Octal Number System

🧮 Octal Number System

📘 Introduction:

The Octal Number System is a base-8 number system.
It uses eight digits:
0 to 7

Since it uses 8 as the base, each position in an octal number represents a power of 8.

🔢 Digits Used:

0, 1, 2, 3, 4, 5, 6, 7

🧠 Positional Value Concept:

Like other positional systems, the value of each digit depends on its position (right to left) and the base raised to that position.

🧮 General Formula:

Value of an Octal number dₙ dₙ₋₁ ... d₀ =
dₙ × 8ⁿ + dₙ₋₁ × 8ⁿ⁻¹ + ... + d₁ × 8¹ + d₀ × 8⁰

✅ Example 5 (Corrected):

= 6 × 8² + 5 × 8¹ + 7 × 8⁰  
= 6 × 64 + 5 × 8 + 7 × 1  
= 384 + 40 + 7  
= (431)₁₀

(657)₈

✅ Another Example:

(123)₈

= 1 × 8² + 2 × 8¹ + 3 × 8⁰  
= 64 + 16 + 3  
= (83)₁₀

🔄 Octal to Decimal Table:

💡 Applications of Octal:

• Used in early computer systems

• Easier to convert to/from binary (1 octal digit = 3 binary digits)

• Still used in Unix file permissions (e.g., chmod 755)

🧾 Summary: