## Binary numbers and logical operators

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An integer literal is of type long if it ends with the letter 'L' or 'l'; otherwise it is of type int. It is recommended that you use the upper case letter 'L' because the lower case letter 'l' is hard to distinguish from the digit 1. Values of the integral types byteshortintand long can be created from int literals. Values of type long that exceed the range of int can be created from long literals. Integer literals can be expressed these number systems:. Base 10, whose digits consists of the numbers 0 through 9; this is the number system you use every day.

Base 16, whose 0b1110 binary systems consist of the numbers 0 through 9 and the letters A through F. Base 2, whose digits consists of the numbers 0 0b1110 binary systems 1 you can create binary literals in Java SE 7 and later. For general-purpose programming, the decimal system is likely to be the only number system you will ever use.

However, if you need to use another number system, the following example shows the correct syntax. The prefix '0x' indicates hexadecimal and '0b' indicates binary:.

In Java SE 7, the integral types byteshortintand long can also be expressed using the binary number system. To specify a binary 0b1110 binary systems, add the prefix 0b or 0B to the number. The following examples show binary literals:. This feature enables you, for example, to separate groups of digits in numeric literals, which can improve the readability of your code.

For instance, if your code contains numbers with many digits, you can 0b1110 binary systems an underscore character to separate digits in groups of three, similar to how you would use a punctuation 0b1110 binary systems like a comma, or a space, as a 0b1110 binary systems.

The following examples demonstrate valid and invalid underscore placements in numeric literals. Use binary literals, numeric literals with underscores. Base 10, whose digits consists of the numbers 0 through 9; this is the number system you use every day Hexadecimal: Base 16, whose digits consist of the 0b1110 binary systems 0 through 9 and the letters A through F Binary: At the beginning or end of a number Adjacent to a decimal point in a floating point literal Prior to an 'F' or 'L' suffix In positions where a string of digits is expected.

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A binary system is a system of two astronomical bodies which are close enough that their gravitational attraction causes them to orbit each other around a barycenter also see animated examples. More restrictive definitions require that this common center of mass is not located within the interior of either object, in order to exclude the typical planetâ€” satellite systems and planetary systems.

The most common binary systems are binary stars and binary asteroid , but brown dwarfs , planets , neutron stars , black holes and galaxies can also form binaries. A multiple system is like a binary system but consists of three or more objects such as for trinary stars and trinary asteroids.

In a binary system the brighter object is referred to as primary , and the other the secondary. They are also classified based on orbit. Wide binaries are objects with orbits that keep them apart from one another. They evolve separately and have very little effect on each other. Close binaries are close to each other and are able to transfer mass from one another.

They can also be classified based on how we observe them. Visual binaries are two stars separated enough that they can be viewed through a telescope or binoculars. Eclipsing binaries are where the objects' orbits are at an angle that when one passes in front of the other it causes an eclipse , as seen from Earth.

Astrometric binaries are objects that seem to move around nothing as their companion object cannot be identified, it can only be inferred. The companion object may not be bright enough or may be hidden in the glare from the primary object. A related classification though not a binary system is Optical binary which refers to objects that are so close together in the sky that they appear to be a binary system but are not.

Such objects merely appear to be close together, but lie at different distances from the solar system. When binary minor planets are similar in size, they may be called " binary companions " instead of referring to the smaller body as a satellite. Pluto and its largest moon Charon are sometimes described as a binary system because the barycenter center of mass of the two objects is not inside either of them.

A binary star that has an orbital period of less than 30 years implies that the two system components are less than about 10 AU apart. Mass transfer occurs at some stage in most close binaries, profoundly affecting the evolution of the component stars. If the two components are in a close binary and do not fill their Roche lobes , the system is considered a detached binary. In a semidetached binary , one star fills its Roche lobe and mass transfer occurs.

In a contact binary , both stars fill their Roche lobes. The evolution of close binaries depends on the initial masses of the two stars and their separation.

When the more-massive star evolves into a red giant first and fills its Roche lobe, material will spill through the inner Lagrangian point onto its companion, thereby affecting its companion's evolution. Mass transfer can also alter the separation and orbital period of the binary star. In binaries that are initially widely separated, material escaping from the Roche lobe of the evolved red giant immerses the system in material, creating a common-envelope binary that contains the core of the red giant a white dwarf and the companion star.

Friction causes the two components to approach, and thus the orbital period to shorten. The common envelope is ejected and a cataclysmic variable star is left, wherein the mass transfer from the companion to the white dwarf causes the periodic outbursts seen in novae , recurrent novae , dwarf novae , and symbiotic novae. If one component of a close binary is massive enough, it may become a neutron star or black hole instead of a white dwarf. Such binary systems are observed see X-ray binary , but often a supernova explosion will blow the system apart into separate single stars.