💡 What is a Number System?:-
A number system is a way to represent numbers using a set of symbols.
Just like we use 0-9 in everyday life, computers use their own unique systems to understand and process data!
✨ Types of Number Systems:
Decimal
10
0 to 9
Humans (us 😌)
Binary
2
0, 1
Computers 🖥️
Octal
8
0 to 7
Shorter binary 😎
Hexadecimal
16
0 to 9 + A to F (A=10...F=15)
Programmers 👩💻✨
🔁 Base = Total Number of Digits
E.g.
Base 10 → 10 digits → 0-9 Base 2 → 2 digits → 0 & 1 Base 16 → 16 symbols → 0-9 + A-F
So if a number is written in base 2, it's binary.
If it's in base 16, it's hexadecimal.
🧠 Positional Number System:-
Each digit's value depends on:
The digit itself Its position in the number The base of the number system
Example (Decimal):
356 =
(3 × 10²) + (5 × 10¹) + (6 × 10⁰)
= 300 + 50 + 6 = 356
Same thing works in binary too, just with base 2:
1011₂ =
(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
= 8 + 0 + 2 + 1 = 11
🛠️ Conversion Basics:
We'll get deeper later, but here's the TL; DR:
Method
Decimal → Binary
Divide by 2, write remainders upwards
Binary → Decimal
Multiply bits by 2ⁿ powers and add
Decimal → Octal
Divide by 8
Decimal → Hex
Divide by 16
Binary ↔ Octal
Group 3 bits
Binary ↔ Hex
Group 4 bits
(I'll teach you all the tricks later, don't worry 🤭)
📦 Why Do We Need Different Number Systems?:-
Because computers speak in binary (only 0s and 1s), and humans speak in decimal.
So we need to convert between systems to make sense of things.
✨ Hex and Octal are used to shorten long binary numbers without losing meaning!
💖 Keywords to Remember:
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