6️⃣ TERABYTE (1,024 GB) 1 TB ≈ 1 trillion bytes

Examples:

250 HD movies

200,000 songs

500,000 photos

Laptop hard drive: 1-2 TB

External backup drive: 4 TB

7️⃣ PETABYTE (1,024 TB) 1 PB ≈ 1 quadrillion bytes

Examples: Netflix's entire library: ~100 PB

Large company data center: 10 PB

The Scale Visualization:

From smallest to largest:

Bit • (one dot)

Byte •••••••• (8 dots)

Kilobyte [Small paragraph] ፨

Megabyte [Entire book] 📖

Gigabyte [Bookshelf - 100 books]📚

Terabyte [Library - 100 bookshelves] 🚪🚪🚪🚪🚪🚪

Petabyte [50 Libraries] 🏫🏫🏫🏫🏫🏫🏫🏫🏫🏫🏫🏫

🎮 Interactive Exercise: Binary to Decimal

Let's learn how binary represents numbers:

DECIMAL SYSTEM (Base 10):

Positions: 1000s 100s 10s 1s Number: 2 5 6 3

2×1000 + 5×100 + 6×10 + 3×1 = 2563

We use 10 digits: 0,1,2,3,4,5,6,7,8,9

BINARY SYSTEM (Base 2):

Positions: 8s 4s 2s 1s Number: 1 0 1 1

1×8 + 0×4 + 1×2 + 1×1 = 11 (decimal)

We use 2 digits: 0, 1

EXAMPLES:

Binary → Decimal:

0001 = 1

0010 = 2

0011 = 3

0100 = 4

0101 = 5

0110 = 6

0111 = 7

1000 = 8

Pattern: Each position doubles!

8 4 2 1

↓ ↓ ↓ ↓

1 0 1 1 = 8 + 2 + 1 = 11

16 8 4 2 1

↓ ↓ ↓ ↓ ↓

1 0 0 1 1 = 16 + 2 + 1 = 19

Try these yourself:

Binary 1111 = ?

Binary 1010 = ?

Binary 0110 = ?

(Answers below)

ANSWERS:

Binary 1111 = 8 + 4 + 2 + 1 = 15

Binary 1010 = 8 + 0 + 2 + 0 = 10

Binary 0110 = 0 + 4 + 2 + 0 = 6

🔤 How Binary Represents Text: ASCII and Unicode

Ever wonder how computers store letters?

ASCII ENCODING:

Each letter = 1 byte (8 bits)

Letter → Decimal → Binary

──────────────────────────────────

A → 65 → 01000001

B → 66 → 01000010

C → 67 → 01000011

a → 97 → 01100001

b → 98 → 01100010

0 → 48 → 00110000

! → 33 → 00100001

Space → 32 → 00100000

Example: The word "Hi!"

Hi ! 01001000 01101001 00100001

Total: 3 bytes (24 bits) to store "Hi!"

Your name in binary:

Example: "Bob"

B → 66 → 01000010

o → 111 → 01101111

b → 98 → 01100010

"Bob" = 01000010 01101111 01100010

3 letters = 3 bytes of storage

🎨 How Binary Represents Colors: RGB

COLOR ENCODING:

Every pixel on your screen = 3 bytes (24 bits)

Red: 1 byte (0-255)

Green: 1 byte (0-255)

Blue: 1 byte (0-255)

Examples:

i) Pure Red:

R: 255 (11111111)

G: 0 (00000000)

B: 0 (00000000)

Red pixel

ii) Pure Green:

R: 0 (00000000)

G: 255 (11111111)

B: 0 (00000000)

Green pixel

iii) Purple:

R: 128 (10000000)

G: 0 (00000000)

B: 128 (10000000)

Purple pixel

iv) White:

R: 255 (11111111)

G: 255 (11111111)

B: 255 (11111111)

White pixel

v) Black:

R: 0 (00000000)

G: 0 (00000000)

B: 0 (00000000)

Black pixel

Your 1920×1080 monitor: = 2,073,600 pixels × 3 bytes per pixel = 6,220,800 bytes ≈ 6 MB for ONE FRAME!

At 60 FPS: 6 MB × 60 = 360 MB per second! (This is why graphics cards need fast memory!)

🚨 Common Misconception: "KB, MB, GB are Exact Thousands"

You might think: "1 KB = 1,000 bytes exactly"

The Reality: It's actually 1,024!

❌ MARKETING NUMBERS (Decimal): 1 KB = 1,000 bytes

1 MB = 1,000 KB = 1,000,000 bytes

1 GB = 1,000 MB = 1,000,000,000 bytes

(Hard drive manufacturers use this!)

✅ COMPUTER NUMBERS (Binary):

1 KB = 1,024 bytes (2¹⁰)

1 MB = 1,024 KB = 1,048,576 bytes (2²⁰)

1 GB = 1,024 MB = 1,073,741,824 bytes (2³⁰)

(Computer systems use this!)

WHY THE DIFFERENCE?

Computers think in powers of 2:

2¹⁰ = 1,024 (close to 1,000)

2²⁰ = 1,048,576 (close to 1 million)

2³⁰ = 1,073,741,824 (close to 1 billion)

THE RESULT:

You buy a "500 GB" hard drive:

Marketing: 500,000,000,000 bytes

Computer sees: 465 GB

You: "Where did my 35 GB go?!" 😡

Reality: Marketing uses 1000, computers use 1024 That's a 7% difference!

Mental model: Computer storage is like buying a "1 pound" of coffee that's actually 0.93 pounds because they use different measuring systems!

🎯 The Power of Binary: Everything is Numbers

WHAT BINARY REPRESENTS:

Text:

"Hello" → 5 bytes

Each letter → specific number → binary

Images:

Photo.jpg → Millions of pixels

Each pixel → RGB values → binary

Videos:

Movie.mp4 → Sequence of images + audio

Each frame → pixels → binary

Audio → sound waves → numbers → binary

Music:

Song.mp3 → Sound wave samples

44,100 samples per second

Each sample → number → binary

Programs:

Chrome.exe → Machine instructions

Each instruction → number → binary

Everything is just different ways of interpreting

patterns of 0s and 1s!

Mind-blowing fact:

This entire article you're reading:

• Every letter: 1 byte

• Total: ~50,000 characters = 50 KB

• In binary: 400,000 bits

• In binary: 400,000 individual 0s and 1s!

01000001 01110010 01100101... (and so on for 50KB!)

Key Takeaways

1. Computers use binary because transistors have two states — on (1) and off (0), making binary the natural number system for hardware
2. All data types are encoded as binary — integers, floating-point numbers, characters (ASCII/UTF-8), and colors are all bit patterns
3. Understanding binary helps you reason about storage sizes — 1 byte = 8 bits = 256 possible values, which is why IP addresses max at 255
4. Hexadecimal is a compact way to represent binary — each hex digit maps to exactly 4 bits, making it useful for memory addresses and colors