Convert Base 4 to Hexadecimal

Convert Base 4 (base 4) to Hexadecimal (hex) 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) → Hexadecimal (base 16)

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 16 repeatedly (read remainders upward):

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

────────────────────────────
Result:  222 (base 4) = 2A (hex)

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 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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