A new fractional binary-to-decimal number conversion for errorless calculation

Abstract

This paper proposes a new fractional decimal format and binary-to-decimal conversion for highly accurate calculation without error. In many cases, a given fractional constant is the decimal number. After converting the decimal constant to a fractional binary number, any calculation can be performed. Because the given constant is originally the decimal number, the result may contain an error, which degrades the system accuracy. We propose a new format for fractional decimal numbers. The proposed format contains a binary integer and fractional bits, where the fractional decimal number can be provided by the proposed binary bit conversion. In a calculation, instead of using fixed-point numbers, scaled integer numbers are adopted. Then, the result is scaled and converted into the fractional decimal number. Considering practical examples and evaluation results, it is concluded that the proposed method can provide the errorless calculation.