In mathematics, the number of different single-digit symbols used in a particular number system. In our usual (decimal) counting system of numbers (with symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) the base is 10. In the binary number system, which has only the symbols 1 and 0, the base is two. A base is also a number that, when raised to a particular power (that is, when multiplied by itself a particular number of times as in 102 = 10 x 10 = 100), has a logarithm equal to the power. For example, the logarithm of 100 to the base ten is 2.
In geometry, the term is used to denote the line or area on which a polygon or solid stands.The bottom side of a geometric figure from which the altitude can be constructed.
(In a digital numeration system) The positive integer that is equivalent to one in the next higher counting place; SYN. radix.
1. In mathematics, a number that is raised to the power specified by an exponent. For example, in 23 = 2 x 2 x 2 = 8, the base is 2. 2. In mathematics, the number of digits in a particular numbering system. With microcomputers, four numbering systems are commonly used or referred tobinary, octal, decimal, and hexadecimaland each is based on a different number of digits. The binary, or base-2, numbering system, which is used to discuss the states of a computers logic, has two digits, 0 and 1. Octal, or base-8, has eight digits, 0 through 7. The familiar decimal, or base-10, numbering system has ten digits, 0 through 9. Hexadecimal, or base-16, has sixteen digits, 0 through 9 and A through F. When numbers are written in a particular base, the base is often subscripted and enclosed in parentheses after the number, as in 24AE(16) = 9,390. Also called: radix. See also binary1, decimal, hexadecimal, octal.
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