Morgan - Numerical Methods (523161), страница 48
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It may be the target ordestination operand for an instruction,and will often have specific instructions that affect it only.To arrange in memory or a register toproduce a proper relationship.accuracyThe degree of correctness of a quantityor expression.arithmeticOperations involving addition, subtraction, multiplication, division, powersand roots.ASCIITo add a value to a destination variablewith the current state of the carry flag.The American Standard Code for Information Interchange. A seven bit codeused for the interpretation of a byte ofdata as a character.addendassociative lawA number or quantity added to another.An arithmetic law which states that theorder of combination or operation ofthe operands has no influence on theresult.
The associative law of multiplication is (a*b)*c=a*(b*c).add-with-carryadditionThe process of incrementing by a value,or joining one set with another.additional numbering systemsNumbering systems in which the symbols combine to form the next highergroup. An example of this is the Romansystem. See Chapter 1.atanArctangent. This is the angle for whichwe have the tangent.atanhThe Inverse Hyperbolic Tangent. This485NUMERICAL METHODSis the angle for which we have thehyperbolic tangent.signed addition or a borrow from anunsigned subtraction might cause a carry.augendceilA number or quantity to which anotheris added.The least integer greater than or equalto a value.basecoefficientA grouping of counting units that israised to various powers to produce theprincipal counting units of a numbering system.A numerical factor, such as 5 in 5x .complement- An inversion or a kind ofnegation.
A one’s complement resultsin each zero of an operand becoming aone and each one becoming a zero. Toperform a two’s complement, first one’scomplement the operand, then increment by one.binaryA system of numeration using base 2.bit— Binary digI T.BooleanA form of algebra proposed by GeorgeBoole in 1847.
This is a combinatorialsystem allowing the processing of operands with operators such as AND,OR, NOT, IF, THEN, and EXCEPT.byteA grouping of bits the computer or CPUoperates upon as a unit. Generally, abyte comprises 8 bits.cardinalA counting number, or natural numberindicating quantity but not order.carry flagA bit in the status register of manymicroprocessors and micro controllersindicating whether the result of an operation was to large for the destinationdata type. An overflow from an un-486commutative lawAn arithmetic law which states that theorder of the operands has no influenceon the result of the operation.
The commutative law of addtition isa+b=b+a.congruenceTwo numbers or quantities are congruent, if, after division by the same value,their remainders are equal.coordinatesA set of two or more numbers determining the position of a point in a space ofa given dimension.CORDICCOrdinate Rotation Digital Computer.The CORDIC functions are a group ofalgorithms that are capable of computing high quality approximations of theGLOSSARYtranscendental functions and requirevery little in the way of arithmetic powerfrom the processor.cosineIn the triangle, the ratio x/r is a functionof the angle θ known as the cosine.Ydistributive lawAn arithmetic law that describesa connection between operations.This distributive law is as follows:a*(b+c)=a*b+a*c. Note thatthe multiplication is distributed overthe addition.dividendThe number to be divided.divisionIterative subtraction of one operandfrom another.divisorThe number used to divide another,such as the dividend.double-precisionFigure 1.
A Right Triangle.For IEEE floating point numbers, it istwice the single precision format lengthor 64 bits.decimaldoubleword (dword)having to do with base 10.Twice the number of bits in a word. Onthe 8086, it is 32 bits.decimal-pointRadix point for base 10.denominatorThe divisor in a fraction.denormalA fraction with a minimum exponentand leading bit of the significand zero.derivativeThe instantaneous rate of change of afunction with respect to a variable.exceptionIn IEEE floating point specification,an exception is a special case thatmay require attention. There are fiveexceptions and each has a trap thatmay be enabled or disabled.
