The arithmetic of binary equivalents of decimal numbers

- Iouri Spiridonov

Iouri Spiridonov

Independent researcher, Independent researcher, Independent researcher, Independent researcher

Corresponding Author:[email protected]

Author Profile## 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.