A Story of Numbers | Binary, Decimal & Ternary | Class 8 Computational Thinking
A Story of Numbers 🔢
Binary, Ternary & the Secret Language of Computers — explained with toffees, light switches & pizza!
Have you ever wondered why computers only use 0 and 1? Or why we count in tens? This chapter uncovers the fascinating world of number systems — and it all starts with a simple question: what if we counted differently?
By the end of this post, you'll be able to convert numbers to binary and ternary, and understand the logic behind how computers store information. 🚀
In This Post
System 01Decimal (Base-10) — What You Already Know
Every day, you count in decimal — prices at the canteen, your exam marks, cricket scores. Decimal uses base 10, which means we count up to 10 before we move to the next place.
Base-10 uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Place values are powers of 10: 1, 10, 100, 1000...
You have 66 toffees. Group them: 6 groups of 10 = 60, plus 6 singles = 6. Total = 66. That's exactly how the tens and ones place works in decimal!
💡 THE PIPE ANALOGY — Measuring 66 Inches
| Pipe Size | 100 inch | 10 inch | 1 inch |
|---|---|---|---|
| How many? | 0 | 6 | 6 |
| Value | 0 | 60 | 6 |
✅ Total pipes used: 12 pipes (6 tens + 6 ones)
System 02Binary (Base-2) — The Language of Computers
Computers are made of millions of tiny switches (transistors). Each switch is either ON or OFF. That gives us exactly 2 states — which is why computers speak binary!
Light Switch
ON = 1, OFF = 0
7 switches = 7-digit binary number!
Open/Closed Door
Open = 1, Closed = 0
Row of doors = binary code
Battery Charged?
Yes = 1, No = 0
Just like a bit in memory!
Base-2 uses only 2 digits: 0 and 1
Place values are powers of 2: 1, 2, 4, 8, 16, 32, 64...
🔢 How to Convert: Decimal → Binary
Find the largest power of 2 that fits
For 55: powers of 2 are 1, 2, 4, 8, 16, 32, 64... Largest that fits = 32
Subtract and repeat
55 − 32 = 23 → 23 − 16 = 7 → 7 − 4 = 3 → 3 − 2 = 1 → 1 − 1 = 0 ✅
Mark 1 where used, 0 where not
Put a 1 under each power you used, 0 under those you skipped.
🔢 EXAMPLE: Convert 55 to Binary
| Power of 2 | 2⁶=64 | 2⁵=32 | 2⁴=16 | 2³=8 | 2²=4 | 2¹=2 | 2⁰=1 |
|---|---|---|---|---|---|---|---|
| Bit (0 or 1) | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
✅ 55 in Binary = (110111)₂
Check: 32+16+4+2+1 = 55 ✔
🔢 TRY IT: Convert 66 to Binary
| Power of 2 | 2⁶=64 | 2⁵=32 | 2⁴=16 | 2³=8 | 2²=4 | 2¹=2 | 2⁰=1 |
|---|---|---|---|---|---|---|---|
| Bit (0 or 1) | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
✅ 66 = 64 + 2 → Binary = (1000010)₂
In binary, we only have 2 digits (0 and 1). Using "2" would mean "take a whole group of 2" — but that's what the NEXT place is for! The digit 2 simply doesn't exist in base-2, just like digit 10 doesn't exist in decimal as a single digit.
System 03Ternary (Base-3) — Three's a Crowd!
What if we had 3 possible states instead of 2? Welcome to ternary — base-3! While not used in everyday computers, it shows us that the rules of number systems work for any base.
Traffic Light
Red=0, Yellow=1, Green=2
3 states → Base-3!
Game Lives
No lives=0, One=1, Max=2
A 3-state system!
Temperature
Cold=0, Warm=1, Hot=2
3 categories = ternary logic!
Base-3 uses 3 digits: 0, 1, 2
Place values are powers of 3: 1, 3, 9, 27, 81...
🔢 EXAMPLE: Convert 55 to Ternary
| Power of 3 | 3³=27 | 3²=9 | 3¹=3 | 3⁰=1 |
|---|---|---|---|---|
| Digit (0,1,2) | 2 | 0 | 0 | 1 |
✅ 55 = 2×27 + 0×9 + 0×3 + 1×1 → Ternary = (2001)₃
🔢 TRY IT: Convert 66 to Ternary
| Power of 3 | 3⁴=81 | 3³=27 | 3²=9 | 3¹=3 | 3⁰=1 |
|---|---|---|---|---|---|
| Digit | 0 | 2 | 2 | 1 | 0 |
✅ 66 = 2×27 + 2×9 + 1×3 + 0 = 54+18+3 → Ternary = (2210)₃
System 04Comparison — Same Number, Different Looks!
Here's the magic: the number 55 is always 55 — it represents the same quantity. But it looks completely different depending on which base you use!
| Number | Decimal (Base-10) | Binary (Base-2) | Ternary (Base-3) |
|---|---|---|---|
| Seven | 7 | 111 | 21 |
| Ten | 10 | 1010 | 101 |
| Thirteen | 13 | 1101 | 111 |
| Fifty-five | 55 | 110111 | 2001 |
| Sixty-six | 66 | 1000010 | 2210 |
| One hundred | 100 | 1100100 | 10201 |
🧠 Key Concepts Summary
- A number system with base n uses exactly n digits: 0 to (n−1)
- Place values are always powers of the base (n⁰, n¹, n², n³...)
- The same number can be written in many ways depending on the base
- Computers choose binary because hardware easily represents 2 states (on/off)
- To convert: find which powers of the base add up to give your number
Hexadecimal (Base-16)
Web colors like #FF5733 are in base-16! Digits go 0–9 then A–F.
Time Uses Base-60!
60 seconds = 1 minute, 60 minutes = 1 hour. That's base-60 from ancient Babylon!
Your Phone's Memory
All photos, texts, videos — stored as millions of 0s and 1s in binary!
DNA Uses Base-4!
DNA stores genetic info using 4 bases: A, T, G, C — nature's own number system!
🎯 Quick Quiz — Test Yourself!
Click an option to check your answer. How many can you get right?
📥 Download Study Materials
Get the complete notes, worksheet with answer key, and activities for offline use!
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