Binary Number System

💻 Binary Number System

📘 Introduction:

The Binary Number System is a base-2 number system. It is used internally by almost all modern computers and digital systems.

• It uses only two digits:
  0 and 1

Each binary digit is known as a bit, and every bit represents a power of 2 based on its position.

🔢 Digits Used:

0, 1

🧠 Positional Value Concept:

Just like the decimal system (base-10), the binary system also follows a positional number system, where:

Value of a binary number =
dₙ × 2ⁿ + dₙ₋₁ × 2ⁿ⁻¹ + ... + d₁ × 2¹ + d₀ × 2⁰

✅ Example:

(1101)₂

Step-by-step breakdown:

= 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰  
= 8 + 4 + 0 + 1  
= (13)₁₀

✅ More Examples:

Example:

= 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰  
= 8 + 0 + 2 + 0  
= (10)₁₀

(1010)₂

Example :

(10001)₂

= 1 × 2⁴ + 0 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰  
= 16 + 0 + 0 + 0 + 1  
= (17)₁₀

🔄 Counting in Binary:

💡 Applications of Binary:

• Used in digital electronics

• Microprocessors and memory represent all values in binary

• All data in computers (text, image, sound) is stored in binary format

🧾 Summary: