base

base, in mathematics, an arbitrarily chosen whole number greater than 1 in terms of which any number can be expressed as a sum of that base raised to various powers. The decimal number system that is commonly used expresses all numbers in base 10. For example, 354.76 = (3 Γ— 102) + (5 Γ— 101) + (4 Γ— 100) + (7 Γ— 10–1) + (6 Γ— 10–2). The binary system used in computers expresses numbers in base 2. For example, 25 in binary is (1 Γ— 24) + (1 Γ— 23) + (0 Γ— 22) + (0 Γ— 21) + (1 Γ— 20) = 16 + 8 + 0 + 0 + 1 = 25. See also numerals and numeral systems.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen.
Citation Information
Article Title: base
Website Name: Encyclopaedia Britannica
Publisher: Encyclopaedia Britannica, Inc.
Date Published: 28 June 2022
Access Date: November 13, 2026