Convert Octal to Base 7

Convert Octal (oct) to Base 7 (base 7) 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 7 (base 7)

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 7 repeatedly (read remainders upward):

        42 ÷ 7 = 6  r 0
         6 ÷ 7 = 0  r 6
        Read remainders upward: 60

────────────────────────────
Result:  52 (oct) = 60 (base 7)

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 7

Septenary (base 7) uses digits 0-6. Each position is a power of 7: 7⁰=1, 7¹=7, 7²=49. Seven is prime, so every fraction p/q (q not divisible by 7) produces a purely repeating expansion. Seven days of the week derive from Babylonian astronomy (the 7 naked-eye celestial objects). Reed-Solomon codes used in QR codes and Blu-ray draw on prime-field properties of GF(7). Conversion: decimal 42 = 6×7+0 = 60₇.

Quick Reference Table

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