Binary, Hex & Base Converter

Low-level software engineering, embedded electronics assembly, and computer network protocol design frequently require manipulating non-decimal representations of numeric values. Microcontrollers, logic gates, and hardware buses communicate through raw binary bit strings, while memory debuggers and operating system kernels express storage addresses in compact hexadecimal notation. By supplying an integer in any supported radix, you can simultaneously evaluate its corresponding binary sequence, octal representation, standard base-ten decimal count, and hexadecimal equivalent without error.

Interpreting these converted values helps engineers verify bitmasks, decode hardware register status flags, and configure device driver parameters without tedious pencil-and-paper calculations. Each output format reflects the exact same underlying numeric magnitude expressed through the positional weighting of the selected base system. However, standard positional base conversion models pure integer magnitudes rather than specialized binary file formats. It does not automatically infer IEEE-754 floating-point mantissas, signed two's complement bit widths, or system endianness conventions without explicit application rules.

Every positional numeral system represents a number n through the summation formula n = Σ (dᵢ × baseⁱ), where each digit dᵢ is multiplied by the base raised to its positional index. Conversion from a non-decimal base first aggregates this weighted polynomial into base-10 decimal form. To convert decimal into a target base, the integer is repeatedly divided by the target radix, recording successive remainders from least to most significant digit.