Numeral system

A numeral system is a set of symbols and rules for writing numbers. Its conventions determine how symbols represent quantities, including whether position changes their value.

Place-value system: A numeral system in which a digit’s position determines its contribution to the number’s value. Position gives the same digit different values in systems such as decimal and binary.
Base conversion: The process of expressing a number in a different radix while preserving its value. Conversion shows how one quantity can have distinct numerals in different systems.
Babylonian numerals: A cuneiform numeral system that used a base-sixty place-value structure. It demonstrates that positional notation predates the modern decimal system.
Hexadecimal: A positional numeral system with radix sixteen, using digits 0–9 and letters A–F. It compactly represents binary values in computing and digital notation.
Unary numeral system: A numeral system that represents a number by repeating one mark once per unit. It encodes quantity by repetition rather than place value or digit weights.
Radix: The number of distinct digit values, including zero, used in a positional numeral system. The radix determines how many digit positions are needed as quantities grow.
Binary numeral system: A positional numeral system with radix two and the digits 0 and 1. Its two-symbol place-value rule is a clear contrast with decimal notation.
Egyptian numerals: An ancient additive numeral system using distinct hieroglyphic symbols for powers of ten. Its repeated symbols illustrate a non-positional way to write quantities.
Octal: A positional numeral system with radix eight and the digits 0 through 7. Groups of three binary digits map directly to one octal digit.
Tally marks: A counting notation that records units as strokes, often grouped in fives. It is a direct additive notation with no positional digit values.

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