Convert Base 4 to Base 9

Convert Base 4 (base 4) to Base 9 (base 9) 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) → Base 9 (base 9)

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 9 repeatedly (read remainders upward):

        42 ÷ 9 = 4  r 6
         4 ÷ 9 = 0  r 4
        Read remainders upward: 46

────────────────────────────
Result:  222 (base 4) = 46 (base 9)

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 Base 9

Nonary (base 9) uses digits 0-8. Each position is a power of 9: 9⁰=1, 9¹=9, 9²=81. Because 9 = 3², each nonary digit maps to exactly 2 ternary digits (0=00 … 8=22). The finite field GF(9) = GF(3²) is used in certain error-correcting codes and algebraic geometry. The 3×3 magic square sums to 15 in every row/column/diagonal and is deeply tied to mod-9 arithmetic. Conversion: decimal 42 = 4×9+6 = 46₉.

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