Binary System (Base 2)
- Uses only 2 digits (0 and 1) (رقمان فقط)
- Each position has a place value (قيمة مكانية)1
- Based on powers of 2 (قوى العدد 2)
- Used by computers (الحواسيب) to represent data
Place Value (القيمة المكانية)
- Each digit depends on its position (الموقع)
- Positions increase by powers of 2 (قوى 2)
- From right to left:
- 2⁰ = 1
- 2¹ = 2
- 2² = 4
- 2³ = 8
- 2⁴ = 16
Example
Binary number: 1011
- 1 × 8 = 8
- 0 × 4 = 0
- 1 × 2 = 2
- 1 × 1 = 1
So:
- 1011 (binary) = 11 (decimal)
Expanded Form (الصيغة الموسعة)2
- Writing a binary number as the sum of powers of 2 (مجموع قوى العدد 2)
- Example:
- 1101 = 1×8 + 1×4 + 0×2 + 1×1
Key Idea
- The value of a binary number =
digit × power of 2 (الرقم × قوة العدد 2)
Intuition
- Binary = ON / OFF (تشغيل / إيقاف)
- 1 = ON (تشغيل)
- 0 = OFF (إيقاف)
- Like switches (مفاتيح) inside a computer