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

Footnotes