Convert Octal to Base 3

Convert Octal (oct) to Base 3 (base 3) 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 3 (base 3)

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 3 repeatedly (read remainders upward):

        42 ÷ 3 = 14  r 0
        14 ÷ 3 =  4  r 2
         4 ÷ 3 =  1  r 1
         1 ÷ 3 =  0  r 1
        Read remainders upward: 1120

────────────────────────────
Result:  52 (oct) = 1120 (base 3)

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 3

Ternary (base 3) uses digits 0, 1, 2. Each position is a power of 3: 3⁰=1, 3¹=3, 3²=9, 3³=27. Balanced ternary (−1, 0, +1) represents negatives without a sign and minimises rounding error. The Soviet Setun computer (1958) was the only practical balanced-ternary machine. Ternary underlies the Cantor set and Toom-Cook multiplication. Conversion: decimal 42 = 1×27+1×9+2×3+0 = 1120₃.

Quick Reference Table

→ Full Number Base Converter