Octal Converter
Convert octal numbers (base-8) to binary, decimal, hexadecimal, and any custom base. Essential for Unix file permissions and programming.
Octal Number Converter
Convert octal numbers (base-8) to binary, decimal, hexadecimal, and any custom base.
Octal (Base-8)
Only digits 0-7 are allowed
Result will appear here
Octal to Decimal Conversion
Conversion Method:
Base 8 to Decimal: Use positional notation
Formula:
Each digit × (base)^position, then sum all values
Examples with Step-by-Step Solutions
Example 1:
(123)8
=
(83)10
Step-by-Step Solution:
Converting 123₍8₎ to base 10:
Step 1: Convert Octal to decimal
123₍8₎ = 1 × 8² = 1 × 64 = 64 + 2 × 8¹ = 2 × 8 = 16 + 3 × 8⁰ = 3 × 1 = 3
= 64 + 16 + 3
= 83₁₀
Therefore: 123₍8₎ = 83₁₀
Example 2:
(456)8
=
(302)10
Step-by-Step Solution:
Converting 456₍8₎ to base 10:
Step 1: Convert Octal to decimal
456₍8₎ = 4 × 8² = 4 × 64 = 256 + 5 × 8¹ = 5 × 8 = 40 + 6 × 8⁰ = 6 × 1 = 6
= 256 + 40 + 6
= 302₁₀
Therefore: 456₍8₎ = 302₁₀
Example 3:
(777)8
=
(511)10
Step-by-Step Solution:
Converting 777₍8₎ to base 10:
Step 1: Convert Octal to decimal
777₍8₎ = 7 × 8² = 7 × 64 = 448 + 7 × 8¹ = 7 × 8 = 56 + 7 × 8⁰ = 7 × 1 = 7
= 448 + 56 + 7
= 511₁₀
Therefore: 777₍8₎ = 511₁₀
Example 4:
(234)8
=
(156)10
Step-by-Step Solution:
Converting 234₍8₎ to base 10:
Step 1: Convert Octal to decimal
234₍8₎ = 2 × 8² = 2 × 64 = 128 + 3 × 8¹ = 3 × 8 = 24 + 4 × 8⁰ = 4 × 1 = 4
= 128 + 24 + 4
= 156₁₀
Therefore: 234₍8₎ = 156₁₀