The exceptions are:Invalid operation, including addition or subtraction with as anoperand, multiplication using asan operand,or 0/0, divisionl487NUMERICAL METHODSwith invalid operands, a remainderoperation where the divisor is zeroor unnormalized or the dividend isinfinite.Division by zero.Overflow. The rounded result produced a legal number but an exponent too large for the floating pointformat.Underflow. The result is too smallfor the floating point format.Inexact result without an invalid operation exception.
The rounded result isnot exact.farA function or pointer is defined as far ifit employs more than a word to identifyit. This usually means that it is notwithin the same 64K segment with thefunction or routine referencing it.fixed-pointA form of arithmetic in which the radixpoint is always assumed to be in thesame place.fractionThe symbolic (or otherwise) quotientof two quantities.guard digitsDigits to the right of the significand orsignificant bits to provide addedprecision to the results of arithmeticcomputations.hidden bitThe most significant bit of the floatingpoint significand.
It exists, but is notrepresented, just to the left of the radixpoint and is always a one (except in thecase of the denormal).integer (int)A whole number. A word on a personalcomputer, 16 bits.interpolateTo determine a value between twoknown values.irrational numberA number that can not be representedexactly in a particular base.floating-pointK-spaceA method of numerical expression, inwhich the number is represented by afraction, a scaling factor (exponent),and a sign.K-spaces are multi-dimensional or kdimensional where K is an integer.floorThe greatest integer less than or equalto a value.488linear congruentialA method of producing pseudo-random numbers using modular arithmetic.linear interpolationThe process of approximating f(x) byfitting a straight line to a function at theGLOSSARYdesired point and using proportion toestimate theposition of the unknown onthat line.
See Chapter 6.example, 4 A.M. plus 16 hours is 8 P.M.((4 + 16) mod 12 = 8).logarithm (log)Micro-Processor- Unit.nIn any base, x, where x = b, n is thelogarithm of b to the base x. AnotherMPUMSBMost Significant Bit.notation is n = log,x b .MSWlongMost significant Word.A double word.
On a personal computer, 32 bits.The number you are multiplying.multiplicandlong realmultiplicationThe long real is defined by IEEE 754 asa double precision floating-point number.Iterative addition of one operand withanother.LSBThe number you are multiplying by.Least Significant Bit.LSWLeast Significant Word.mantissaThe fractional part of a floating pointnumber.multipliermultiprecisionMethods of performing arithmetic thatuse a greater number of bits that provided in the word size of the computer.NANA mathematical technique that producesa polynomial approximation optimizedfor the least maximum error.These can be either Signaling or Quietaccording to the IEEE 754 specification.
A NAN (Not A Number) is theresult of an operation that has not mathematical interpretation, such as 0 ÷ 0.minuendnatural numbersThe number you are subtracting from.All positive integers beginning withzero.minimaxmodulusThe range of values of a particular systern.
This is the basis of modular arithmetic, such as used in telling time. FornearA function or pointer is defined as nearif it is within a 64K segment with the489NUMERICAL METHODSfunction or routine referencing it. Thus,it requires only a single 16 bit word toidentify it.operandnegativeordinalA negative quantity, minus. Beginningat zero, the number line stretches in twodirections.
In one direction, there arethe natural numbers, which are positiveintegers. In the other direction, thereare the negative numbers. The oppositeof a positive number.A number that indicates position, suchas first or second.nibbleHalf a byte, typically four bits.normalizationThe process of producing a numberwhose left most significant digit is aone.number rayAn illustration of the basic conceptsassociated with natural numbers.
Anytwo natural numbers may have onlyone of the following relationships: n1 <A number or value with which or uponwhich an operation is performed.ordinateOn the Cartesian Axes, it is the distancefrom a point to the x axis.overflowWhen a number grows to great throughrounding or another arithmetic processfor its data type, it overflows.packed decimalMethod for storage of decimal numbersin which each of the two nibbles in ahexadecimal byte are used to hold decimal digits.polynomialSystem for counting or numbering.An algebraic function of summedterms, where each term consists of aconstant multiplier (factor) and atleast one variable raised to an integerpower.
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