Convert Hexadecimal to Base 3

Convert Hexadecimal (hex) to Base 3 (base 3) instantly and accurately.

Selected Hexadecimal (hex) - available characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Conversion Formula

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

Convert Hexadecimal (base 16) → Base 3 (base 3)

Step 1: Expand each digit of 2A (hex) by position:

        2 × 16^1 = 32
        A × 16^0 = 10
        ────────────
        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:  2A (hex) = 1120 (base 3)

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.

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.

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