A modern digital computer represents data using the binary numeral system.

The ASCII codes for the word " Wikipedia ", given here in Binary numeral system | binary, provide a way of representing the word in information theory, as well as for information-processing algorithm s.

Leibniz also described the binary numeral system, a central ingredient of all modern computers.

In this binary numeral system ( base 2 ), x

The most common representation of a positive integer is a string of bits, using the binary numeral system.

There are four different ways to represent negative numbers in a binary numeral system.

Microprocessors operate on numbers and symbols represented in the binary numeral system.

Elias gamma coding, which is commonly used in data compression, expresses arbitrary-sized numbers by using unary to indicate the length of a binary numeral.

Gottfried Leibniz ( 1646 – 1716 ) refined the binary numeral system | binary system, foundation of virtually all modern computer architectures.

# each decimal digit is represented by a binary numeral consisting of five bits of which two are of one kind, called " ones ," and three are of the other kind, called " zeros ", and

A prefix that indicates an integer, e. g., " bin ", " tern ," or " quatern ", may be used in lieu of a numeral, to produce " binary ", " ternary ", or " quaternary " ( 2, 3, and 4 states respectively ).

The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one bit.

Hard drive s store information in binary numeral system | binary form and so are considered a type of physical digital media.

The binary numeral system of Gray codes gives an alternative way of solving the puzzle.

In the Gray system, numbers are expressed in a binary combination of 0s and 1s, but rather than being a standard positional numeral system, Gray code operates on the premise that each value differs from its predecessor by only one ( and exactly one ) bit changed.

The sequence of numbers generated by an LFSR or its XNOR counterpart can be considered a binary numeral system just as valid as Gray code or the natural binary code.

Performing this operation is simple in decimal arithmetic, in the binary numeral system used in computer programming, and in other even-numbered bases.

# redirect binary numeral system

In particular, a number expressed in the binary numeral system is odd if its last digit is 1 and even if its last digit is 0.

The unsigned binary numeral system | binary representation of decimal 149, with the msb highlighted.

The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII.

In this respect, all of the various forms of an alloy containing only two constituents, like iron and carbon, is called a binary system, while all of the alloy combinations possible with a ternary alloy, such as alloys of iron, carbon and chromium, is called a ternary system.

* Finger binary, a system for counting in binary numbers on the fingers of human hands

Early computers used one of two addressing methods to access the system memory ; binary ( base 2 )

The binary system has a period of 790 years and is 73 light-years from Earth.

* The Braille system was the first binary format for character encoding, using a six-bit code rendered as dot patterns.

This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary, octal and hexadecimal systems, although the sexagesimal system ( where the reciprocals of all 5-smooth numbers terminate ) does better in this respect ( but at the cost of an unwieldy multiplication table ).

Some software providers also produced compilers for BASIC, and other languages, to produce binary ( or " machine ") code which would run many times faster and make better use of the small system RAM.

Most digital circuits use a binary system with two voltage levels labeled " 0 " and " 1 ".

Kepler-16 contains the first discovered planet that orbits around a binary star system.

If a planet orbits one member of a binary star system, then an uppercase letter for the star will be followed by a lowercase letter for the planet.

However, the " A " is sometimes omitted ; for example the first planet discovered around the primary star of the Tau Boötis binary system is usually called simply Tau Boötis b.

The system, 197 light-years away, has a primary of magnitude 5. 4 that is itself a binary star ; its components are of magnitude 6. 0 and 6. 3 and have a period of 101 years.

A binary star system can also produce eclipses if the plane of the orbit of its constituent stars intersects the observer's position.

On a typical computer system, a ' double precision ' ( 64-bit ) binary floating-point number has a coefficient of 53 bits ( one of which is implied ), an exponent of 11 bits, and one sign bit.

It is located in a binary star system ( Gridlock ) within the constellation of Kasterborous ( Pyramids of Mars, Attack of the Cybermen and Voyage of the Damned ), at " galactic coordinates ten-zero-eleven-zero-zero by zero-two from galactic zero centre " ( Pyramids of Mars ( 1975 ), Full Circle ( 1980 ) and partially in " The Family of Blood " ( 2007 )), which is some 250 million light years away from Earth ( as stated in the 1996 Doctor Who television movie ).

Because the Doom engine uses the binary space partitioning system for rendering, it does not enable moving walls.

Replacement of the hard-to-implement decimal system ( used in Charles Babbage's earlier design ) by the simpler binary system meant that Zuse's machines were easier to build and potentially more reliable, given the technologies available at that time.

The observations show that the cloud is asymmetrical and matches the pattern of X-ray binaries ( binary star systems containing black holes or neutron stars ), mostly on one side of the galactic center.

Intermediate results were binary, written onto paper sheets by electrostatically modifying the resistance at 1500 locations to represent 30 of the 50 bit numbers ( one equation ).

* Did the ancient egyptians record the period of the eclipsing binary Algol-the Raging one?

Basic operations of an AVL tree involve carrying out the same actions as would be carried out on an unbalanced binary search tree, but modifications are preceded or followed by one or more operations called tree rotations, which help to restore the height balance of the subtrees.

A bit ( a contraction of binary digit ) is the basic capacity of information in computing and telecommunications ; a bit can have the value of either 1 or 0 ( one or zero ) only.

In information theory, one bit is typically defined as the uncertainty of a binary random variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known.

Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.

In turn, one can also derive ordinary functions of one variable from a binary function.

In the case of a binary CPU, a bit refers to one significant place in the numbers a CPU deals with.

For example, if a binary CPU uses 32 bits to represent a memory address, and each memory address represents one octet ( 8 bits ), the maximum quantity of memory that CPU can address is 2 < sup > 32 </ sup > octets, or 4 GiB.

Suppose that F is a partial function that takes one argument, a finite binary string, and possibly returns a single binary string as output.

A simple way to enforce prefix-free-ness is to use machines whose means of input is a binary stream from which bits can be read one at a time.

This " knowledge " then leads to a tendency towards a binary opposition of the orient vs. the occident, where one is defined in opposition to the other, and they are unequal in value.

As a crude example, each finger might control one key which corresponds to one bit in a byte, so that using seven keys and seven fingers, one could enter any character in the ASCII set — if the user could remember the binary codes.

The semiconductor memory is organized into memory cells or bistable flip-flops, each storing one binary bit ( 0 or 1 ).

The term ' dualism ' was originally coined to denote co-eternal binary opposition, a meaning that is preserved in metaphysical and philosophical duality discourse but has been diluted in general or common usages .— which is also uncreated — is an absolute one.

The components of the primary are becoming closer together and will not be divisible in amateur telescopes beginning in 2015. δ Equ is a binary star with an orbital period of 5. 7 years, which at one time was the shortest known orbital period for an optical binary.

* is a Unix binary utility that displays information about one or more ELF files.