2 in the context of "Power of two"

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically 0 (zero) and 1 (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two.

The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation.

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard bold ⁠${\displaystyle \mathbb {N} }$⁠.

The natural numbers are used for counting, and for labeling the result of a count, like "there are seven days in a week", in which case they are called cardinal numbers. They are also used to label places in an ordered series, like "the third day of the month", in which case they are called ordinal numbers. Natural numbers may also be used to label, like the jersey numbers of a sports team; in this case, they have no specific mathematical properties and are called nominal numbers.

One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2. It often appears in mathematical equations, recipes and measurements.

A power of two is a number of the form 2 where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. In the fast-growing hierarchy, 2 is exactly equal to ${\displaystyle f_{1}^{n}(1)}$. In the Hardy hierarchy, 2 is exactly equal to ${\displaystyle H_{\omega {n}}(1)}$.

Powers of two with non-negative exponents are integers: 2 = 1, 2 = 2, and 2 is two multiplied by itself n times. The first ten powers of 2 for non-negative values of n are: