Convert Base 4 to Octal

Convert Base 4 (base 4) to Octal (oct) instantly and accurately.

Selected Base 4 (base 4) - available characters: 0, 1, 2, 3

Conversion Formula

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

Convert Base 4 (base 4) → Octal (base 8)

Step 1: Expand each digit of 222 (base 4) by position:

        2 × 4^2 = 32
        2 × 4^1 =  8
        2 × 4^0 =  2
        ────────────
        Sum = 42 (decimal)

Step 2: Divide 42 by 8 repeatedly (read remainders upward):

        42 ÷ 8 = 5  r 2
         5 ÷ 8 = 0  r 5
        Read remainders upward: 52

────────────────────────────
Result:  222 (base 4) = 52 (oct)

About Base 4

Quaternary (base 4) uses digits 0-3. Each position is a power of 4: 4⁰=1, 4¹=4, 4²=16. Because 4 = 2², each quaternary digit maps to exactly 2 bits (0=00, 1=01, 2=10, 3=11). Used in bioinformatics to encode DNA nucleotides (A, C, G, T = 0-3), storing the human genome (3.2 Gbp) in ≈750 MB. 4-QAM encodes exactly 2 bits per symbol. Conversion: decimal 42 = 2×16+2×4+2 = 222₄.

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.

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