Convert Base 9 to Hexadecimal

Convert Base 9 (base 9) to Hexadecimal (hex) instantly and accurately.

Selected Base 9 (base 9) - available characters: 0, 1, 2, 3, 4, 5, 6, 7, 8

Conversion Formula

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

Convert Base 9 (base 9) → Hexadecimal (base 16)

Step 1: Expand each digit of 46 (base 9) by position:

        4 × 9^1 = 36
        6 × 9^0 =  6
        ────────────
        Sum = 42 (decimal)

Step 2: Divide 42 by 16 repeatedly (read remainders upward):

        42 ÷ 16 = 2  r 10 (A)
         2 ÷ 16 = 0  r 2
        Read remainders upward: 2A

────────────────────────────
Result:  46 (base 9) = 2A (hex)

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.

About Hexadecimal

Hexadecimal (base 16) uses digits 0-9 and A-F (A=10, B=11, C=12, D=13, E=14, F=15). Each position is a power of 16: 16⁰=1, 16¹=16, 16²=256. Because 16 = 2⁴, each hex digit = exactly 4 bits (one nibble). Ubiquitous in computing: memory addresses (0x7FFF…), CSS colours (#FF5733), IPv6, SHA-256 hashes (64 hex digits = 256 bits), MAC addresses, UUID/GUIDs, and binary file magic numbers. The '0x' prefix originated in C (1972) and is standard in C++, Java, Python, JS, Rust, and Go. Conversion: decimal 42 = 2×16+10 = 2A₁₆.

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