Table of Contents

    Octal Number System

    Rumman Ansari July 20, 2026 836 views Subject Details

    🧮 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:

    Octal Decimal
    0 0
    1 1
    2 2
    3 3
    4 4
    5 5
    6 6
    7 7
    10 8
    11 9
    12 10

    💡 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:

    Feature Description
    Base 8
    Digits Used 0 to 7
    Positional System Yes
    Easy to Convert With Binary
    Used In Legacy computing, Unix permissions

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