Convert numbers across binary, decimal, hexadecimal, octal, and Roman numeral systems with instant calculations and step-by-step formulas.
1,010 Binary
Positional number systems use the position of each digit to denote its value as a power of the base. Base-10 (decimal) represents powers of 10, while base-2 (binary) represents powers of 2. Hexadecimal (base-16) and octal (base-8) cleanly align with power-of-two groupings, making them ideal for computer science.
Unlike positional systems, the Roman numeral system is a non-positional, additive and subtractive notation that originated in ancient Rome. It remains common today on clock faces, book chapters, royal titles, and formal monumental inscriptions.
To convert decimal to binary, divide the number by 2 repeatedly and record the remainder of each division in reverse order. For example, 13 in binary is 1101₂.
Hexadecimal is a base-16 numbering system using 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). It provides a human-friendly representation of binary-coded values because one hex digit corresponds exactly to four binary bits (a nibble).
Roman numerals use seven basic symbols: I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). Values are formed by adding symbols, or subtracting a smaller symbol placed before a larger one (such as IV for 4 or IX for 9).
Octal is base-8 (digits 0–7). It is widely used in Unix and Linux operating systems to specify file permissions (e.g., chmod 755), where each digit represents three binary permission bits (read, write, execute).
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