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Abstracts

XVII conference

Elimination of mathematical lacks of computers

Filippov N.A.

Wyatka of the state university, Faculty of automatic and information technic, department of the computer, Russia. 610000, Kirov, Moscow, 36, Ph.: (8332) 38-10-70, a fax: (8332) 64-51-76, E-mail: filippov_kirov@mail.ru

1 pp. (accepted)

In modern computers (working on a binary notation), all computing operations of quantitative tasks are decide only by one, the operation of addition added with shifts of codes of binary numbers to the left, to the right and their inversion (change of them 1 on 0, and 0 on 1). Moreover, operation of addition, as well as all logic operations, is made by logic operations of binary logic which results and their operands (logic statements), have values "true" or "false", differently - "yes" or "not" and are represented as, as well as arguments of quantitative operations, figures 1 and 0. This overlapping of quantitative and logic calculations provides to computers universality - all variety of computable logic operations on binary logic provides calculation quantitative tasks corresponding to them.

However computers have the following lacks. At use in them of arguments with one unit of measurements the constancy of the maximal absolute errors and hyperbolic dependence of maxima of the relative errors, more full reflecting accuracy of measurements, codings and results of calculations takes place. This lack has been in part removed by use of several units of measurements (for example, mm, sm, dm, m, or mк, mv, v, кv) or (and) replacement of one number to two: a mantissa and the order. Graphically maxima of relative errors of the first way of their alignment and the second with one unit of measurements are represented in everyone part of range equally: a saw with falling on hyperboles of teeth, relations of maxima of maximumes which to their maxima minimumes, as well as lengths of anyone of tooth by the length previous are equal to the relation of the next units of measurements. Use in the second method of several units of measurements is displayed by the same quantity of different saws on height. These both methods only in part level maxima of relative errors. Consequences of it are, first, not equal precision on maxima of relative errors in everyone of part of range (in each of the tooth), second, the excessive quantity of mutually different codes, in the third, is not realized possible speed.

Full alignment of maxima of relative errors is reached by use of quantization not on arithmetic, and on geometrical progressions. Numbers of the last as it turned are integer logarithms, and their values are coded by multiplicative notations. Thus besides equal precision codes on a maximum of a relative error on all a range, the minimum of quantity of all mutually different codes and the increased speed is achieved, is especial calculations, because of their carrying out on integer logarithms.



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