The arithmetic of binary equivalents of decimal numbers

A new concept of binary calculations over floating-point decimal numbers
is being proposed. The criterion for the accuracy of the representation
of a decimal number by a binary code is the number of matching certain
digits of this decimal number and the decimal value of its binary
equivalent of limited size. The specified decimal accuracy in binary
calculations is provided by the correct decimal rounding of binary
numbers. This helps to significantly reduce the dimensionality of binary
numbers to approximate the decimal floating-point numbers. It allows
you to get a strict value of zero when subtracting decimal numbers in
binary code. It provides the implementation of bitwise comparison of
binary numbers, which are binary equivalents of decimal numbers. The
paper provides algorithms for the correct rounding and exact
comparison/subtraction of decimal numbers presented in binary.