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The arithmetic of binary equivalents of decimal numbers
  • Iouri Spiridonov
Iouri Spiridonov
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Abstract

A new concept of binary calculations over decimal floating-point numbers is proposed. Binary calculations are performed on the binary equivalents of decimal numbers. Binary representations of decimal numbers that are rounded to a given number of certain decimal digits are taken as the binary equivalents of decimal numbers. The arithmetic of binary equivalents is fully consistent with the decimal arithmetic of numbers with limited capacity. The proposed approach made it possible to significantly reduce the dimension of binary numbers for approximating decimal floating-point numbers. The obtained decimal precision of calculations made it possible to obtain a strict zero value during subtraction, which in turn made the task of comparing binary equivalents trivial. Correct decimal rounding of binary numbers made it possible to calculate the difference of numbers close in value with decimal precision. The paper considers algorithms for basic arithmetic operations with binary equivalents of decimal numbers.