Arithmetic of binary equivalents of decimal numbers
- Iouri Spiridonov
Iouri Spiridonov
Independent researcher, Independent researcher, Independent researcher, Independent researcher
Corresponding Author:[email protected]
Author ProfileAbstract
Within the framework of the concept of decimal calculations proposed in
the article using binary arithmetic, a theory of binary equivalents of
decimal floating-point numbers has been developed. According to this
theory, basic decimal arithmetic operations on finite decimal numbers
are performed with decimal precision by a binary processor according to
the rules of binary arithmetic on the binary equivalents of decimal
numbers. These calculation results are entirely consistent with the
classical decimal finite number arithmetic and do not require the use of
test programs. The identity of calculation results in decimal and binary
equivalent arithmetics guarantees the repeatability of results on any
platform. The article shows that implementing binary equivalents
arithmetic with an acceptable decimal calculation error requires
significantly fewer bits of binary processor registers than in modern
computers. Because of the uniqueness of binary decimal equivalents, the
difference between equal, properly rounded binary decimal equivalents is
strictly zero. The presence of an explicit zero in the arithmetic of
binary equivalents of decimal numbers makes it possible to implement a
bitwise comparison of such numbers and introduce the concept of an
infinitesimal number when the significand of a floating-point number is
equal to zero.