MATHEMATICAL DESCRIPTION THE DIVIDE OF INTEGER NUMBERS

Abstract

Computer division of integers is given by polynomial transformation of complementary codes. The positive property of the mathematical model of these polynomials is characterized by the formation of polynomials of positive and negative integers with an equivalent expression. Іn the general form, the dependence of the function domain of the number’s representation in the two’s complementary code and the polynomial capacity is established. Adequate polynomial bit capacity of the complementary code dividend for defined formats of the divisor and the quotient is determined. The algorithm for determining the special polynomial of the quotient for all combinations of the operands sign polarity is formed. It is shown that the content of the quotient polynomial is determined by the partial remainder’s polarity of the dividend, which are determined by adding the transformed or untransformed complementary code of the divisor to the doubled code of the previous partial remainder complementary code. It is proved that increasing the value of the complementary code of the dividend partial remainder is reduced to a modified left shift of the dividend remainder complementary code with the loss of the sign bit. Logical expressions for fixing the overflow of the quotient are synthesized, the determination of which is combined with the calculation of the highest bit of the quotient polynomial. A reasonable algorithm for converting the calculated polynomial of the quotient into the resulting complementary code of the quotient during dividing operands with the same and different signs. For the mathematical description of the complementary code of integers, a special form of the shortened modulo-shifted code is introduced. The task of dividing integers is reduced to the operation of dividing complementary codes polynomials. In the system of complementary codes, an algorithm for determining the quotient polynomial, which is invariant to the signs of the operands, is proposed. The algorithm for calculating the correct complementary code of the dividend remainder for all combinations of the sign bits of the operands is indicated.