The implementation of the algorithm converts decimal reals to Binary, The coefficients are written in the order they obtained and the number is the equivalent in the new base. Take in account the new fraction part as a new number and execute Step1 The integral part is a digit in the new base The fraction part is multiplied by the new base and we obtain an integral part and a fraction part. The generalized algorithm for this method is: In order to realize the check for precision you must realize the difference between two consecutive values for the result and to compare the difference with the desired precision (for example, the precision for money is at two decimals that mean the value to check can be 0.009, typically four decimals for quantities and so on). The process of multiplying the fraction numbers by q is ended in the moment where desired precision is obtained. NF(b)*q=a′ -1+a′ -2*q -2+1+.+a′ -m*q -m+1 ⇒ a′ -1 the most significant digit in base q.īy this process we obtain a new fraction part: a′ -2*q -1+.+a′ -m*q -m+1 that mean N'F (b). We must determine the coefficients a′-j, and that is to do by multiplying repeatedly (the original number first and the fraction part of each cycle latter) with the new base: Given a fraction number NF (b) it can be represented in a base q as: If we intend to convert the number in a new base q ( q>1), we mustįirst isolate the integral part from the fraction part.īe converted by using the algorithm described in the page Integer Numbersīelow is a conversion algorithm for the fraction part of the real number.įraction Part. The number can be expressed as a sum of an integral part NI(b) and a fraction one NF(b), N(b)=NI(b) + NF(b). Given a real number N expressed in a base b, denoted by N(b). The generalized division-multiplication algorithm for converting decimal real numbers in Processor of your computer have the "Pentium floating-point bug" discovered in The Check Processor button activate a floating-point computation to check if the
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