Binary, Decimal & Hex Converter
Convert any number between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8). Essential for computer science and digital electronics.
Number Systems
Why Different Bases?
Decimal (base 10) uses 10 digits (0–9). Binary (base 2) uses 2 states (0 and 1) — perfect for digital circuits. Hexadecimal (base 16) uses 0–9 and A–F — each hex digit represents exactly 4 binary bits, making it compact and human-readable for binary data.
Binary to Decimal
Read binary digits from right to left as powers of 2. 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1 = 11₁₀. Decimal to binary: repeatedly divide by 2 and read remainders from bottom to top.
Hexadecimal in Computing
Hex is ubiquitous in computing: memory addresses (0x7FFF), colour codes (#FF5733), MAC addresses (AA:BB:CC:DD:EE:FF). A byte (8 bits) is represented by exactly 2 hex digits — 00 to FF (0 to 255 in decimal).
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