Number Base Converter (binary, octal, decimal, hex)

How positional number bases work

Every base uses positional notation: the rightmost digit is base⁰ = 1, the next is base¹, then base², and so on. In decimal, '255' means 2×100 + 5×10 + 5×1. In binary, '11111111' means 1×128 + 1×64 + ... + 1×1 = 255. The same number, different bases.

Hexadecimal uses 0-9 and A-F to fit 16 values per digit. 'FF' = 15×16 + 15×1 = 255. Octal uses 0-7 (3 bits per digit), and binary uses just 0 and 1. The conversion is mechanical — convert to decimal then back to the target base — and the calculator does it for you for any non-negative integer.

When you'll use each base

Binary (base 2): low-level computer work — bit fields, masks, embedded firmware. Reading register layouts, debugging at the hardware level.

Octal (base 8): Unix file permissions (chmod 755 = rwxr-xr-x), some legacy file formats. Less common today.

Decimal (base 10): everything humans count. The default for normal arithmetic.

Hexadecimal (base 16): most common in software — colors (#FF6B35), memory addresses (0x7fff...), MAC addresses, byte representations of binary data, encoded hashes.

Quick reference

1 byte = 8 bits = 2 hex digits = 256 values (0-255). 1 hex digit = 4 bits = 16 values. 1 octal digit = 3 bits. Hex 'FF' = decimal 255 = binary 11111111. Hex '100' = decimal 256. Hex 'FFFF' = decimal 65535 (max for 16-bit unsigned). Hex 'FFFFFFFF' = decimal 4294967295 (max for 32-bit unsigned).