Hexadecimal Number System

🔷 Hexadecimal Number System

📘 Introduction:

The Hexadecimal Number System is a base-16 number system.
It is widely used in computer systems and digital electronics.

• It uses 16 digits:

  • From 0 to 9

  • And A to F, where:

    • A = 10

    • B = 11

    • C = 12

    • D = 13

    • E = 14

    • F = 15

🔢 Digits Used:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

🧠 Positional Value Concept:

Each digit in a hexadecimal number represents a power of 16, depending on its position.

Value of a Hexadecimal Number dₙ dₙ₋₁ ... d₀ =
dₙ × 16ⁿ + dₙ₋₁ × 16ⁿ⁻¹ + ... + d₁ × 16¹ + d₀ × 16⁰

✅ Example 6:

Convert (1A5C)₁₆ to Decimal:

Step-by-step:

= 1 × 16³ + A × 16² + 5 × 16¹ + C × 16⁰  
= 1 × 4096 + 10 × 256 + 5 × 16 + 12 × 1  
= 4096 + 2560 + 80 + 12  
= (6748)₁₀

✔ So, (1A5C)₁₆ = (6748)₁₀

✅ Another Example:

(2F)₁₆ to Decimal

= 2 × 16¹ + F × 16⁰  
= 2 × 16 + 15 × 1  
= 32 + 15  
= (47)₁₀

🔄 Hexadecimal to Decimal Table:

💡 Applications of Hexadecimal:

• Memory addresses in programming (e.g., 0xFF2A)

• Color codes in web design (e.g., #FF5733)

• Compact representation of binary data (1 hex digit = 4 binary bits)

• Used in machine-level programming

🧾 Summary: