Hexadecimal Number System
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Table of Content:
🔷 Hexadecimal Number System
📘 Introduction:
The Hexadecimal Number System is a base-16 number system.
It is widely used in computer systems and digital electronics.
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It uses 16 digits:
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From 0 to 9
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And A to F, where:
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
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🔢 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:
| Hex | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| A | 10 |
| B | 11 |
| C | 12 |
| D | 13 |
| E | 14 |
| F | 15 |
💡 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:
| Feature | Description |
|---|---|
| Base | 16 |
| Digits Used | 0–9, A–F |
| Positional System | Yes |
| Easy to Convert With | Binary |
| Commonly Used In | Computers, Web, Memory addresses |