Floating-point recurring rational arithmetic system

Major computer arithmetic systems are based on the concept of realizing only terminate rationals in positional notation. This paper proposes a new arithmetic scheme of indicating periodicity in the radix representation of a mantissa to realize recurring rationals as well as terminate rationals. A new arithmetic system adopting the scheme, called the “FLP/R* arithmetic system”, is proposed. Properties of the FLP/R* numbers and the procedure of the FLP/R* arithmetic are described.