Base
A base is the number of distinct digit symbols in a positional numeral system, including zero. It determines how place values scale.
Positional notation: A numeral system in which a digit’s position determines its value. Base specifies how each position’s value changes from the one to its right.
Exponentiation: The operation of raising a number to a power by repeated multiplication. Powers of the base determine the place values in positional notation.
Binary number: A number written in base two using the digits 0 and 1. Binary is the base used to represent data in digital circuits.
Unary numeral system: A numeral system that represents a number by repeating a single mark that many times. Unary lacks positional place values, unlike systems characterized by a base.
Place value: The value contributed by a digit according to its position in a numeral. In base b, each position represents a power of b.
Integer: A number with no fractional part, including zero and negative whole numbers. Integer representations expose the repeated grouping that underlies base notation.
Hexadecimal: A positional numeral system with base sixteen, using 0–9 and A–F. Each hexadecimal digit compactly encodes four binary digits.
Roman numerals: A numeral system using letters such as I, V, X, L, C, D, and M. Roman numerals are not a positional system with a fixed base.
Radix point: A symbol separating integer and fractional digits in a positional numeral. Base determines the powers of the radix to either side of this point.
Division algorithm: A theorem expressing an integer as a quotient times a positive divisor plus a remainder. Repeated division by the base yields the digits of an integer representation.