Search results
Results from the WOW.Com Content Network
Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For semigroups for which additive notation is commonly used, like elliptic curves used in cryptography, this method is also referred to as double-and-add.
When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.
In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together. So: n 6 = n × n × n × n × n × n. Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its fourth power, by cubing a square, or by squaring a cube. The sequence of sixth ...
For instance, the addition chain for 31 leads to a method for computing the 31st power of any number n using only seven multiplications, instead of the 30 multiplications that one would get from repeated multiplication, and eight multiplications with exponentiation by squaring: n 2 = n × n n 3 = n 2 × n n 6 = n 3 × n 3 n 12 = n 6 × n 6 n 24 ...
When multiplication is repeated, the resulting operation is known as exponentiation. For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 2 3, a two with a superscript three. In this example, the number two is the base, and three is the exponent. [26]
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Stanley is recalling 2.6 million mugs sold in the U.S. after the company received dozens of consumer complaints, including some users who reported getting burned and requiring medical attention ...
When expressed as exponents, the geometric series is: 2 0 + 2 1 + 2 2 + 2 3 + ... and so forth, up to 2 63. The base of each exponentiation, "2", expresses the doubling at each square, while the exponents represent the position of each square (0 for the first square, 1 for the second, and so on.). The number of grains is the 64th Mersenne number.