Convert Base 4 to Base 6

Convert Base 4 (base 4) to Base 6 (base 6) 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 6 (base 6)

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 6 repeatedly (read remainders upward):

        42 ÷ 6 = 7  r 0
         7 ÷ 6 = 1  r 1
         1 ÷ 6 = 0  r 1
        Read remainders upward: 110

────────────────────────────
Result:  222 (base 4) = 110 (base 6)

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 6

Senary (base 6) uses digits 0-5. Each position is a power of 6: 6⁰=1, 6¹=6, 6²=36. Six is divisible by 1, 2, 3, and 6, making fractions clean: 1/2 = 0.3, 1/3 = 0.2 (both terminating). Native to the Ndom language of Papua New Guinea. Standard dice produce one uniform senary digit per roll. Donald Knuth noted senary's compact multiplication table. Conversion: decimal 42 = 1×36+1×6+0 = 110₆.

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