Convert Octal to Base 5

Convert Octal (oct) to Base 5 (base 5) instantly and accurately.

Selected Octal (oct) - available characters: 0, 1, 2, 3, 4, 5, 6, 7

Conversion Formula

Step-by-step example using the value 42 (decimal):

Convert Octal (base 8) → Base 5 (base 5)

Step 1: Expand each digit of 52 (oct) by position:

        5 × 8^1 = 40
        2 × 8^0 =  2
        ────────────
        Sum = 42 (decimal)

Step 2: Divide 42 by 5 repeatedly (read remainders upward):

        42 ÷ 5 = 8  r 2
         8 ÷ 5 = 1  r 3
         1 ÷ 5 = 0  r 1
        Read remainders upward: 132

────────────────────────────
Result:  52 (oct) = 132 (base 5)

About Octal

Octal (base 8) uses digits 0-7. Each position is a power of 8: 8⁰=1, 8¹=8, 8²=64. Because 8 = 2³, each octal digit = exactly 3 binary bits. The Unix/Linux file permission system (chmod 755 = rwxr-xr-x; 7=111, 5=101) uses octal for concise 3-bit rwx triplets. The DEC PDP series encoded 12- and 16-bit words naturally in octal. In C/C++/JS a leading zero denotes octal: 0755 = 493₁₀. Conversion: decimal 42 = 5×8+2 = 52₈.

About Base 5

Quinary (base 5) uses digits 0-4. Each position is a power of 5: 5⁰=1, 5¹=5, 5²=25. One of the most historically widespread alternative bases, reflecting one-hand finger counting - Proto-Indo-European *penkwe = 'five/fist'. Tally marks group strokes in fives. Babylonian sexagesimal (base 60) used a 5×12 sub-structure. Fibonacci numbers mod 5 have Pisano period 20. Conversion: decimal 42 = 1×25+3×5+2 = 132₅.

Quick Reference Table

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