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binary digit (bit) raqame dorin, ~ dodoi, bit Fr.: chiffre binaire Either of the digits 0 or 1, used in the → binary number system. 
binary galaxy kahkašâne dorin Fr.: galaxie binaire A pair of galaxies in orbit around each other. → binary; → galaxy. 
binary number system râžmâne adadhâye dirini Fr.: système des nombres binaires A → numeral system that has 2 as its base and uses only two digits, 0 and 1. The positional value of each digit in a binary number is twice the place value of the digit of its right side. Each binary digit is known as a bit. The decimal numbers from 0 to 10 are thus in binary 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, and 1010. And, for example, the binary number 11101_{2} represents the decimal number (1 × 2^{4}) + (1 × 2^{3}) + (1 × 2^{2}) + (0 × 2^{1}) + (1 × 2^{0}), or 29. In electronics, binary numbers are the flow of information in the form of zeros and ones used by computers. Computers use it to manipulate and store all of their data including numbers, words, videos, graphics, and music. 
binary operation âpâreše dorin Fr.: opération binaire A mathematical operation that combines two numbers, quantities, sets, etc.,
to give a third. For example, multiplication of two numbers is a binary operation. 
binary pulsar pulsâre dorin, tapâre ~ Fr.: pulsar binaire A pulsar in a → binary system, the companion of which often being a → neutron star or a → white dwarf. The only known binary system with two pulsars components is the → double pulsar. As of 2010 about 70 binary pulsars have been identified. They are ideal laboratories for testing and studying the effects predicted by → general relativity, such as → spin precession, → Shapiro time delay, and → gravitational waves. The prototype, called PSR 1913+16, was discovered in 1974 by Russell A. Hulse and Joseph H. Taylor, Jr., who received the Nobel Prize for Physics in 1993. → HulseTaylor pulsar. 
binary star setâreye dorin Fr.: étoile binaire Two stars gravitationally bound to each other, so that they revolve around their common center of gravity. → double star; → spectroscopic binary. → binary; → star. 
binary supermassive black hole siyahcâle abarporjerme dorin Fr.: trou noir supermassif double A → dual supermassive black hole whose components are separated by a few parsecs. → binary; → supermassive; → black; → hole. 
binary system râžmâne dorin Fr.: système binaire Two astronomical objects revolving around their common center of mass. → binary; → system. 
binary tree deraxte dorin Fr.: arbre binaire In → graph theory, an → ordered tree with all → nodes having at most two → children. 
bind bandidan (#) Fr.: lier To tie, to fasten, to cause ti stick together. O.E. bindan "to tie up with bonds," PIE base *bhendh "to bind;" cf. Av./O.Pers. band "to bind, fetter," banda "band, tie," Skt. bandh "to bind, tie, fasten," bandhah "a tying, bandage." Bandidan "to bind, confine" [Mo'in, Dehxodâ], from band "band, tie" + idan infinitive suffix; cognate with E. bind, as explained above. 
binding energy kâruže bandeš, ~ hamgiri Fr.: énergie de liaison 1) Of a gravitational system, the difference
in energies between the hypothetical state where all bodies of
the system are infinitely separated from each other and the actual bound state.

binning bâvineš Fr.: binage Combining a few adjacent CCD pixels in bins, during readout; the method used to assemble the bins and transfer the charge by means of an electronic clock. Binning improves signaltonoise ratio at the expense of spatial resolution. Binning, from → bin. Bâvineš, from bâvin, → bin. 
binoculars docašmi (#), durbine ~ (#) Fr.: binoculaire A small optical instrument with two tubes that is used to magnify the view of distant or astronomical objects. → prism binoculars. From Fr. binoculaire, from binocle, from L. bini "double" (L. bis, bi "twice," Av. biš "twice") + ocularis "of the eye," from oculus "eye" (compare with Av. axš, aš "eye," Skt. akshi "eye," Gk. ops "eye," opsis "sight, appearance," from PIE okw "to see;" also O.E. ege, eage, from P.Gmc. *augon, Goth. augo, Lith. akis, Armenian aku). Docašmi "binocular," from do, → two + cašm, → eye, + i adj. suffix; durbin, → telescope. 
binomial donâmin Fr.: 1) binôme; 2) binomial 1a) An algebraic expression containing 2 terms, as x + y and
2x^{2}  3x. In other words, a → polynomial
with 2 terms. From L.L. binomi(us) "having two names," + → al, → nominal. 
binomial coefficient hamgare donâmin Fr.: coefficient binomial
The factor multiplying the variable in a term of a → binomial expansion. For example, in (x + y)^{4} = x^{4} + 4x^{3}y + 6x^{2}y^{2} + 4xy^{3} + y^{4} the binomial coefficients are 1, 4, 6, 4, and 1. In general, the rth binomial coefficient in the expression (x + y)^{n} is: (n,r) = n!/[r!(n  r)!]. → binomial; → coefficient. 
binomial differential degarsâneye donâmin Fr.: binôme différentiel An expression of the form x^{m}(a + bx^{n})^{p}dx, where m, n, p, a, and b are constants. → binomial; → differential. 
binomial distribution vâbâžeše donâmin Fr.: distribution binomiale A probability distribution for independent events for which there are only two possible outcomes i.e., success and failure. The probability of x successes in n trials is: P(x) = [n!/x!(n  x)!] p^{x}.q^{n  x}, where p is the probability of success and q = 1  p the probability of failure on each trial. These probabilities are given in terms of the → binomial theorem expansion of (p + q)^{n}. → binomial; → distribution. 
binomial expansion gostareše donâmin Fr.: expansion binomiale A rule for the expansion of an expression of the form (x + y)^{n}. The variables x and y can be any → real numbers and n is an → integer. The general formula is known as the → binomial theorem. 
binomial nomenclature nâmgozâriye donâmin Fr.: nomenclature binomiale A system introduced by Carl von Linné (17071778), the Swedish botanist, in which each organism is identified by two names. The first is the name of the genus (generic name), written with a capital letter. The second is the name of the species (specific name). The generic and specific names are in Latin and are printed in italic type. For example, human beings belong to species Homo sapiens. → binomial; → nomenclature. 
binomial theorem farbine donâmin Fr.: théorème du binôme A rule for writing an equivalent expansion of an expression such as (a + b)^{n} without having to perform all multiplications involved. → binomial expansion. The general expression is (a + b)^{n} = &Sigma (n,k)a^{k}b^{n  k}, where the summation is from k = 0 to n, and (n,k) = n!/[r!(n  k)!]. For n = 2, (a + b)^{2} = a^{2} + 2ab + b^{2}. Historically, the binomial theorem as applied to (a + b)^{2} was known to Euclid (320 B.C.) and other early Greek mathematicians. In the tenth century the Iranian mathematician Karaji (9531029) knew the binomial theorem and its accompanying table of → binomial coefficients, now known as → Pascal's triangle. Subsequently Omar Khayyam (10481131) asserted that he could find the 4th, 5th, 6th, and higher roots of numbers by a special law which did not depend on geometric figures. Khayyam's treatise concerned with his findings is lost. In China there appeared in 1303 a work containing the binomial coefficients arranged in triangular form. The complete generalization of the binomial theorem for all values of n, including negative integers, was established by Isaac Newton (16421727). 
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