Synthesis of composite schem addition and subtraction of integers in codes with positive zero

DOI: 10.31673/2412-4338.2020.011896

Abstract

Code on the outputs of adder binary numbers described as the remainder of the sum the initial data on the adder module is equal to output carry weight. An original technique for synthesizing a way of operands representation in the addition and subtraction schemes of integers in a code with a positive zero was devel-oped, which is based on the representation the source data in the form a remainder on the adder module. A method of computer representation for integer numbers is proposed, in which the codes of positive and negative numbers are formed by the same procedure. The property of duality the addition and subtraction opera-tions on the initial data in the code with a positive zero have justified analytically, which is based on the fact that certain adder outputs union give the result just as in the two’s complement so too in the positive zero codes. Areas of allowable results values for the correct input data addition and subtraction operations are determined. It is identified combination of the adder output signals, which determine the presence and polarity the adder bit grid overflow. It is shown that designed fixing scheme bit grid overflow of adder outputs invariant with respect to operations of addition and subtraction of source data with a positive zero code. For the analytical description of arithmetic operations on integer numbers represented with the proposed encoding method, a technique of calculating the sum and difference of numbers using the biased supplementary code has been proposed. Analytically substantiated, that the technique makes the scheme of the operational adder homogeneous. The rules for establishing the correctness of the addition and subtraction operations of the integers given in the proposed encoding form are given. For true values of the initial arguments, the sums and the differences codes ranges are obtained, and the rules for positive and negative overflows identification are proposed. The original usage of a common numerical bias during the operands encoding, that evinces itself in the advantages of basic computer operations technical implementation, predetermines positive properties in practical implementations of more complex arithmetical actions.

Keywords: adder binary numbers, code with positive zero, the remainder modulo, signs of overflow, two's complement code.

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